diff --git "a/data/track_pure_gps/splits/task6_interpolation_train.json" "b/data/track_pure_gps/splits/task6_interpolation_train.json" new file mode 100644--- /dev/null +++ "b/data/track_pure_gps/splits/task6_interpolation_train.json" @@ -0,0 +1,79562 @@ +[ + { + "task": "interpolation", + "point_a": { + "lat": -16.65, + "lon": -68.3, + "name": "Viacha" + }, + "point_b": { + "lat": -18.90556, + "lon": -40.07611, + "name": "Jaguaré" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -17.595827, + "lon": -61.32132 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-16.65°, -68.3°)", + " Point B: (-18.90556°, -40.07611°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -17.595827°", + " Longitude: -61.321320°", + "FINAL ANSWER: -17.595827, -61.321320" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 32.38472, + "lon": 109.34556, + "name": "Pingli" + }, + "point_b": { + "lat": -22.09198, + "lon": -70.19792, + "name": "Tocopilla" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 20.305797, + "lon": -68.646904 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (32.38472°, 109.34556°)", + " Point B: (-22.09198°, -70.19792°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 20.305797°", + " Longitude: -68.646904°", + "FINAL ANSWER: 20.305797, -68.646904" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 36.56471, + "lon": 4.30619, + "name": "’Aïn el Hammam" + }, + "point_b": { + "lat": 27.10383, + "lon": 84.46185, + "name": "Narkatiāganj" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 39.029494, + "lon": 46.85928 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (36.56471°, 4.30619°)", + " Point B: (27.10383°, 84.46185°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 39.029494°", + " Longitude: 46.859280°", + "FINAL ANSWER: 39.029494, 46.859280" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -27.62563, + "lon": 152.96883, + "name": "Forest Lake" + }, + "point_b": { + "lat": -22.10861, + "lon": -50.17167, + "name": "Pompéia" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -66.476198, + "lon": -122.376209 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-27.62563°, 152.96883°)", + " Point B: (-22.10861°, -50.17167°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -66.476198°", + " Longitude: -122.376209°", + "FINAL ANSWER: -66.476198, -122.376209" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 34.00583, + "lon": 36.21806, + "name": "Baalbek" + }, + "point_b": { + "lat": 53.47095, + "lon": 8.64584, + "name": "Loxstedt" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 44.552196, + "lon": 24.738067 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (34.00583°, 36.21806°)", + " Point B: (53.47095°, 8.64584°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 44.552196°", + " Longitude: 24.738067°", + "FINAL ANSWER: 44.552196, 24.738067" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 5.60105, + "lon": -0.07713, + "name": "Nungua" + }, + "point_b": { + "lat": 26.30938, + "lon": 100.62513, + "name": "Qina" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 24.092965, + "lon": 46.667249 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (5.60105°, -0.07713°)", + " Point B: (26.30938°, 100.62513°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 24.092965°", + " Longitude: 46.667249°", + "FINAL ANSWER: 24.092965, 46.667249" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 28.72249, + "lon": 78.28436, + "name": "Hasanpur" + }, + "point_b": { + "lat": 20.88197, + "lon": 85.83334, + "name": "Bhuban" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 22.876217, + "lon": 84.032649 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (28.72249°, 78.28436°)", + " Point B: (20.88197°, 85.83334°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 22.876217°", + " Longitude: 84.032649°", + "FINAL ANSWER: 22.876217, 84.032649" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -0.96667, + "lon": 30.6, + "name": "Iryango" + }, + "point_b": { + "lat": 8.23073, + "lon": 77.18626, + "name": "Keezhkulam" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 6.220505, + "lon": 65.429391 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-0.96667°, 30.6°)", + " Point B: (8.23073°, 77.18626°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 6.220505°", + " Longitude: 65.429391°", + "FINAL ANSWER: 6.220505, 65.429391" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -8.00611, + "lon": -35.69722, + "name": "Cumaru" + }, + "point_b": { + "lat": -27.71773, + "lon": -48.56266, + "name": "Freguesia do Ribeirao da Ilha" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -17.9675, + "lon": -41.768276 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-8.00611°, -35.69722°)", + " Point B: (-27.71773°, -48.56266°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -17.967500°", + " Longitude: -41.768276°", + "FINAL ANSWER: -17.967500, -41.768276" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 28.61031, + "lon": 79.16997, + "name": "Milak" + }, + "point_b": { + "lat": 26.61708, + "lon": -80.07231, + "name": "Lake Worth Beach" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 53.814973, + "lon": -61.93135 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (28.61031°, 79.16997°)", + " Point B: (26.61708°, -80.07231°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 53.814973°", + " Longitude: -61.931350°", + "FINAL ANSWER: 53.814973, -61.931350" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -10.42172, + "lon": 105.67912, + "name": "Flying Fish Cove" + }, + "point_b": { + "lat": 24.85798, + "lon": -99.56768, + "name": "Linares" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 11.514163, + "lon": 136.911511 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-10.42172°, 105.67912°)", + " Point B: (24.85798°, -99.56768°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 11.514163°", + " Longitude: 136.911511°", + "FINAL ANSWER: 11.514163, 136.911511" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 50.01997, + "lon": 8.69611, + "name": "Dreieich" + }, + "point_b": { + "lat": 41.18883, + "lon": -8.49857, + "name": "Valongo" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 45.925977, + "lon": -0.584368 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (50.01997°, 8.69611°)", + " Point B: (41.18883°, -8.49857°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 45.925977°", + " Longitude: -0.584368°", + "FINAL ANSWER: 45.925977, -0.584368" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 8.97054, + "lon": 37.76117, + "name": "Guder" + }, + "point_b": { + "lat": -3.16667, + "lon": 33.76667, + "name": "Shanwa" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -0.131507, + "lon": 34.760032 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (8.97054°, 37.76117°)", + " Point B: (-3.16667°, 33.76667°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -0.131507°", + " Longitude: 34.760032°", + "FINAL ANSWER: -0.131507, 34.760032" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 5.26667, + "lon": -73.91667, + "name": "La Mesa" + }, + "point_b": { + "lat": 49.1643, + "lon": -121.95907, + "name": "Chilliwack-Downtown" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 17.490385, + "lon": -82.663508 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (5.26667°, -73.91667°)", + " Point B: (49.1643°, -121.95907°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 17.490385°", + " Longitude: -82.663508°", + "FINAL ANSWER: 17.490385, -82.663508" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 39.21311, + "lon": -84.59939, + "name": "White Oak" + }, + "point_b": { + "lat": 7.13333, + "lon": -7.18333, + "name": "Bléniméouin" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 28.629659, + "lon": -40.259033 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (39.21311°, -84.59939°)", + " Point B: (7.13333°, -7.18333°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 28.629659°", + " Longitude: -40.259033°", + "FINAL ANSWER: 28.629659, -40.259033" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -9.10611, + "lon": 124.8925, + "name": "Atambua" + }, + "point_b": { + "lat": 43.56775, + "lon": 3.90279, + "name": "Lattes" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 31.289382, + "lon": 79.576984 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-9.10611°, 124.8925°)", + " Point B: (43.56775°, 3.90279°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 31.289382°", + " Longitude: 79.576984°", + "FINAL ANSWER: 31.289382, 79.576984" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -0.15837, + "lon": 29.23859, + "name": "Lubero" + }, + "point_b": { + "lat": 29.70579, + "lon": -95.45883, + "name": "Bellaire" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 29.388328, + "lon": -25.464797 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-0.15837°, 29.23859°)", + " Point B: (29.70579°, -95.45883°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 29.388328°", + " Longitude: -25.464797°", + "FINAL ANSWER: 29.388328, -25.464797" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -6.82222, + "lon": 107.13944, + "name": "Cianjur" + }, + "point_b": { + "lat": 42.45948, + "lon": -83.18271, + "name": "Oak Park" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 73.658824, + "lon": -121.333258 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-6.82222°, 107.13944°)", + " Point B: (42.45948°, -83.18271°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 73.658824°", + " Longitude: -121.333258°", + "FINAL ANSWER: 73.658824, -121.333258" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 50.49613, + "lon": 29.22911, + "name": "Radomyshl" + }, + "point_b": { + "lat": -9.34506, + "lon": 28.73396, + "name": "Nchelenge" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 20.575703, + "lon": 28.928049 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (50.49613°, 29.22911°)", + " Point B: (-9.34506°, 28.73396°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 20.575703°", + " Longitude: 28.928049°", + "FINAL ANSWER: 20.575703, 28.928049" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -24.56694, + "lon": 25.87417, + "name": "Mmopone" + }, + "point_b": { + "lat": 35.25968, + "lon": -118.91427, + "name": "Lamont" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 16.963912, + "lon": -36.890292 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-24.56694°, 25.87417°)", + " Point B: (35.25968°, -118.91427°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 16.963912°", + " Longitude: -36.890292°", + "FINAL ANSWER: 16.963912, -36.890292" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 44.29109, + "lon": -105.50222, + "name": "Gillette" + }, + "point_b": { + "lat": 21.03907, + "lon": -104.37116, + "name": "Ixtlán del Río" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 38.479141, + "lon": -105.156258 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (44.29109°, -105.50222°)", + " Point B: (21.03907°, -104.37116°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 38.479141°", + " Longitude: -105.156258°", + "FINAL ANSWER: 38.479141, -105.156258" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 30.22243, + "lon": 78.78341, + "name": "Srīnagar" + }, + "point_b": { + "lat": -17.31197, + "lon": 37.50784, + "name": "Maganja" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -5.286093, + "lon": 47.482313 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (30.22243°, 78.78341°)", + " Point B: (-17.31197°, 37.50784°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -5.286093°", + " Longitude: 47.482313°", + "FINAL ANSWER: -5.286093, 47.482313" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 63.43049, + "lon": 10.39506, + "name": "Trondheim" + }, + "point_b": { + "lat": 55.68333, + "lon": 37.55, + "name": "Semënovskoye" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 62.049625, + "lon": 18.376211 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (63.43049°, 10.39506°)", + " Point B: (55.68333°, 37.55°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 62.049625°", + " Longitude: 18.376211°", + "FINAL ANSWER: 62.049625, 18.376211" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 5.25198, + "lon": 100.49046, + "name": "Val Dor" + }, + "point_b": { + "lat": 48.09872, + "lon": 19.80303, + "name": "Salgótarján" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 43.308105, + "lon": 47.739397 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (5.25198°, 100.49046°)", + " Point B: (48.09872°, 19.80303°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 43.308105°", + " Longitude: 47.739397°", + "FINAL ANSWER: 43.308105, 47.739397" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 46.42135, + "lon": 26.43645, + "name": "Comăneşti" + }, + "point_b": { + "lat": -2.13396, + "lon": -79.59337, + "name": "Milagro" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 16.495338, + "lon": -61.758828 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (46.42135°, 26.43645°)", + " Point B: (-2.13396°, -79.59337°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 16.495338°", + " Longitude: -61.758828°", + "FINAL ANSWER: 16.495338, -61.758828" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -37.96667, + "lon": 145.16667, + "name": "Noble Park" + }, + "point_b": { + "lat": 43.86544, + "lon": -79.99322, + "name": "Caledon" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 30.860837, + "lon": -123.495807 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-37.96667°, 145.16667°)", + " Point B: (43.86544°, -79.99322°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 30.860837°", + " Longitude: -123.495807°", + "FINAL ANSWER: 30.860837, -123.495807" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 40.34872, + "lon": -74.65905, + "name": "Princeton" + }, + "point_b": { + "lat": 38.04937, + "lon": -122.15858, + "name": "Benicia" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 41.660977, + "lon": -86.614356 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (40.34872°, -74.65905°)", + " Point B: (38.04937°, -122.15858°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 41.660977°", + " Longitude: -86.614356°", + "FINAL ANSWER: 41.660977, -86.614356" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 44.30905, + "lon": 8.47715, + "name": "Savona" + }, + "point_b": { + "lat": -21.05, + "lon": 31.66667, + "name": "Chiredzi" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 11.860758, + "lon": 21.623542 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (44.30905°, 8.47715°)", + " Point B: (-21.05°, 31.66667°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 11.860758°", + " Longitude: 21.623542°", + "FINAL ANSWER: 11.860758, 21.623542" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -20.71333, + "lon": -48.54083, + "name": "Colina" + }, + "point_b": { + "lat": 27.75225, + "lon": -98.06972, + "name": "Alice" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -8.605017, + "lon": -60.950598 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-20.71333°, -48.54083°)", + " Point B: (27.75225°, -98.06972°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -8.605017°", + " Longitude: -60.950598°", + "FINAL ANSWER: -8.605017, -60.950598" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 13.55285, + "lon": 76.01164, + "name": "Kadūr" + }, + "point_b": { + "lat": -4.54167, + "lon": -40.71889, + "name": "Ipueiras" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 2.278025, + "lon": -12.244784 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (13.55285°, 76.01164°)", + " Point B: (-4.54167°, -40.71889°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 2.278025°", + " Longitude: -12.244784°", + "FINAL ANSWER: 2.278025, -12.244784" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 59.54, + "lon": 30.8775, + "name": "Tosno" + }, + "point_b": { + "lat": 50.86117, + "lon": 4.33136, + "name": "Koekelberg" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 57.941555, + "lon": 23.131745 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (59.54°, 30.8775°)", + " Point B: (50.86117°, 4.33136°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 57.941555°", + " Longitude: 23.131745°", + "FINAL ANSWER: 57.941555, 23.131745" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -17.81667, + "lon": -63.05, + "name": "Cotoca" + }, + "point_b": { + "lat": 11.48682, + "lon": 105.32533, + "name": "Prey Veng" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -31.59917, + "lon": -19.267962 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-17.81667°, -63.05°)", + " Point B: (11.48682°, 105.32533°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -31.599170°", + " Longitude: -19.267962°", + "FINAL ANSWER: -31.599170, -19.267962" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 14.76181, + "lon": -90.99247, + "name": "Tecpán Guatemala" + }, + "point_b": { + "lat": 43.25433, + "lon": 5.4057, + "name": "Marseille 09" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 45.04024, + "lon": -24.088317 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (14.76181°, -90.99247°)", + " Point B: (43.25433°, 5.4057°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 45.040240°", + " Longitude: -24.088317°", + "FINAL ANSWER: 45.040240, -24.088317" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 40.66677, + "lon": -73.88236, + "name": "East New York" + }, + "point_b": { + "lat": 34.76954, + "lon": -92.26709, + "name": "North Little Rock" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 38.076544, + "lon": -83.444085 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (40.66677°, -73.88236°)", + " Point B: (34.76954°, -92.26709°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 38.076544°", + " Longitude: -83.444085°", + "FINAL ANSWER: 38.076544, -83.444085" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 48.38202, + "lon": -89.25018, + "name": "Thunder Bay" + }, + "point_b": { + "lat": -36.88158, + "lon": 174.76204, + "name": "Mount Eden" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -15.142204, + "lon": -161.848624 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (48.38202°, -89.25018°)", + " Point B: (-36.88158°, 174.76204°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -15.142204°", + " Longitude: -161.848624°", + "FINAL ANSWER: -15.142204, -161.848624" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 30.59936, + "lon": -87.16108, + "name": "Pace" + }, + "point_b": { + "lat": -32.03077, + "lon": -60.30619, + "name": "Crespo" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 15.028147, + "lon": -79.998821 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (30.59936°, -87.16108°)", + " Point B: (-32.03077°, -60.30619°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 15.028147°", + " Longitude: -79.998821°", + "FINAL ANSWER: 15.028147, -79.998821" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 46.92436, + "lon": 7.41457, + "name": "Köniz" + }, + "point_b": { + "lat": 3.84878, + "lon": 47.18064, + "name": "Ceeldheer" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 26.724136, + "lon": 31.172654 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (46.92436°, 7.41457°)", + " Point B: (3.84878°, 47.18064°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 26.724136°", + " Longitude: 31.172654°", + "FINAL ANSWER: 26.724136, 31.172654" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 0.67028, + "lon": 35.50806, + "name": "Iten" + }, + "point_b": { + "lat": 35.66667, + "lon": 138.56667, + "name": "Kofu" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 35.281788, + "lon": 107.68859 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (0.67028°, 35.50806°)", + " Point B: (35.66667°, 138.56667°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 35.281788°", + " Longitude: 107.688590°", + "FINAL ANSWER: 35.281788, 107.688590" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 48.5665, + "lon": 13.43122, + "name": "Passau" + }, + "point_b": { + "lat": -16.03163, + "lon": 35.5, + "name": "Mulanje" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 0.258525, + "lon": 31.018766 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (48.5665°, 13.43122°)", + " Point B: (-16.03163°, 35.5°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 0.258525°", + " Longitude: 31.018766°", + "FINAL ANSWER: 0.258525, 31.018766" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 0.35462, + "lon": 37.58218, + "name": "Isiolo" + }, + "point_b": { + "lat": 30.1764, + "lon": 121.2457, + "name": "Cixi" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 20.078044, + "lon": 75.692034 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (0.35462°, 37.58218°)", + " Point B: (30.1764°, 121.2457°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 20.078044°", + " Longitude: 75.692034°", + "FINAL ANSWER: 20.078044, 75.692034" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 38.78333, + "lon": 0.16667, + "name": "Javea" + }, + "point_b": { + "lat": 21.49837, + "lon": -158.06515, + "name": "Schofield Barracks" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 70.311804, + "lon": -103.603262 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (38.78333°, 0.16667°)", + " Point B: (21.49837°, -158.06515°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 70.311804°", + " Longitude: -103.603262°", + "FINAL ANSWER: 70.311804, -103.603262" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 49.27784, + "lon": -123.12794, + "name": "Downtown" + }, + "point_b": { + "lat": 26.42237, + "lon": 90.98004, + "name": "Howli" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 48.678903, + "lon": 104.466266 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (49.27784°, -123.12794°)", + " Point B: (26.42237°, 90.98004°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 48.678903°", + " Longitude: 104.466266°", + "FINAL ANSWER: 48.678903, 104.466266" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 10.53689, + "lon": -2.70155, + "name": "Jirapa" + }, + "point_b": { + "lat": 33.38291, + "lon": 71.33733, + "name": "Lachi" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 19.407542, + "lon": 13.221606 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (10.53689°, -2.70155°)", + " Point B: (33.38291°, 71.33733°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 19.407542°", + " Longitude: 13.221606°", + "FINAL ANSWER: 19.407542, 13.221606" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 14.2897, + "lon": 120.7168, + "name": "Ternate" + }, + "point_b": { + "lat": -33.78269, + "lon": 151.04888, + "name": "Carlingford" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -22.138023, + "lon": 142.175546 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (14.2897°, 120.7168°)", + " Point B: (-33.78269°, 151.04888°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -22.138023°", + " Longitude: 142.175546°", + "FINAL ANSWER: -22.138023, 142.175546" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 35.46522, + "lon": -6.03415, + "name": "Asilah" + }, + "point_b": { + "lat": -15.83722, + "lon": -54.38917, + "name": "Poxoréu" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 10.729359, + "lon": -32.347434 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (35.46522°, -6.03415°)", + " Point B: (-15.83722°, -54.38917°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 10.729359°", + " Longitude: -32.347434°", + "FINAL ANSWER: 10.729359, -32.347434" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 20.40953, + "lon": 72.88339, + "name": "Dabhel" + }, + "point_b": { + "lat": -4.4835, + "lon": -46.85326, + "name": "Bom Jesus das Selvas" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 20.828129, + "lon": 40.944118 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (20.40953°, 72.88339°)", + " Point B: (-4.4835°, -46.85326°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 20.828129°", + " Longitude: 40.944118°", + "FINAL ANSWER: 20.828129, 40.944118" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 60.98267, + "lon": 25.66151, + "name": "Lahti" + }, + "point_b": { + "lat": 35.75459, + "lon": 139.46852, + "name": "Higashimurayama" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 67.332986, + "lon": 63.520403 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (60.98267°, 25.66151°)", + " Point B: (35.75459°, 139.46852°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 67.332986°", + " Longitude: 63.520403°", + "FINAL ANSWER: 67.332986, 63.520403" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 51.25167, + "lon": 5.70694, + "name": "Weert" + }, + "point_b": { + "lat": 41.31429, + "lon": 16.28165, + "name": "Barletta" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 46.403988, + "lon": 11.476387 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (51.25167°, 5.70694°)", + " Point B: (41.31429°, 16.28165°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 46.403988°", + " Longitude: 11.476387°", + "FINAL ANSWER: 46.403988, 11.476387" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 6.95, + "lon": 1.16667, + "name": "Notsé" + }, + "point_b": { + "lat": 25.67317, + "lon": -97.81272, + "name": "Valle Hermoso" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 24.217576, + "lon": -45.091154 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (6.95°, 1.16667°)", + " Point B: (25.67317°, -97.81272°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 24.217576°", + " Longitude: -45.091154°", + "FINAL ANSWER: 24.217576, -45.091154" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 22.6493, + "lon": -80.04935, + "name": "Cifuentes" + }, + "point_b": { + "lat": 32.46739, + "lon": 14.56874, + "name": "Zliten" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 37.551336, + "lon": -35.522056 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (22.6493°, -80.04935°)", + " Point B: (32.46739°, 14.56874°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 37.551336°", + " Longitude: -35.522056°", + "FINAL ANSWER: 37.551336, -35.522056" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 11.02682, + "lon": 76.0987, + "name": "Peringottupulam" + }, + "point_b": { + "lat": 52.32333, + "lon": 9.20311, + "name": "Stadthagen" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 46.188436, + "lon": 33.345309 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (11.02682°, 76.0987°)", + " Point B: (52.32333°, 9.20311°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 46.188436°", + " Longitude: 33.345309°", + "FINAL ANSWER: 46.188436, 33.345309" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -38.07018, + "lon": 145.47411, + "name": "Pakenham" + }, + "point_b": { + "lat": 13.5, + "lon": 7.10174, + "name": "Maradi" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -42.694193, + "lon": 100.812178 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-38.07018°, 145.47411°)", + " Point B: (13.5°, 7.10174°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -42.694193°", + " Longitude: 100.812178°", + "FINAL ANSWER: -42.694193, 100.812178" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -6.74504, + "lon": 23.95328, + "name": "Gandajika" + }, + "point_b": { + "lat": 26.43864, + "lon": 85.13573, + "name": "Madhuban" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 2.400407, + "lon": 38.277786 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-6.74504°, 23.95328°)", + " Point B: (26.43864°, 85.13573°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 2.400407°", + " Longitude: 38.277786°", + "FINAL ANSWER: 2.400407, 38.277786" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 58.39418, + "lon": 33.91864, + "name": "Borovichi" + }, + "point_b": { + "lat": 49.97143, + "lon": 82.60586, + "name": "Ust-Kamenogorsk" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 53.799796, + "lon": 72.615011 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (58.39418°, 33.91864°)", + " Point B: (49.97143°, 82.60586°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 53.799796°", + " Longitude: 72.615011°", + "FINAL ANSWER: 53.799796, 72.615011" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 17.7, + "lon": 83.21667, + "name": "Gajuwaka" + }, + "point_b": { + "lat": 57.10557, + "lon": 12.25078, + "name": "Varberg" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 42.664574, + "lon": 58.778506 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (17.7°, 83.21667°)", + " Point B: (57.10557°, 12.25078°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 42.664574°", + " Longitude: 58.778506°", + "FINAL ANSWER: 42.664574, 58.778506" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 5.3378, + "lon": 116.1602, + "name": "Keningau" + }, + "point_b": { + "lat": -17.83917, + "lon": -40.35389, + "name": "Nanuque" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -28.149444, + "lon": 44.069971 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (5.3378°, 116.1602°)", + " Point B: (-17.83917°, -40.35389°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -28.149444°", + " Longitude: 44.069971°", + "FINAL ANSWER: -28.149444, 44.069971" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 43.47064, + "lon": 11.14804, + "name": "Poggibonsi" + }, + "point_b": { + "lat": 25.90417, + "lon": -100.15972, + "name": "Fraccionamiento Real Palmas" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 50.473984, + "lon": -53.400057 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (43.47064°, 11.14804°)", + " Point B: (25.90417°, -100.15972°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 50.473984°", + " Longitude: -53.400057°", + "FINAL ANSWER: 50.473984, -53.400057" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 4.80293, + "lon": 8.25341, + "name": "Esuk Oron" + }, + "point_b": { + "lat": 26.31008, + "lon": -80.23727, + "name": "Parkland" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 25.658829, + "lon": -56.150058 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (4.80293°, 8.25341°)", + " Point B: (26.31008°, -80.23727°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 25.658829°", + " Longitude: -56.150058°", + "FINAL ANSWER: 25.658829, -56.150058" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 48.8449, + "lon": 17.22635, + "name": "Skalica" + }, + "point_b": { + "lat": 29.15299, + "lon": 79.10814, + "name": "Bāzpur" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 36.915072, + "lon": 67.248584 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (48.8449°, 17.22635°)", + " Point B: (29.15299°, 79.10814°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 36.915072°", + " Longitude: 67.248584°", + "FINAL ANSWER: 36.915072, 67.248584" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 25.87577, + "lon": 87.84009, + "name": "Dalkola" + }, + "point_b": { + "lat": -18.93444, + "lon": 32.87556, + "name": "Manica" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 3.910512, + "lon": 59.612656 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (25.87577°, 87.84009°)", + " Point B: (-18.93444°, 32.87556°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 3.910512°", + " Longitude: 59.612656°", + "FINAL ANSWER: 3.910512, 59.612656" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 8.56744, + "lon": -10.1336, + "name": "Gueckedou" + }, + "point_b": { + "lat": -37.71667, + "lon": 145.0, + "name": "Reservoir" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -47.160222, + "lon": 40.682937 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (8.56744°, -10.1336°)", + " Point B: (-37.71667°, 145.0°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -47.160222°", + " Longitude: 40.682937°", + "FINAL ANSWER: -47.160222, 40.682937" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 37.34772, + "lon": -120.60908, + "name": "Atwater" + }, + "point_b": { + "lat": 51.69833, + "lon": 5.97361, + "name": "Gennep" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 64.796736, + "lon": -71.142483 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (37.34772°, -120.60908°)", + " Point B: (51.69833°, 5.97361°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 64.796736°", + " Longitude: -71.142483°", + "FINAL ANSWER: 64.796736, -71.142483" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 22.38124, + "lon": 112.68492, + "name": "Changsha" + }, + "point_b": { + "lat": 12.75142, + "lon": 77.80169, + "name": "Mūkondapalli" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 15.717541, + "lon": 86.166081 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (22.38124°, 112.68492°)", + " Point B: (12.75142°, 77.80169°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 15.717541°", + " Longitude: 86.166081°", + "FINAL ANSWER: 15.717541, 86.166081" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 36.75452, + "lon": 10.22167, + "name": "Ben Arous" + }, + "point_b": { + "lat": 36.05528, + "lon": 139.31503, + "name": "Ranzan" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 59.76401, + "lon": 75.309982 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (36.75452°, 10.22167°)", + " Point B: (36.05528°, 139.31503°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 59.764010°", + " Longitude: 75.309982°", + "FINAL ANSWER: 59.764010, 75.309982" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 1.13864, + "lon": 111.66665, + "name": "Engkilili" + }, + "point_b": { + "lat": 55.77043, + "lon": 9.7011, + "name": "Hedensted" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 39.133087, + "lon": 79.740639 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (1.13864°, 111.66665°)", + " Point B: (55.77043°, 9.7011°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 39.133087°", + " Longitude: 79.740639°", + "FINAL ANSWER: 39.133087, 79.740639" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 31.28837, + "lon": 31.67719, + "name": "Mīt Abū Ghālib" + }, + "point_b": { + "lat": 51.08022, + "lon": -4.05808, + "name": "Barnstaple" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 47.283912, + "lon": 7.114405 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (31.28837°, 31.67719°)", + " Point B: (51.08022°, -4.05808°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 47.283912°", + " Longitude: 7.114405°", + "FINAL ANSWER: 47.283912, 7.114405" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 37.75993, + "lon": -122.41914, + "name": "Mission District" + }, + "point_b": { + "lat": 32.74583, + "lon": 105.24139, + "name": "Bikou" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 54.20676, + "lon": -148.414398 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (37.75993°, -122.41914°)", + " Point B: (32.74583°, 105.24139°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 54.206760°", + " Longitude: -148.414398°", + "FINAL ANSWER: 54.206760, -148.414398" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 36.08497, + "lon": 9.37082, + "name": "Siliana" + }, + "point_b": { + "lat": 35.6253, + "lon": 139.63891, + "name": "Yōga" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 52.17138, + "lon": 115.748811 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (36.08497°, 9.37082°)", + " Point B: (35.6253°, 139.63891°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 52.171380°", + " Longitude: 115.748811°", + "FINAL ANSWER: 52.171380, 115.748811" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -3.38361, + "lon": -57.71861, + "name": "Maués" + }, + "point_b": { + "lat": 19.28786, + "lon": -99.65324, + "name": "Toluca" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 8.507547, + "lon": -78.071102 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-3.38361°, -57.71861°)", + " Point B: (19.28786°, -99.65324°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 8.507547°", + " Longitude: -78.071102°", + "FINAL ANSWER: 8.507547, -78.071102" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 27.8428, + "lon": -82.69954, + "name": "Pinellas Park" + }, + "point_b": { + "lat": 8.55083, + "lon": -0.51875, + "name": "Salaga" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 23.539985, + "lon": -38.819759 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (27.8428°, -82.69954°)", + " Point B: (8.55083°, -0.51875°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 23.539985°", + " Longitude: -38.819759°", + "FINAL ANSWER: 23.539985, -38.819759" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 2.3829, + "lon": 102.3311, + "name": "Kampung Machap Baru" + }, + "point_b": { + "lat": 25.26302, + "lon": 63.46921, + "name": "Pasni" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 14.620835, + "lon": 83.906421 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (2.3829°, 102.3311°)", + " Point B: (25.26302°, 63.46921°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 14.620835°", + " Longitude: 83.906421°", + "FINAL ANSWER: 14.620835, 83.906421" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -22.15194, + "lon": -42.41944, + "name": "Bom Jardim" + }, + "point_b": { + "lat": 11.69917, + "lon": 0.50611, + "name": "Natiaboani" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -5.613075, + "lon": -20.329651 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-22.15194°, -42.41944°)", + " Point B: (11.69917°, 0.50611°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -5.613075°", + " Longitude: -20.329651°", + "FINAL ANSWER: -5.613075, -20.329651" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 38.76098, + "lon": -9.20508, + "name": "Alfornelos" + }, + "point_b": { + "lat": -21.52944, + "lon": -46.64389, + "name": "Caconde" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 24.259335, + "lon": -20.631754 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (38.76098°, -9.20508°)", + " Point B: (-21.52944°, -46.64389°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 24.259335°", + " Longitude: -20.631754°", + "FINAL ANSWER: 24.259335, -20.631754" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 54.33901, + "lon": -1.43243, + "name": "Northallerton" + }, + "point_b": { + "lat": 42.33437, + "lon": -71.10845, + "name": "Mission Hill" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 53.765916, + "lon": -40.972027 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (54.33901°, -1.43243°)", + " Point B: (42.33437°, -71.10845°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 53.765916°", + " Longitude: -40.972027°", + "FINAL ANSWER: 53.765916, -40.972027" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 51.44491, + "lon": -0.02043, + "name": "Catford" + }, + "point_b": { + "lat": 9.7174, + "lon": -75.12023, + "name": "El Carmen de Bolívar" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 23.61564, + "lon": -62.674545 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (51.44491°, -0.02043°)", + " Point B: (9.7174°, -75.12023°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 23.615640°", + " Longitude: -62.674545°", + "FINAL ANSWER: 23.615640, -62.674545" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 38.79073, + "lon": -121.23578, + "name": "Rocklin" + }, + "point_b": { + "lat": 10.53689, + "lon": -2.70155, + "name": "Jirapa" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 41.41309, + "lon": -50.968405 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (38.79073°, -121.23578°)", + " Point B: (10.53689°, -2.70155°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 41.413090°", + " Longitude: -50.968405°", + "FINAL ANSWER: 41.413090, -50.968405" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 40.96836, + "lon": 17.11329, + "name": "Conversano" + }, + "point_b": { + "lat": -12.06866, + "lon": -75.21027, + "name": "Huancayo" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 20.24139, + "lon": -36.67523 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (40.96836°, 17.11329°)", + " Point B: (-12.06866°, -75.21027°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 20.241390°", + " Longitude: -36.675230°", + "FINAL ANSWER: 20.241390, -36.675230" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 34.0363, + "lon": -118.44949, + "name": "Sawtelle" + }, + "point_b": { + "lat": -2.13389, + "lon": -47.55889, + "name": "Aurora do Pará" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 19.293853, + "lon": -79.202818 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (34.0363°, -118.44949°)", + " Point B: (-2.13389°, -47.55889°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 19.293853°", + " Longitude: -79.202818°", + "FINAL ANSWER: 19.293853, -79.202818" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 26.72882, + "lon": 85.92628, + "name": "Janakpur" + }, + "point_b": { + "lat": 36.06629, + "lon": 1.12602, + "name": "Boukadir" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 39.545174, + "lon": 46.13212 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (26.72882°, 85.92628°)", + " Point B: (36.06629°, 1.12602°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 39.545174°", + " Longitude: 46.132120°", + "FINAL ANSWER: 39.545174, 46.132120" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 50.55667, + "lon": 6.76424, + "name": "Bad Münstereifel" + }, + "point_b": { + "lat": 14.2698, + "lon": 75.35643, + "name": "Shikaripura" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 45.890363, + "lon": 30.439619 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (50.55667°, 6.76424°)", + " Point B: (14.2698°, 75.35643°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 45.890363°", + " Longitude: 30.439619°", + "FINAL ANSWER: 45.890363, 30.439619" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -34.7524, + "lon": -56.00259, + "name": "Barros Blancos" + }, + "point_b": { + "lat": 8.27338, + "lon": 5.83526, + "name": "Isanlu-Itedoijowa" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -26.027614, + "lon": -37.548326 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-34.7524°, -56.00259°)", + " Point B: (8.27338°, 5.83526°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -26.027614°", + " Longitude: -37.548326°", + "FINAL ANSWER: -26.027614, -37.548326" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 10.30416, + "lon": 1.37962, + "name": "Natitingou" + }, + "point_b": { + "lat": -20.26389, + "lon": -40.42, + "name": "Cariacica" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -5.328415, + "lon": -18.999241 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (10.30416°, 1.37962°)", + " Point B: (-20.26389°, -40.42°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -5.328415°", + " Longitude: -18.999241°", + "FINAL ANSWER: -5.328415, -18.999241" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 8.36028, + "lon": -10.20639, + "name": "Foya Kamara" + }, + "point_b": { + "lat": 53.34855, + "lon": 18.4251, + "name": "Chełmno" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 20.062784, + "lon": -5.256068 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (8.36028°, -10.20639°)", + " Point B: (53.34855°, 18.4251°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 20.062784°", + " Longitude: -5.256068°", + "FINAL ANSWER: 20.062784, -5.256068" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -23.4837, + "lon": -46.41309, + "name": "Jardim Helena" + }, + "point_b": { + "lat": 6.90306, + "lon": -1.65199, + "name": "Ahwiaa" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -16.541438, + "lon": -34.317741 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-23.4837°, -46.41309°)", + " Point B: (6.90306°, -1.65199°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -16.541438°", + " Longitude: -34.317741°", + "FINAL ANSWER: -16.541438, -34.317741" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 42.33143, + "lon": -83.04575, + "name": "Detroit" + }, + "point_b": { + "lat": 35.89232, + "lon": 139.84184, + "name": "Yoshikawa" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 65.643558, + "lon": -158.243324 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (42.33143°, -83.04575°)", + " Point B: (35.89232°, 139.84184°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 65.643558°", + " Longitude: -158.243324°", + "FINAL ANSWER: 65.643558, -158.243324" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 35.01361, + "lon": -1.74799, + "name": "Nedroma" + }, + "point_b": { + "lat": 36.18683, + "lon": 5.31347, + "name": "Aïn Arnat" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 35.651757, + "lon": 1.756826 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (35.01361°, -1.74799°)", + " Point B: (36.18683°, 5.31347°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 35.651757°", + " Longitude: 1.756826°", + "FINAL ANSWER: 35.651757, 1.756826" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 29.92885, + "lon": 117.94638, + "name": "Biyang" + }, + "point_b": { + "lat": -6.9875, + "lon": 106.55139, + "name": "Pelabuhanratu" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 11.525846, + "lon": 111.861716 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (29.92885°, 117.94638°)", + " Point B: (-6.9875°, 106.55139°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 11.525846°", + " Longitude: 111.861716°", + "FINAL ANSWER: 11.525846, 111.861716" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 9.45803, + "lon": -5.62961, + "name": "Korhogo" + }, + "point_b": { + "lat": 7.85868, + "lon": 10.97187, + "name": "Beli" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 9.126954, + "lon": -1.466223 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (9.45803°, -5.62961°)", + " Point B: (7.85868°, 10.97187°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 9.126954°", + " Longitude: -1.466223°", + "FINAL ANSWER: 9.126954, -1.466223" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 55.67719, + "lon": 37.89322, + "name": "Lyubertsy" + }, + "point_b": { + "lat": 20.26961, + "lon": -98.94377, + "name": "Actopan" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 60.884801, + "lon": -62.73195 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (55.67719°, 37.89322°)", + " Point B: (20.26961°, -98.94377°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 60.884801°", + " Longitude: -62.731950°", + "FINAL ANSWER: 60.884801, -62.731950" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 27.20201, + "lon": 73.73394, + "name": "Nāgaur" + }, + "point_b": { + "lat": -11.13556, + "lon": -42.11278, + "name": "Central" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 14.839474, + "lon": 11.334526 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (27.20201°, 73.73394°)", + " Point B: (-11.13556°, -42.11278°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 14.839474°", + " Longitude: 11.334526°", + "FINAL ANSWER: 14.839474, 11.334526" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 34.50083, + "lon": -117.18588, + "name": "Apple Valley" + }, + "point_b": { + "lat": 51.55242, + "lon": -0.29686, + "name": "Wembley" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 61.036051, + "lon": -31.424812 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (34.50083°, -117.18588°)", + " Point B: (51.55242°, -0.29686°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 61.036051°", + " Longitude: -31.424812°", + "FINAL ANSWER: 61.036051, -31.424812" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -3.24401, + "lon": -79.82874, + "name": "Guabo" + }, + "point_b": { + "lat": -29.58667, + "lon": -51.37556, + "name": "São Sebastião do Caí" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -10.139573, + "lon": -73.357466 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-3.24401°, -79.82874°)", + " Point B: (-29.58667°, -51.37556°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -10.139573°", + " Longitude: -73.357466°", + "FINAL ANSWER: -10.139573, -73.357466" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 44.08333, + "lon": 26.63333, + "name": "Olteniţa" + }, + "point_b": { + "lat": 32.74506, + "lon": 13.71467, + "name": "Qaşr al Qarabūllī" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 41.389596, + "lon": 23.001118 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (44.08333°, 26.63333°)", + " Point B: (32.74506°, 13.71467°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 41.389596°", + " Longitude: 23.001118°", + "FINAL ANSWER: 41.389596, 23.001118" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 20.97173, + "lon": 81.85884, + "name": "Nawāpāra" + }, + "point_b": { + "lat": 12.95706, + "lon": 77.22374, + "name": "Māgadi" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 16.977478, + "lon": 79.491736 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (20.97173°, 81.85884°)", + " Point B: (12.95706°, 77.22374°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 16.977478°", + " Longitude: 79.491736°", + "FINAL ANSWER: 16.977478, 79.491736" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 43.75741, + "lon": 44.0297, + "name": "Prokhladnyy" + }, + "point_b": { + "lat": -0.98169, + "lon": 36.58642, + "name": "Mai" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 32.610862, + "lon": 41.5957 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (43.75741°, 44.0297°)", + " Point B: (-0.98169°, 36.58642°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 32.610862°", + " Longitude: 41.595700°", + "FINAL ANSWER: 32.610862, 41.595700" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 18.37477, + "lon": -95.75444, + "name": "Carlos A. Carrillo" + }, + "point_b": { + "lat": 5.46651, + "lon": -5.58678, + "name": "Gbabam" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 18.946401, + "lon": -72.409165 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (18.37477°, -95.75444°)", + " Point B: (5.46651°, -5.58678°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 18.946401°", + " Longitude: -72.409165°", + "FINAL ANSWER: 18.946401, -72.409165" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 10.97747, + "lon": 77.02601, + "name": "Vellalūr" + }, + "point_b": { + "lat": 25.80062, + "lon": 100.57435, + "name": "Jinniu" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 18.756188, + "lon": 88.283728 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (10.97747°, 77.02601°)", + " Point B: (25.80062°, 100.57435°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 18.756188°", + " Longitude: 88.283728°", + "FINAL ANSWER: 18.756188, 88.283728" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -15.80152, + "lon": -47.92706, + "name": "Sudoeste/Octagonal" + }, + "point_b": { + "lat": -33.9205, + "lon": 151.25522, + "name": "Coogee" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -61.108093, + "lon": 176.809654 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-15.80152°, -47.92706°)", + " Point B: (-33.9205°, 151.25522°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -61.108093°", + " Longitude: 176.809654°", + "FINAL ANSWER: -61.108093, 176.809654" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 13.13607, + "lon": -13.75566, + "name": "Médina Gounas" + }, + "point_b": { + "lat": -8.02167, + "lon": -34.98111, + "name": "Camaragibe" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -2.721465, + "lon": -29.696301 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (13.13607°, -13.75566°)", + " Point B: (-8.02167°, -34.98111°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -2.721465°", + " Longitude: -29.696301°", + "FINAL ANSWER: -2.721465, -29.696301" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 55.92791, + "lon": 12.30081, + "name": "Hillerød" + }, + "point_b": { + "lat": 13.78126, + "lon": 100.64506, + "name": "Khlong Chan" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 53.340746, + "lon": 45.905621 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (55.92791°, 12.30081°)", + " Point B: (13.78126°, 100.64506°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 53.340746°", + " Longitude: 45.905621°", + "FINAL ANSWER: 53.340746, 45.905621" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 36.51076, + "lon": 1.30809, + "name": "Ténès" + }, + "point_b": { + "lat": 23.89154, + "lon": 90.40232, + "name": "Tungi" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 39.182317, + "lon": 49.479893 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (36.51076°, 1.30809°)", + " Point B: (23.89154°, 90.40232°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 39.182317°", + " Longitude: 49.479893°", + "FINAL ANSWER: 39.182317, 49.479893" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 12.47255, + "lon": -85.65956, + "name": "Boaco" + }, + "point_b": { + "lat": 58.045, + "lon": 60.551, + "name": "Verkhnyaya Salda" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 72.706477, + "lon": 4.647867 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (12.47255°, -85.65956°)", + " Point B: (58.045°, 60.551°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 72.706477°", + " Longitude: 4.647867°", + "FINAL ANSWER: 72.706477, 4.647867" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 52.71667, + "lon": -1.15, + "name": "Mountsorrel" + }, + "point_b": { + "lat": 40.74199, + "lon": 14.61448, + "name": "Pagani" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 46.997305, + "lon": 7.615921 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (52.71667°, -1.15°)", + " Point B: (40.74199°, 14.61448°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 46.997305°", + " Longitude: 7.615921°", + "FINAL ANSWER: 46.997305, 7.615921" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 23.42045, + "lon": 85.21459, + "name": "Rātu" + }, + "point_b": { + "lat": -19.51889, + "lon": -41.01583, + "name": "Baixo Guandu" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -8.83589, + "lon": -9.252829 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (23.42045°, 85.21459°)", + " Point B: (-19.51889°, -41.01583°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -8.835890°", + " Longitude: -9.252829°", + "FINAL ANSWER: -8.835890, -9.252829" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 34.10834, + "lon": -117.28977, + "name": "San Bernardino" + }, + "point_b": { + "lat": 9.27304, + "lon": -65.77153, + "name": "Tucupido" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 16.870317, + "lon": -76.992863 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (34.10834°, -117.28977°)", + " Point B: (9.27304°, -65.77153°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 16.870317°", + " Longitude: -76.992863°", + "FINAL ANSWER: 16.870317, -76.992863" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 51.10628, + "lon": 7.01873, + "name": "Leichlingen" + }, + "point_b": { + "lat": 41.89381, + "lon": -87.67493, + "name": "West Town" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 51.411026, + "lon": -70.088697 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (51.10628°, 7.01873°)", + " Point B: (41.89381°, -87.67493°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 51.411026°", + " Longitude: -70.088697°", + "FINAL ANSWER: 51.411026, -70.088697" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -32.83211, + "lon": 151.35623, + "name": "Cessnock" + }, + "point_b": { + "lat": -6.53722, + "lon": -39.49667, + "name": "Cariús" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -64.79075, + "lon": 173.976926 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-32.83211°, 151.35623°)", + " Point B: (-6.53722°, -39.49667°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -64.790750°", + " Longitude: 173.976926°", + "FINAL ANSWER: -64.790750, 173.976926" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 50.10038, + "lon": 8.6295, + "name": "Gallus" + }, + "point_b": { + "lat": -36.8582, + "lon": 174.62019, + "name": "Lincoln" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 35.334766, + "lon": 133.481141 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (50.10038°, 8.6295°)", + " Point B: (-36.8582°, 174.62019°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 35.334766°", + " Longitude: 133.481141°", + "FINAL ANSWER: 35.334766, 133.481141" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 36.58597, + "lon": -79.39502, + "name": "Danville" + }, + "point_b": { + "lat": 52.22904, + "lon": 21.01644, + "name": "Śródmieście" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 58.076223, + "lon": -6.97536 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (36.58597°, -79.39502°)", + " Point B: (52.22904°, 21.01644°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 58.076223°", + " Longitude: -6.975360°", + "FINAL ANSWER: 58.076223, -6.975360" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 50.72044, + "lon": -3.49646, + "name": "Heavitree" + }, + "point_b": { + "lat": 40.60822, + "lon": -74.51803, + "name": "Warren Township" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 51.445016, + "lon": -42.704296 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (50.72044°, -3.49646°)", + " Point B: (40.60822°, -74.51803°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 51.445016°", + " Longitude: -42.704296°", + "FINAL ANSWER: 51.445016, -42.704296" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 46.18981, + "lon": 6.11441, + "name": "Lancy" + }, + "point_b": { + "lat": -19.01809, + "lon": -40.5373, + "name": "São Gabriel da Palha" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -2.183996, + "lon": -30.668761 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (46.18981°, 6.11441°)", + " Point B: (-19.01809°, -40.5373°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -2.183996°", + " Longitude: -30.668761°", + "FINAL ANSWER: -2.183996, -30.668761" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 36.14074, + "lon": 139.46011, + "name": "Gyōda" + }, + "point_b": { + "lat": 54.98877, + "lon": 82.71337, + "name": "Ob’" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 43.199792, + "lon": 129.111436 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (36.14074°, 139.46011°)", + " Point B: (54.98877°, 82.71337°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 43.199792°", + " Longitude: 129.111436°", + "FINAL ANSWER: 43.199792, 129.111436" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 41.16161, + "lon": -112.02633, + "name": "Roy" + }, + "point_b": { + "lat": 47.0458, + "lon": 21.91833, + "name": "Oradea" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 62.418352, + "lon": -2.728751 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (41.16161°, -112.02633°)", + " Point B: (47.0458°, 21.91833°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 62.418352°", + " Longitude: -2.728751°", + "FINAL ANSWER: 62.418352, -2.728751" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 8.0618, + "lon": 123.7477, + "name": "Tangub" + }, + "point_b": { + "lat": -7.18833, + "lon": -39.73694, + "name": "Santana do Cariri" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 3.037929, + "lon": 41.602517 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (8.0618°, 123.7477°)", + " Point B: (-7.18833°, -39.73694°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 3.037929°", + " Longitude: 41.602517°", + "FINAL ANSWER: 3.037929, 41.602517" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -10.97141, + "lon": -41.0796, + "name": "Ourolândia" + }, + "point_b": { + "lat": -33.75881, + "lon": 150.99292, + "name": "Baulkham Hills" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -64.555919, + "lon": 172.4093 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-10.97141°, -41.0796°)", + " Point B: (-33.75881°, 150.99292°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -64.555919°", + " Longitude: 172.409300°", + "FINAL ANSWER: -64.555919, 172.409300" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 33.52111, + "lon": 130.42444, + "name": "Katanawa" + }, + "point_b": { + "lat": 43.85495, + "lon": 41.59019, + "name": "Zelenchukskaya" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 48.197846, + "lon": 90.065909 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (33.52111°, 130.42444°)", + " Point B: (43.85495°, 41.59019°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 48.197846°", + " Longitude: 90.065909°", + "FINAL ANSWER: 48.197846, 90.065909" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 35.67384, + "lon": 5.6453, + "name": "Râs el Aïoun" + }, + "point_b": { + "lat": -19.05294, + "lon": -169.91957, + "name": "Alofi" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 20.800381, + "lon": -161.331415 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (35.67384°, 5.6453°)", + " Point B: (-19.05294°, -169.91957°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 20.800381°", + " Longitude: -161.331415°", + "FINAL ANSWER: 20.800381, -161.331415" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 39.49524, + "lon": 67.60931, + "name": "Panjakent" + }, + "point_b": { + "lat": 18.62936, + "lon": -95.51968, + "name": "Lerdo de Tejada" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 66.413077, + "lon": 44.328261 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (39.49524°, 67.60931°)", + " Point B: (18.62936°, -95.51968°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 66.413077°", + " Longitude: 44.328261°", + "FINAL ANSWER: 66.413077, 44.328261" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 7.7782, + "lon": 81.6038, + "name": "Eravur Town" + }, + "point_b": { + "lat": 32.10197, + "lon": 74.87303, + "name": "Narowal" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 13.879793, + "lon": 80.093749 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (7.7782°, 81.6038°)", + " Point B: (32.10197°, 74.87303°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 13.879793°", + " Longitude: 80.093749°", + "FINAL ANSWER: 13.879793, 80.093749" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 52.13129, + "lon": 11.63189, + "name": "Magdeburg" + }, + "point_b": { + "lat": 39.55493, + "lon": 21.76837, + "name": "Tríkala" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 49.076852, + "lon": 14.629942 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (52.13129°, 11.63189°)", + " Point B: (39.55493°, 21.76837°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 49.076852°", + " Longitude: 14.629942°", + "FINAL ANSWER: 49.076852, 14.629942" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 36.53628, + "lon": 3.8334, + "name": "Draa el Mizan" + }, + "point_b": { + "lat": 30.19327, + "lon": 31.13703, + "name": "Al Qanāţir al Khayrīyah" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 32.328086, + "lon": 24.707342 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (36.53628°, 3.8334°)", + " Point B: (30.19327°, 31.13703°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 32.328086°", + " Longitude: 24.707342°", + "FINAL ANSWER: 32.328086, 24.707342" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 4.51667, + "lon": 12.03333, + "name": "Nkoteng" + }, + "point_b": { + "lat": 19.38119, + "lon": -99.13685, + "name": "Colonia Nativitas" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 22.525259, + "lon": -70.304088 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (4.51667°, 12.03333°)", + " Point B: (19.38119°, -99.13685°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 22.525259°", + " Longitude: -70.304088°", + "FINAL ANSWER: 22.525259, -70.304088" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -33.4019, + "lon": -70.70619, + "name": "Renca" + }, + "point_b": { + "lat": 8.6989, + "lon": -62.19656, + "name": "Barrancas" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -1.843788, + "lon": -64.132679 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-33.4019°, -70.70619°)", + " Point B: (8.6989°, -62.19656°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -1.843788°", + " Longitude: -64.132679°", + "FINAL ANSWER: -1.843788, -64.132679" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 36.89244, + "lon": 15.06977, + "name": "Noto" + }, + "point_b": { + "lat": 14.47418, + "lon": 100.12218, + "name": "Suphan Buri" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 24.918858, + "lon": 82.755558 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (36.89244°, 15.06977°)", + " Point B: (14.47418°, 100.12218°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 24.918858°", + " Longitude: 82.755558°", + "FINAL ANSWER: 24.918858, 82.755558" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 51.01678, + "lon": -4.20832, + "name": "Bideford" + }, + "point_b": { + "lat": 51.84417, + "lon": 4.63889, + "name": "Hendrik-Ido-Ambacht" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 51.513764, + "lon": 0.17515 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (51.01678°, -4.20832°)", + " Point B: (51.84417°, 4.63889°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 51.513764°", + " Longitude: 0.175150°", + "FINAL ANSWER: 51.513764, 0.175150" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 57.47908, + "lon": -4.22398, + "name": "Inverness" + }, + "point_b": { + "lat": 14.6, + "lon": 121.0333, + "name": "San Juan" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 35.498608, + "lon": 108.436676 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (57.47908°, -4.22398°)", + " Point B: (14.6°, 121.0333°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 35.498608°", + " Longitude: 108.436676°", + "FINAL ANSWER: 35.498608, 108.436676" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -12.15, + "lon": 17.28333, + "name": "Catabola" + }, + "point_b": { + "lat": 20.85829, + "lon": 92.29773, + "name": "Teknāf" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 5.481788, + "lon": 53.798533 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-12.15°, 17.28333°)", + " Point B: (20.85829°, 92.29773°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 5.481788°", + " Longitude: 53.798533°", + "FINAL ANSWER: 5.481788, 53.798533" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 17.49326, + "lon": 44.12766, + "name": "Najrān" + }, + "point_b": { + "lat": 35.20913, + "lon": -118.82843, + "name": "Arvin" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 63.025733, + "lon": -95.915439 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (17.49326°, 44.12766°)", + " Point B: (35.20913°, -118.82843°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 63.025733°", + " Longitude: -95.915439°", + "FINAL ANSWER: 63.025733, -95.915439" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 8.58165, + "lon": 76.92242, + "name": "Uliyazhathura" + }, + "point_b": { + "lat": 5.78917, + "lon": 7.83829, + "name": "Amaigbo" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 8.701702, + "lon": 42.259162 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (8.58165°, 76.92242°)", + " Point B: (5.78917°, 7.83829°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 8.701702°", + " Longitude: 42.259162°", + "FINAL ANSWER: 8.701702, 42.259162" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 49.26667, + "lon": -123.16667, + "name": "Kitsilano" + }, + "point_b": { + "lat": 11.71733, + "lon": 75.6419, + "name": "Chekkiād" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 66.477461, + "lon": 105.842444 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (49.26667°, -123.16667°)", + " Point B: (11.71733°, 75.6419°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 66.477461°", + " Longitude: 105.842444°", + "FINAL ANSWER: 66.477461, 105.842444" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -22.23, + "lon": -45.93639, + "name": "Pouso Alegre" + }, + "point_b": { + "lat": 11.9801, + "lon": 18.2138, + "name": "Bitkine" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -14.718357, + "lon": -28.794226 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-22.23°, -45.93639°)", + " Point B: (11.9801°, 18.2138°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -14.718357°", + " Longitude: -28.794226°", + "FINAL ANSWER: -14.718357, -28.794226" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 39.38333, + "lon": 141.11667, + "name": "Hanamaki" + }, + "point_b": { + "lat": 32.17222, + "lon": 13.02028, + "name": "Gharyan" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 54.200961, + "lon": 114.113144 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (39.38333°, 141.11667°)", + " Point B: (32.17222°, 13.02028°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 54.200961°", + " Longitude: 114.113144°", + "FINAL ANSWER: 54.200961, 114.113144" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -37.73333, + "lon": 144.8, + "name": "Saint Albans" + }, + "point_b": { + "lat": -22.80389, + "lon": -43.37222, + "name": "São João de Meriti" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -66.82433, + "lon": 155.684576 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-37.73333°, 144.8°)", + " Point B: (-22.80389°, -43.37222°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -66.824330°", + " Longitude: 155.684576°", + "FINAL ANSWER: -66.824330, 155.684576" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 50.80225, + "lon": 4.33943, + "name": "Uccle" + }, + "point_b": { + "lat": 35.01127, + "lon": 37.05324, + "name": "As Salamīyah" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 39.75518, + "lon": 30.42435 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (50.80225°, 4.33943°)", + " Point B: (35.01127°, 37.05324°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 39.755180°", + " Longitude: 30.424350°", + "FINAL ANSWER: 39.755180, 30.424350" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 51.55912, + "lon": 21.84829, + "name": "Dęblin" + }, + "point_b": { + "lat": 5.62135, + "lon": -0.05193, + "name": "Sakumona" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 29.010555, + "lon": 8.339286 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (51.55912°, 21.84829°)", + " Point B: (5.62135°, -0.05193°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 29.010555°", + " Longitude: 8.339286°", + "FINAL ANSWER: 29.010555, 8.339286" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -41.33333, + "lon": 173.18333, + "name": "Richmond" + }, + "point_b": { + "lat": 16.07114, + "lon": 80.54944, + "name": "Ponnur" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -32.418064, + "lon": 142.948573 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-41.33333°, 173.18333°)", + " Point B: (16.07114°, 80.54944°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -32.418064°", + " Longitude: 142.948573°", + "FINAL ANSWER: -32.418064, 142.948573" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 9.43056, + "lon": -13.08806, + "name": "Forécariah" + }, + "point_b": { + "lat": 22.20928, + "lon": 75.47057, + "name": "Dhāmnod" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 16.577031, + "lon": 7.507363 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (9.43056°, -13.08806��)", + " Point B: (22.20928°, 75.47057°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 16.577031°", + " Longitude: 7.507363°", + "FINAL ANSWER: 16.577031, 7.507363" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 1.28722, + "lon": 103.80833, + "name": "Brickworks Estate" + }, + "point_b": { + "lat": -4.85187, + "lon": 21.5595, + "name": "Mweka" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -3.854563, + "lon": 42.192926 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (1.28722°, 103.80833°)", + " Point B: (-4.85187°, 21.5595°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -3.854563°", + " Longitude: 42.192926°", + "FINAL ANSWER: -3.854563, 42.192926" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 48.78232, + "lon": 9.17702, + "name": "Stuttgart" + }, + "point_b": { + "lat": 11.68178, + "lon": 75.6248, + "name": "Edacchēri" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 34.644207, + "lon": 49.699975 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (48.78232°, 9.17702°)", + " Point B: (11.68178°, 75.6248°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 34.644207°", + " Longitude: 49.699975°", + "FINAL ANSWER: 34.644207, 49.699975" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 11.66667, + "lon": 39.65, + "name": "Mersa" + }, + "point_b": { + "lat": -35.03264, + "lon": -63.01484, + "name": "General Villegas" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -18.206751, + "lon": -5.317291 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (11.66667°, 39.65°)", + " Point B: (-35.03264°, -63.01484°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -18.206751°", + " Longitude: -5.317291°", + "FINAL ANSWER: -18.206751, -5.317291" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 50.71717, + "lon": 4.60138, + "name": "Wavre" + }, + "point_b": { + "lat": 54.30911, + "lon": 13.0818, + "name": "Stralsund" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 52.588823, + "lon": 8.66792 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (50.71717°, 4.60138°)", + " Point B: (54.30911°, 13.0818°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 52.588823°", + " Longitude: 8.667920°", + "FINAL ANSWER: 52.588823, 8.667920" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 11.31755, + "lon": -5.66654, + "name": "Sikasso" + }, + "point_b": { + "lat": 49.59786, + "lon": 8.4725, + "name": "Lampertheim" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 21.002264, + "lon": -3.040301 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (11.31755°, -5.66654°)", + " Point B: (49.59786°, 8.4725°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 21.002264°", + " Longitude: -3.040301°", + "FINAL ANSWER: 21.002264, -3.040301" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -27.93994, + "lon": 153.31436, + "name": "Pacific Pines" + }, + "point_b": { + "lat": 31.3141, + "lon": 34.62025, + "name": "Ofaqim" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 19.862537, + "lon": 67.722985 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-27.93994°, 153.31436°)", + " Point B: (31.3141°, 34.62025°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 19.862537°", + " Longitude: 67.722985°", + "FINAL ANSWER: 19.862537, 67.722985" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 36.02361, + "lon": 119.17611, + "name": "Jiayue" + }, + "point_b": { + "lat": -42.76848, + "lon": -65.03827, + "name": "Puerto Madryn" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -70.422998, + "lon": -133.565502 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (36.02361°, 119.17611°)", + " Point B: (-42.76848°, -65.03827°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -70.422998°", + " Longitude: -133.565502°", + "FINAL ANSWER: -70.422998, -133.565502" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -21.53944, + "lon": -42.18028, + "name": "Santo Antônio de Pádua" + }, + "point_b": { + "lat": 41.00711, + "lon": 28.88795, + "name": "güngören merter" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 27.84503, + "lon": 6.315516 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-21.53944°, -42.18028°)", + " Point B: (41.00711°, 28.88795°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 27.845030°", + " Longitude: 6.315516°", + "FINAL ANSWER: 27.845030, 6.315516" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 52.41667, + "lon": 0.75, + "name": "Thetford" + }, + "point_b": { + "lat": 28.0653, + "lon": -81.78869, + "name": "Auburndale" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 39.140765, + "lon": -67.980226 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (52.41667°, 0.75°)", + " Point B: (28.0653°, -81.78869°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 39.140765°", + " Longitude: -67.980226°", + "FINAL ANSWER: 39.140765, -67.980226" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 63.11045, + "lon": 7.72795, + "name": "Kristiansund" + }, + "point_b": { + "lat": 35.06667, + "lon": 135.21667, + "name": "Sasayama" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 72.022624, + "lon": 51.420468 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (63.11045°, 7.72795°)", + " Point B: (35.06667°, 135.21667°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 72.022624°", + " Longitude: 51.420468°", + "FINAL ANSWER: 72.022624, 51.420468" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 19.25465, + "lon": -99.10356, + "name": "Xochimilco" + }, + "point_b": { + "lat": 45.4859, + "lon": -73.63103, + "name": "Snowdon" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 26.230595, + "lon": -94.012455 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (19.25465°, -99.10356°)", + " Point B: (45.4859°, -73.63103°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 26.230595°", + " Longitude: -94.012455°", + "FINAL ANSWER: 26.230595, -94.012455" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -22.81667, + "lon": 47.28333, + "name": "Vondrozo" + }, + "point_b": { + "lat": 40.7602, + "lon": 14.53723, + "name": "Scafati" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -6.793459, + "lon": 39.668001 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-22.81667°, 47.28333°)", + " Point B: (40.7602°, 14.53723°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -6.793459°", + " Longitude: 39.668001°", + "FINAL ANSWER: -6.793459, 39.668001" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -18.72472, + "lon": -47.49861, + "name": "Monte Carmelo" + }, + "point_b": { + "lat": 51.46839, + "lon": -0.36092, + "name": "Hounslow" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -0.516765, + "lon": -38.260077 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-18.72472°, -47.49861°)", + " Point B: (51.46839°, -0.36092°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -0.516765°", + " Longitude: -38.260077°", + "FINAL ANSWER: -0.516765, -38.260077" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 3.08385, + "lon": 101.70895, + "name": "Desa Petaling" + }, + "point_b": { + "lat": 6.11982, + "lon": 1.19012, + "name": "Aflao" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 7.339993, + "lon": 26.36436 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (3.08385°, 101.70895°)", + " Point B: (6.11982°, 1.19012°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 7.339993°", + " Longitude: 26.364360°", + "FINAL ANSWER: 7.339993, 26.364360" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 40.97782, + "lon": 37.89047, + "name": "Ordu" + }, + "point_b": { + "lat": 47.40165, + "lon": 8.40015, + "name": "Dietikon" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 45.146007, + "lon": 23.967875 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (40.97782°, 37.89047°)", + " Point B: (47.40165°, 8.40015°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 45.146007°", + " Longitude: 23.967875°", + "FINAL ANSWER: 45.146007, 23.967875" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -1.9509, + "lon": 30.5205, + "name": "Kayonza" + }, + "point_b": { + "lat": 10.33137, + "lon": -3.18202, + "name": "Gaoua" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 4.377506, + "lon": 13.806044 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-1.9509°, 30.5205°)", + " Point B: (10.33137°, -3.18202°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 4.377506°", + " Longitude: 13.806044°", + "FINAL ANSWER: 4.377506, 13.806044" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 42.20704, + "lon": -71.68562, + "name": "Grafton" + }, + "point_b": { + "lat": -27.63917, + "lon": 153.10944, + "name": "Logan City" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -5.352964, + "lon": -178.144929 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (42.20704°, -71.68562°)", + " Point B: (-27.63917°, 153.10944°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -5.352964°", + " Longitude: -178.144929°", + "FINAL ANSWER: -5.352964, -178.144929" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 36.70456, + "lon": 3.02462, + "name": "Saoula" + }, + "point_b": { + "lat": 43.51345, + "lon": 4.98747, + "name": "Istres" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 41.814444, + "lon": 4.458483 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (36.70456°, 3.02462°)", + " Point B: (43.51345°, 4.98747°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 41.814444°", + " Longitude: 4.458483°", + "FINAL ANSWER: 41.814444, 4.458483" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 45.77437, + "lon": 4.77758, + "name": "Écully" + }, + "point_b": { + "lat": -28.46667, + "lon": -49.00694, + "name": "Tubarão" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -9.596887, + "lon": -36.54923 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (45.77437°, 4.77758°)", + " Point B: (-28.46667°, -49.00694°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -9.596887°", + " Longitude: -36.549230°", + "FINAL ANSWER: -9.596887, -36.549230" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 52.97633, + "lon": -0.02664, + "name": "Boston" + }, + "point_b": { + "lat": 34.49162, + "lon": -5.50846, + "name": "Souk et Tnine Jorf el Mellah" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 43.765941, + "lon": -3.194591 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (52.97633°, -0.02664°)", + " Point B: (34.49162°, -5.50846°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 43.765941°", + " Longitude: -3.194591°", + "FINAL ANSWER: 43.765941, -3.194591" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 35.57525, + "lon": 10.73456, + "name": "Zeramedine" + }, + "point_b": { + "lat": 52.99505, + "lon": 16.9198, + "name": "Chodzież" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 44.325957, + "lon": 13.364634 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (35.57525°, 10.73456°)", + " Point B: (52.99505°, 16.9198°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 44.325957°", + " Longitude: 13.364634°", + "FINAL ANSWER: 44.325957, 13.364634" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 9.01667, + "lon": 37.45, + "name": "Gēdo" + }, + "point_b": { + "lat": 35.38329, + "lon": 139.93254, + "name": "Kisarazu" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 32.914497, + "lon": 81.901164 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (9.01667°, 37.45°)", + " Point B: (35.38329°, 139.93254°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 32.914497°", + " Longitude: 81.901164°", + "FINAL ANSWER: 32.914497, 81.901164" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 40.19944, + "lon": 124.53167, + "name": "Uiju" + }, + "point_b": { + "lat": 18.79284, + "lon": 78.27666, + "name": "Āmūr" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 25.537527, + "lon": 87.987334 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (40.19944°, 124.53167°)", + " Point B: (18.79284°, 78.27666°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 25.537527°", + " Longitude: 87.987334°", + "FINAL ANSWER: 25.537527, 87.987334" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -27.56056, + "lon": 151.95386, + "name": "Toowoomba" + }, + "point_b": { + "lat": 35.45139, + "lon": 2.90583, + "name": "Aïn Oussera" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 31.745818, + "lon": 48.900252 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-27.56056°, 151.95386°)", + " Point B: (35.45139°, 2.90583°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 31.745818°", + " Longitude: 48.900252°", + "FINAL ANSWER: 31.745818, 48.900252" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 39.91987, + "lon": 32.85427, + "name": "Ankara" + }, + "point_b": { + "lat": -14.08239, + "lon": 34.91652, + "name": "Monkey Bay" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 12.920734, + "lon": 34.005924 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (39.91987°, 32.85427°)", + " Point B: (-14.08239°, 34.91652°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 12.920734°", + " Longitude: 34.005924°", + "FINAL ANSWER: 12.920734, 34.005924" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 56.85853, + "lon": 40.54028, + "name": "Teykovo" + }, + "point_b": { + "lat": 14.76457, + "lon": -17.39071, + "name": "Pikine" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 39.184107, + "lon": 2.837678 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (56.85853°, 40.54028°)", + " Point B: (14.76457°, -17.39071°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 39.184107°", + " Longitude: 2.837678°", + "FINAL ANSWER: 39.184107, 2.837678" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 30.81479, + "lon": 107.5418, + "name": "Hucheng" + }, + "point_b": { + "lat": 40.64575, + "lon": -8.64643, + "name": "Aveiro" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 51.64835, + "lon": 18.904657 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (30.81479°, 107.5418°)", + " Point B: (40.64575°, -8.64643°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 51.648350°", + " Longitude: 18.904657°", + "FINAL ANSWER: 51.648350, 18.904657" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 10.47027, + "lon": -66.61934, + "name": "Guarenas" + }, + "point_b": { + "lat": -26.63222, + "lon": -48.68472, + "name": "Barra Velha" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -8.179394, + "lon": -58.082818 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (10.47027°, -66.61934°)", + " Point B: (-26.63222°, -48.68472°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -8.179394°", + " Longitude: -58.082818°", + "FINAL ANSWER: -8.179394, -58.082818" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -19.46583, + "lon": -44.24667, + "name": "Sete Lagoas" + }, + "point_b": { + "lat": 41.69809, + "lon": -87.70866, + "name": "Mount Greenwood" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 27.334122, + "lon": -73.855925 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-19.46583°, -44.24667°)", + " Point B: (41.69809°, -87.70866°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 27.334122°", + " Longitude: -73.855925°", + "FINAL ANSWER: 27.334122, -73.855925" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 41.07871, + "lon": -73.46929, + "name": "Darien" + }, + "point_b": { + "lat": 6.24585, + "lon": 46.2247, + "name": "Cabudwaaq" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 25.067621, + "lon": 26.204082 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (41.07871°, -73.46929°)", + " Point B: (6.24585°, 46.2247°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 25.067621°", + " Longitude: 26.204082°", + "FINAL ANSWER: 25.067621, 26.204082" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 41.47309, + "lon": -87.06114, + "name": "Valparaiso" + }, + "point_b": { + "lat": 24.0299, + "lon": 73.04632, + "name": "Khedbrahma" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 66.363592, + "lon": -63.970932 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (41.47309°, -87.06114°)", + " Point B: (24.0299°, 73.04632°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 66.363592°", + " Longitude: -63.970932°", + "FINAL ANSWER: 66.363592, -63.970932" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 41.99232, + "lon": 12.71876, + "name": "Guidonia" + }, + "point_b": { + "lat": -6.03389, + "lon": -37.02028, + "name": "Jucurutu" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 19.640838, + "lon": -15.984735 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (41.99232°, 12.71876°)", + " Point B: (-6.03389°, -37.02028°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 19.640838°", + " Longitude: -15.984735°", + "FINAL ANSWER: 19.640838, -15.984735" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 40.73542, + "lon": 8.56771, + "name": "Monte Rosello" + }, + "point_b": { + "lat": 47.98522, + "lon": 37.2821, + "name": "Kurakhovo" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 45.265642, + "lon": 22.016428 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (40.73542°, 8.56771°)", + " Point B: (47.98522°, 37.2821°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 45.265642°", + " Longitude: 22.016428°", + "FINAL ANSWER: 45.265642, 22.016428" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -3.22083, + "lon": -64.80417, + "name": "Alvarães" + }, + "point_b": { + "lat": 53.9202, + "lon": 102.0442, + "name": "Zima" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 28.315542, + "lon": -58.908893 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-3.22083°, -64.80417°)", + " Point B: (53.9202°, 102.0442°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 28.315542°", + " Longitude: -58.908893°", + "FINAL ANSWER: 28.315542, -58.908893" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 22.22819, + "lon": -102.32216, + "name": "Rincón de Romos" + }, + "point_b": { + "lat": 45.50147, + "lon": 9.33053, + "name": "Pioltello" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 49.49682, + "lon": -58.001585 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (22.22819°, -102.32216°)", + " Point B: (45.50147°, 9.33053°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 49.496820°", + " Longitude: -58.001585°", + "FINAL ANSWER: 49.496820, -58.001585" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -22.33028, + "lon": -47.1725, + "name": "Conchal" + }, + "point_b": { + "lat": 29.40031, + "lon": 105.83781, + "name": "Shuangshi" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -4.625223, + "lon": -11.592758 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-22.33028°, -47.1725°)", + " Point B: (29.40031°, 105.83781°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -4.625223°", + " Longitude: -11.592758°", + "FINAL ANSWER: -4.625223, -11.592758" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 16.58225, + "lon": 81.38112, + "name": "Akivīdu" + }, + "point_b": { + "lat": 25.06889, + "lon": 91.40243, + "name": "Sunāmganj" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 18.756125, + "lon": 83.784418 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (16.58225°, 81.38112°)", + " Point B: (25.06889°, 91.40243°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 18.756125°", + " Longitude: 83.784418°", + "FINAL ANSWER: 18.756125, 83.784418" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -27.94972, + "lon": -51.80667, + "name": "Sananduva" + }, + "point_b": { + "lat": 16.4821, + "lon": 78.32471, + "name": "Nāgar Karnūl" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -24.705708, + "lon": -14.813206 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-27.94972°, -51.80667°)", + " Point B: (16.4821°, 78.32471°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a��A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -24.705708°", + " Longitude: -14.813206°", + "FINAL ANSWER: -24.705708, -14.813206" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -25.44227, + "lon": -49.06795, + "name": "Piraquara" + }, + "point_b": { + "lat": 64.446, + "lon": 40.6531, + "name": "Isakogorka" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -0.105825, + "lon": -36.31626 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-25.44227°, -49.06795°)", + " Point B: (64.446°, 40.6531°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -0.105825°", + " Longitude: -36.316260°", + "FINAL ANSWER: -0.105825, -36.316260" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 4.3324, + "lon": -75.82665, + "name": "Caicedonia" + }, + "point_b": { + "lat": 30.07994, + "lon": -95.41716, + "name": "Spring" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 23.850705, + "lon": -89.912995 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (4.3324°, -75.82665°)", + " Point B: (30.07994°, -95.41716°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 23.850705°", + " Longitude: -89.912995°", + "FINAL ANSWER: 23.850705, -89.912995" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 51.47566, + "lon": 0.32521, + "name": "Grays" + }, + "point_b": { + "lat": 9.3045, + "lon": -75.3905, + "name": "Sincelejo" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 23.357588, + "lon": -62.871362 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (51.47566°, 0.32521°)", + " Point B: (9.3045°, -75.3905°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 23.357588°", + " Longitude: -62.871362°", + "FINAL ANSWER: 23.357588, -62.871362" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 51.60946, + "lon": 16.85852, + "name": "Rawicz" + }, + "point_b": { + "lat": 37.7966, + "lon": -122.40858, + "name": "Chinatown" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 67.190065, + "lon": -11.711175 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (51.60946°, 16.85852°)", + " Point B: (37.7966°, -122.40858°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 67.190065°", + " Longitude: -11.711175°", + "FINAL ANSWER: 67.190065, -11.711175" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 37.50693, + "lon": 13.08399, + "name": "Sciacca" + }, + "point_b": { + "lat": 51.77714, + "lon": -3.20792, + "name": "Ebbw Vale" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 41.272364, + "lon": 9.720746 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (37.50693°, 13.08399°)", + " Point B: (51.77714°, -3.20792°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 41.272364°", + " Longitude: 9.720746°", + "FINAL ANSWER: 41.272364, 9.720746" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 9.83847, + "lon": -83.86655, + "name": "Paraíso" + }, + "point_b": { + "lat": 16.4625, + "lon": -15.70083, + "name": "Richard-Toll" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 15.752697, + "lon": -50.307829 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (9.83847°, -83.86655°)", + " Point B: (16.4625°, -15.70083°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 15.752697°", + " Longitude: -50.307829°", + "FINAL ANSWER: 15.752697, -50.307829" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 50.5107, + "lon": 18.30056, + "name": "Strzelce Opolskie" + }, + "point_b": { + "lat": 47.47038, + "lon": -122.34679, + "name": "Burien" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 73.624245, + "lon": -56.90123 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (50.5107°, 18.30056°)", + " Point B: (47.47038°, -122.34679°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 73.624245°", + " Longitude: -56.901230°", + "FINAL ANSWER: 73.624245, -56.901230" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 6.83333, + "lon": 38.08333, + "name": "Bedēsa" + }, + "point_b": { + "lat": -3.54964, + "lon": 143.63229, + "name": "Wewak" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -0.466743, + "lon": 117.331942 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (6.83333°, 38.08333°)", + " Point B: (-3.54964°, 143.63229°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -0.466743°", + " Longitude: 117.331942°", + "FINAL ANSWER: -0.466743, 117.331942" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 39.20889, + "lon": 45.41222, + "name": "Naxçıvan" + }, + "point_b": { + "lat": 47.65688, + "lon": -2.76205, + "name": "Vannes" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 47.576691, + "lon": 10.376331 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (39.20889°, 45.41222°)", + " Point B: (47.65688°, -2.76205°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 47.576691°", + " Longitude: 10.376331°", + "FINAL ANSWER: 47.576691, 10.376331" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 10.18634, + "lon": -67.45935, + "name": "Cagua" + }, + "point_b": { + "lat": 36.41976, + "lon": -6.14367, + "name": "Chiclana de la Frontera" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 32.641088, + "lon": -24.102412 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (10.18634°, -67.45935°)", + " Point B: (36.41976°, -6.14367°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 32.641088°", + " Longitude: -24.102412°", + "FINAL ANSWER: 32.641088, -24.102412" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 34.89638, + "lon": 3.48543, + "name": "Dar Chioukh" + }, + "point_b": { + "lat": 41.68199, + "lon": -85.97667, + "name": "Elkhart" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 47.985533, + "lon": -38.591007 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (34.89638°, 3.48543°)", + " Point B: (41.68199°, -85.97667°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 47.985533°", + " Longitude: -38.591007°", + "FINAL ANSWER: 47.985533, -38.591007" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -15.025, + "lon": 38.0425, + "name": "Iapala" + }, + "point_b": { + "lat": 26.94442, + "lon": 84.5377, + "name": "Chanpatia" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -4.353526, + "lon": 49.3335 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-15.025°, 38.0425°)", + " Point B: (26.94442°, 84.5377°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -4.353526°", + " Longitude: 49.333500°", + "FINAL ANSWER: -4.353526, 49.333500" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -20.31833, + "lon": -48.31056, + "name": "Guaíra" + }, + "point_b": { + "lat": 4.74215, + "lon": 7.08368, + "name": "Okrika" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -14.993782, + "lon": -33.621805 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-20.31833°, -48.31056°)", + " Point B: (4.74215°, 7.08368°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -14.993782°", + " Longitude: -33.621805°", + "FINAL ANSWER: -14.993782, -33.621805" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 19.96268, + "lon": -97.21141, + "name": "Tlapacoyan" + }, + "point_b": { + "lat": 1.38028, + "lon": 103.83972, + "name": "Ang Mo Kio New Town" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 41.7113, + "lon": -133.527255 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (19.96268°, -97.21141°)", + " Point B: (1.38028°, 103.83972°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 41.711300°", + " Longitude: -133.527255°", + "FINAL ANSWER: 41.711300, -133.527255" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -11.13556, + "lon": -42.11278, + "name": "Central" + }, + "point_b": { + "lat": 16.0009, + "lon": 120.4023, + "name": "Santa Barbara" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 20.998036, + "lon": 77.812136 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-11.13556°, -42.11278°)", + " Point B: (16.0009°, 120.4023°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 20.998036°", + " Longitude: 77.812136°", + "FINAL ANSWER: 20.998036, 77.812136" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -28.872, + "lon": 27.87506, + "name": "Ficksburg" + }, + "point_b": { + "lat": 42.76537, + "lon": -71.46757, + "name": "Nashua" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 29.533132, + "lon": -39.308116 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-28.872°, 27.87506°)", + " Point B: (42.76537°, -71.46757°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 29.533132°", + " Longitude: -39.308116°", + "FINAL ANSWER: 29.533132, -39.308116" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 42.44775, + "lon": -8.68594, + "name": "Poio" + }, + "point_b": { + "lat": 22.31693, + "lon": 114.19052, + "name": "To Kwa Wan" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 52.40951, + "lon": 64.436239 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (42.44775°, -8.68594°)", + " Point B: (22.31693°, 114.19052°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 52.409510°", + " Longitude: 64.436239°", + "FINAL ANSWER: 52.409510, 64.436239" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 13.41033, + "lon": -16.70815, + "name": "Sukuta" + }, + "point_b": { + "lat": -7.83306, + "lon": -35.75472, + "name": "Surubim" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 8.147186, + "lon": -21.577336 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (13.41033°, -16.70815°)", + " Point B: (-7.83306°, -35.75472°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 8.147186°", + " Longitude: -21.577336°", + "FINAL ANSWER: 8.147186, -21.577336" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 45.45008, + "lon": -73.86586, + "name": "Kirkland" + }, + "point_b": { + "lat": 23.64824, + "lon": -100.64334, + "name": "Matehuala" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 29.587737, + "lon": -95.18711 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (45.45008°, -73.86586°)", + " Point B: (23.64824°, -100.64334°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 29.587737°", + " Longitude: -95.187110°", + "FINAL ANSWER: 29.587737, -95.187110" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -0.30719, + "lon": 36.07225, + "name": "Nakuru" + }, + "point_b": { + "lat": -25.23, + "lon": -50.60444, + "name": "Imbituva" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -9.370812, + "lon": 16.245939 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-0.30719°, 36.07225°)", + " Point B: (-25.23°, -50.60444°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -9.370812°", + " Longitude: 16.245939°", + "FINAL ANSWER: -9.370812, 16.245939" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 42.4251, + "lon": -71.06616, + "name": "Malden" + }, + "point_b": { + "lat": -10.71667, + "lon": 39.73333, + "name": "Kitama" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 39.19086, + "lon": -33.84643 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (42.4251°, -71.06616°)", + " Point B: (-10.71667°, 39.73333°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 39.190860°", + " Longitude: -33.846430°", + "FINAL ANSWER: 39.190860, -33.846430" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 52.51167, + "lon": 6.25694, + "name": "Dalfsen" + }, + "point_b": { + "lat": -27.27888, + "lon": 28.49696, + "name": "Frankfort" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -7.240815, + "lon": 23.781236 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (52.51167°, 6.25694°)", + " Point B: (-27.27888°, 28.49696°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -7.240815°", + " Longitude: 23.781236°", + "FINAL ANSWER: -7.240815, 23.781236" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 27.79449, + "lon": 77.4368, + "name": "Kosi" + }, + "point_b": { + "lat": -13.06667, + "lon": 22.68333, + "name": "Chavuma" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 8.277963, + "lon": 48.632018 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (27.79449°, 77.4368°)", + " Point B: (-13.06667°, 22.68333°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 8.277963°", + " Longitude: 48.632018°", + "FINAL ANSWER: 8.277963, 48.632018" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -37.86667, + "lon": 145.28333, + "name": "Boronia" + }, + "point_b": { + "lat": 36.90123, + "lon": 137.44955, + "name": "Kurobe-shi" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -19.185637, + "lon": 143.080271 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-37.86667°, 145.28333°)", + " Point B: (36.90123°, 137.44955°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -19.185637°", + " Longitude: 143.080271°", + "FINAL ANSWER: -19.185637, 143.080271" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 25.05823, + "lon": -77.34306, + "name": "Nassau" + }, + "point_b": { + "lat": 34.79528, + "lon": 116.08167, + "name": "Shancheng" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 77.594415, + "lon": -138.013495 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (25.05823°, -77.34306°)", + " Point B: (34.79528°, 116.08167°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 77.594415°", + " Longitude: -138.013495°", + "FINAL ANSWER: 77.594415, -138.013495" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 17.67924, + "lon": 75.33098, + "name": "Pandharpur" + }, + "point_b": { + "lat": -3.63222, + "lon": -44.55583, + "name": "Matões do Norte" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 13.808688, + "lon": 13.093625 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (17.67924°, 75.33098°)", + " Point B: (-3.63222°, -44.55583°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 13.808688°", + " Longitude: 13.093625°", + "FINAL ANSWER: 13.808688, 13.093625" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 31.08351, + "lon": -97.65974, + "name": "Harker Heights" + }, + "point_b": { + "lat": -3.89174, + "lon": -59.09542, + "name": "Nova Olinda do Norte" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 5.300464, + "lon": -67.841182 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (31.08351°, -97.65974°)", + " Point B: (-3.89174°, -59.09542°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 5.300464°", + " Longitude: -67.841182°", + "FINAL ANSWER: 5.300464, -67.841182" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 53.58399, + "lon": 9.97585, + "name": "Hoheluft-Ost" + }, + "point_b": { + "lat": -34.06251, + "lon": 151.14961, + "name": "Cronulla" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -4.850315, + "lon": 127.340085 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (53.58399°, 9.97585°)", + " Point B: (-34.06251°, 151.14961°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -4.850315°", + " Longitude: 127.340085°", + "FINAL ANSWER: -4.850315, 127.340085" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 40.48622, + "lon": -74.45182, + "name": "New Brunswick" + }, + "point_b": { + "lat": 38.2278, + "lon": 27.96955, + "name": "Ödemiş" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 52.620705, + "lon": -22.088833 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (40.48622°, -74.45182°)", + " Point B: (38.2278°, 27.96955°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 52.620705°", + " Longitude: -22.088833°", + "FINAL ANSWER: 52.620705, -22.088833" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 8.6989, + "lon": -62.19656, + "name": "Barrancas" + }, + "point_b": { + "lat": 21.00153, + "lon": -100.38416, + "name": "San José Iturbide" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 12.341859, + "lon": -71.337119 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (8.6989°, -62.19656°)", + " Point B: (21.00153°, -100.38416°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 12.341859°", + " Longitude: -71.337119°", + "FINAL ANSWER: 12.341859, -71.337119" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -6.3084, + "lon": 106.1067, + "name": "Pandeglang" + }, + "point_b": { + "lat": 45.25167, + "lon": 19.83694, + "name": "Novi Sad" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 10.060649, + "lon": 89.93412 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-6.3084°, 106.1067°)", + " Point B: (45.25167°, 19.83694°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 10.060649°", + " Longitude: 89.934120°", + "FINAL ANSWER: 10.060649, 89.934120" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 12.28, + "lon": -14.22222, + "name": "Gabú" + }, + "point_b": { + "lat": -28.45917, + "lon": -52.82083, + "name": "Não-Me-Toque" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 1.88235, + "lon": -23.397403 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (12.28°, -14.22222°)", + " Point B: (-28.45917°, -52.82083°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 1.882350°", + " Longitude: -23.397403°", + "FINAL ANSWER: 1.882350, -23.397403" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 19.32932, + "lon": -98.1664, + "name": "Contla" + }, + "point_b": { + "lat": 48.64244, + "lon": 12.49283, + "name": "Dingolfing" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 54.290822, + "lon": -22.199871 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (19.32932°, -98.1664°)", + " Point B: (48.64244°, 12.49283°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 54.290822°", + " Longitude: -22.199871°", + "FINAL ANSWER: 54.290822, -22.199871" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 8.88902, + "lon": -64.2527, + "name": "El Tigre" + }, + "point_b": { + "lat": 35.9441, + "lon": 5.03107, + "name": "Râs el Oued" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 32.74202, + "lon": -15.2482 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (8.88902°, -64.2527°)", + " Point B: (35.9441°, 5.03107°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 32.742020°", + " Longitude: -15.248200°", + "FINAL ANSWER: 32.742020, -15.248200" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 42.10148, + "lon": -72.58981, + "name": "Springfield" + }, + "point_b": { + "lat": 22.53884, + "lon": 72.71984, + "name": "Sojītra" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 45.803267, + "lon": 55.950007 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (42.10148°, -72.58981°)", + " Point B: (22.53884°, 72.71984°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 45.803267°", + " Longitude: 55.950007°", + "FINAL ANSWER: 45.803267, 55.950007" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -31.89578, + "lon": 115.76431, + "name": "Scarborough" + }, + "point_b": { + "lat": 32.34153, + "lon": -90.32176, + "name": "Clinton" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -19.339246, + "lon": 157.611184 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-31.89578°, 115.76431°)", + " Point B: (32.34153°, -90.32176°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -19.339246°", + " Longitude: 157.611184°", + "FINAL ANSWER: -19.339246, 157.611184" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -21.93361, + "lon": -42.60861, + "name": "Carmo" + }, + "point_b": { + "lat": 50.09, + "lon": 19.09291, + "name": "Bieruń" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -2.937825, + "lon": -30.073383 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-21.93361°, -42.60861°)", + " Point B: (50.09°, 19.09291°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -2.937825°", + " Longitude: -30.073383°", + "FINAL ANSWER: -2.937825, -30.073383" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 34.41333, + "lon": -119.86097, + "name": "Isla Vista" + }, + "point_b": { + "lat": 27.44023, + "lon": 30.81712, + "name": "Al Qūşīyah" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 57.279975, + "lon": -95.756335 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (34.41333°, -119.86097°)", + " Point B: (27.44023°, 30.81712°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 57.279975°", + " Longitude: -95.756335°", + "FINAL ANSWER: 57.279975, -95.756335" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 51.11963, + "lon": 9.12475, + "name": "Bad Wildungen" + }, + "point_b": { + "lat": -25.34682, + "lon": -57.60647, + "name": "Lambaré" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 34.751753, + "lon": -15.3658 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (51.11963°, 9.12475°)", + " Point B: (-25.34682°, -57.60647°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 34.751753°", + " Longitude: -15.365800°", + "FINAL ANSWER: 34.751753, -15.365800" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 20.29879, + "lon": -76.24511, + "name": "Contramaestre" + }, + "point_b": { + "lat": -38.14458, + "lon": 145.12291, + "name": "Frankston" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -38.302925, + "lon": -169.814 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (20.29879°, -76.24511°)", + " Point B: (-38.14458°, 145.12291°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -38.302925°", + " Longitude: -169.814000°", + "FINAL ANSWER: -38.302925, -169.814000" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -12.80243, + "lon": 28.21323, + "name": "Kitwe" + }, + "point_b": { + "lat": 11.47197, + "lon": 49.87282, + "name": "Qandala" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -0.677292, + "lon": 39.070394 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-12.80243°, 28.21323°)", + " Point B: (11.47197°, 49.87282°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -0.677292°", + " Longitude: 39.070394°", + "FINAL ANSWER: -0.677292, 39.070394" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -37.68611, + "lon": 176.16667, + "name": "Tauranga" + }, + "point_b": { + "lat": 51.13128, + "lon": 4.57041, + "name": "Lier" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 1.612815, + "lon": 162.35547 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-37.68611°, 176.16667°)", + " Point B: (51.13128°, 4.57041°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 1.612815°", + " Longitude: 162.355470°", + "FINAL ANSWER: 1.612815, 162.355470" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 41.93415, + "lon": 25.55557, + "name": "Haskovo" + }, + "point_b": { + "lat": -2.14092, + "lon": -46.12387, + "name": "Centro Novo do Maranhão" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 23.940424, + "lon": -16.324524 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (41.93415°, 25.55557°)", + " Point B: (-2.14092°, -46.12387°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 23.940424°", + " Longitude: -16.324524°", + "FINAL ANSWER: 23.940424, -16.324524" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -27.16825, + "lon": -65.49892, + "name": "Monteros" + }, + "point_b": { + "lat": 52.80521, + "lon": -2.11636, + "name": "Stafford" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 35.285623, + "lon": -25.910568 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-27.16825°, -65.49892°)", + " Point B: (52.80521°, -2.11636°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 35.285623°", + " Longitude: -25.910568°", + "FINAL ANSWER: 35.285623, -25.910568" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -29.45986, + "lon": -60.21315, + "name": "Vera" + }, + "point_b": { + "lat": 48.88126, + "lon": 12.57385, + "name": "Straubing" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 32.10686, + "lon": -12.889653 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-29.45986°, -60.21315°)", + " Point B: (48.88126°, 12.57385°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 32.106860°", + " Longitude: -12.889653°", + "FINAL ANSWER: 32.106860, -12.889653" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 39.61332, + "lon": -105.01665, + "name": "Littleton" + }, + "point_b": { + "lat": 13.83576, + "lon": 100.46001, + "name": "Bang O" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 62.83389, + "lon": -137.884919 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (39.61332°, -105.01665°)", + " Point B: (13.83576°, 100.46001°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 62.833890°", + " Longitude: -137.884919°", + "FINAL ANSWER: 62.833890, -137.884919" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 39.16667, + "lon": 140.5, + "name": "Yuzawa" + }, + "point_b": { + "lat": 34.51667, + "lon": 135.75, + "name": "Yamato-Takada" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 38.022313, + "lon": 139.257139 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (39.16667°, 140.5°)", + " Point B: (34.51667°, 135.75°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 38.022313°", + " Longitude: 139.257139°", + "FINAL ANSWER: 38.022313, 139.257139" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 45.45008, + "lon": -73.28246, + "name": "Chambly" + }, + "point_b": { + "lat": 35.17959, + "lon": -80.64729, + "name": "Mint Hill" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 40.372922, + "lon": -77.246057 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (45.45008°, -73.28246°)", + " Point B: (35.17959°, -80.64729°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 40.372922°", + " Longitude: -77.246057°", + "FINAL ANSWER: 40.372922, -77.246057" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 54.76032, + "lon": -1.33649, + "name": "Peterlee" + }, + "point_b": { + "lat": 12.97389, + "lon": 123.99333, + "name": "Sorsogon" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 34.072134, + "lon": 110.200195 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (54.76032°, -1.33649°)", + " Point B: (12.97389°, 123.99333°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 34.072134°", + " Longitude: 110.200195°", + "FINAL ANSWER: 34.072134, 110.200195" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 16.43281, + "lon": 103.50658, + "name": "Kalasin" + }, + "point_b": { + "lat": 15.33805, + "lon": 38.93184, + "name": "Asmara" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 17.62166, + "lon": 54.882438 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (16.43281°, 103.50658°)", + " Point B: (15.33805°, 38.93184°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 17.621660°", + " Longitude: 54.882438°", + "FINAL ANSWER: 17.621660, 54.882438" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 36.06997, + "lon": 139.86705, + "name": "Bandō" + }, + "point_b": { + "lat": 51.53333, + "lon": -0.23333, + "name": "Willesden" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 69.294739, + "lon": 89.550371 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (36.06997°, 139.86705°)", + " Point B: (51.53333°, -0.23333°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 69.294739°", + " Longitude: 89.550371°", + "FINAL ANSWER: 69.294739, 89.550371" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 40.16557, + "lon": 44.29462, + "name": "Vagharshapat" + }, + "point_b": { + "lat": -3.39605, + "lon": 38.55609, + "name": "Voi" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 29.295459, + "lon": 42.494053 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (40.16557°, 44.29462°)", + " Point B: (-3.39605°, 38.55609°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 29.295459°", + " Longitude: 42.494053°", + "FINAL ANSWER: 29.295459, 42.494053" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -33.56839, + "lon": -70.80584, + "name": "Padre Hurtado" + }, + "point_b": { + "lat": 32.79211, + "lon": 4.49949, + "name": "Guerara" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -17.933366, + "lon": -50.095478 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-33.56839°, -70.80584°)", + " Point B: (32.79211°, 4.49949°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -17.933366°", + " Longitude: -50.095478°", + "FINAL ANSWER: -17.933366, -50.095478" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -33.2792, + "lon": 115.71504, + "name": "Australind" + }, + "point_b": { + "lat": -34.91119, + "lon": 138.70735, + "name": "Adelaide Hills" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -34.911768, + "lon": 132.893392 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-33.2792°, 115.71504°)", + " Point B: (-34.91119°, 138.70735°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -34.911768°", + " Longitude: 132.893392°", + "FINAL ANSWER: -34.911768, 132.893392" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 38.74761, + "lon": -77.08303, + "name": "Hybla Valley" + }, + "point_b": { + "lat": 60.72383, + "lon": 114.93447, + "name": "Lensk" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 78.004154, + "lon": -95.737043 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (38.74761°, -77.08303°)", + " Point B: (60.72383°, 114.93447°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 78.004154°", + " Longitude: -95.737043°", + "FINAL ANSWER: 78.004154, -95.737043" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -6.31056, + "lon": -35.47889, + "name": "Santo Antônio" + }, + "point_b": { + "lat": 30.61927, + "lon": 31.46165, + "name": "Al Qanāyāt" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 23.583892, + "lon": 12.262529 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-6.31056°, -35.47889°)", + " Point B: (30.61927°, 31.46165°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 23.583892°", + " Longitude: 12.262529°", + "FINAL ANSWER: 23.583892, 12.262529" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -0.11306, + "lon": 31.85389, + "name": "Lukaya" + }, + "point_b": { + "lat": 36.40937, + "lon": 5.94463, + "name": "Fedj M’Zala" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 9.281852, + "lon": 26.244026 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-0.11306°, 31.85389°)", + " Point B: (36.40937°, 5.94463°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 9.281852°", + " Longitude: 26.244026°", + "FINAL ANSWER: 9.281852, 26.244026" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 40.8351, + "lon": -73.13122, + "name": "Lake Ronkonkoma" + }, + "point_b": { + "lat": 51.55295, + "lon": -0.19157, + "name": "Kilburn" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 52.283607, + "lon": -40.79595 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (40.8351°, -73.13122°)", + " Point B: (51.55295°, -0.19157°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 52.283607°", + " Longitude: -40.795950°", + "FINAL ANSWER: 52.283607, -40.795950" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 29.70997, + "lon": 107.39391, + "name": "Fuling" + }, + "point_b": { + "lat": 47.17242, + "lon": 8.51745, + "name": "Zug" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 50.392601, + "lon": 66.061326 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (29.70997°, 107.39391°)", + " Point B: (47.17242°, 8.51745°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 50.392601°", + " Longitude: 66.061326°", + "FINAL ANSWER: 50.392601, 66.061326" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 24.65667, + "lon": -107.545, + "name": "Licenciado Benito Juárez" + }, + "point_b": { + "lat": 42.28314, + "lon": 22.69224, + "name": "Kyustendil" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 56.905526, + "lon": -54.889296 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (24.65667°, -107.545°)", + " Point B: (42.28314°, 22.69224°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 56.905526°", + " Longitude: -54.889296°", + "FINAL ANSWER: 56.905526, -54.889296" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -9.17307, + "lon": 33.54152, + "name": "Kiwira" + }, + "point_b": { + "lat": 32.54193, + "lon": 44.22469, + "name": "Al Hindīyah" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 11.733672, + "lon": 38.460993 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-9.17307°, 33.54152°)", + " Point B: (32.54193°, 44.22469°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 11.733672°", + " Longitude: 38.460993°", + "FINAL ANSWER: 11.733672, 38.460993" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 8.14911, + "lon": 4.72074, + "name": "Offa" + }, + "point_b": { + "lat": -17.83333, + "lon": 48.41667, + "name": "Ambatondrazaka" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 1.493174, + "lon": 15.452729 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (8.14911°, 4.72074°)", + " Point B: (-17.83333°, 48.41667°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 1.493174°", + " Longitude: 15.452729°", + "FINAL ANSWER: 1.493174, 15.452729" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -7.0496, + "lon": 109.1441, + "name": "Lebaksiu" + }, + "point_b": { + "lat": 2.81972, + "lon": -60.67333, + "name": "Boa Vista" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -13.070986, + "lon": -21.227924 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-7.0496°, 109.1441°)", + " Point B: (2.81972°, -60.67333°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -13.070986°", + " Longitude: -21.227924°", + "FINAL ANSWER: -13.070986, -21.227924" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 36.19611, + "lon": 118.465, + "name": "Jiushan" + }, + "point_b": { + "lat": 50.82928, + "lon": 6.90499, + "name": "Brühl" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 58.960771, + "lon": 72.846427 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (36.19611°, 118.465°)", + " Point B: (50.82928°, 6.90499°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 58.960771°", + " Longitude: 72.846427°", + "FINAL ANSWER: 58.960771, 72.846427" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -25.61692, + "lon": 27.99471, + "name": "Ga-Rankuwa" + }, + "point_b": { + "lat": -31.88822, + "lon": 115.87186, + "name": "Dianella" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -33.252211, + "lon": 47.748847 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-25.61692°, 27.99471°)", + " Point B: (-31.88822°, 115.87186°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -33.252211°", + " Longitude: 47.748847°", + "FINAL ANSWER: -33.252211, 47.748847" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 23.19014, + "lon": 94.06405, + "name": "Kalemyo" + }, + "point_b": { + "lat": -7.4289, + "lon": -79.50416, + "name": "San Pedro de Lloc" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 58.548555, + "lon": 65.548267 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (23.19014°, 94.06405°)", + " Point B: (-7.4289°, -79.50416°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 58.548555°", + " Longitude: 65.548267°", + "FINAL ANSWER: 58.548555, 65.548267" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 52.76588, + "lon": -0.88693, + "name": "Melton Mowbray" + }, + "point_b": { + "lat": 34.9072, + "lon": 48.4414, + "name": "Bahār" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 41.169056, + "lon": 39.005248 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (52.76588°, -0.88693°)", + " Point B: (34.9072°, 48.4414°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 41.169056°", + " Longitude: 39.005248°", + "FINAL ANSWER: 41.169056, 39.005248" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 34.99591, + "lon": -85.15023, + "name": "East Brainerd" + }, + "point_b": { + "lat": 26.72022, + "lon": 86.48258, + "name": "Lahān" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 55.755005, + "lon": 79.723337 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (34.99591°, -85.15023°)", + " Point B: (26.72022°, 86.48258°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 55.755005°", + " Longitude: 79.723337°", + "FINAL ANSWER: 55.755005, 79.723337" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 52.55035, + "lon": 13.39139, + "name": "Gesundbrunnen" + }, + "point_b": { + "lat": 12.15, + "lon": 27.35, + "name": "Ghubaysh" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 22.363083, + "lon": 24.875023 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (52.55035°, 13.39139°)", + " Point B: (12.15°, 27.35°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 22.363083°", + " Longitude: 24.875023°", + "FINAL ANSWER: 22.363083, 24.875023" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 41.45139, + "lon": 31.79305, + "name": "Zonguldak" + }, + "point_b": { + "lat": 41.4349, + "lon": 2.17883, + "name": "Porta" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 42.405031, + "lon": 16.984016 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (41.45139°, 31.79305°)", + " Point B: (41.4349°, 2.17883°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 42.405031°", + " Longitude: 16.984016°", + "FINAL ANSWER: 42.405031, 16.984016" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 23.45944, + "lon": 120.33222, + "name": "Taibao" + }, + "point_b": { + "lat": 17.46982, + "lon": 78.12574, + "name": "Singāpur" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 21.80127, + "lon": 98.797274 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (23.45944°, 120.33222°)", + " Point B: (17.46982°, 78.12574°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 21.801270°", + " Longitude: 98.797274°", + "FINAL ANSWER: 21.801270, 98.797274" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -0.87944, + "lon": 30.26417, + "name": "Ntungamo" + }, + "point_b": { + "lat": -12.55708, + "lon": 16.33805, + "name": "Chinguar" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -9.680349, + "lon": 19.8921 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-0.87944°, 30.26417°)", + " Point B: (-12.55708°, 16.33805°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -9.680349°", + " Longitude: 19.892100°", + "FINAL ANSWER: -9.680349, 19.892100" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 39.82894, + "lon": -84.89024, + "name": "Richmond" + }, + "point_b": { + "lat": 35.68449, + "lon": 139.75056, + "name": "Chiyoda" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 56.988604, + "lon": -109.653268 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (39.82894°, -84.89024°)", + " Point B: (35.68449°, 139.75056°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 56.988604°", + " Longitude: -109.653268°", + "FINAL ANSWER: 56.988604, -109.653268" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -16.4332, + "lon": 179.36451, + "name": "Labasa" + }, + "point_b": { + "lat": 10.36556, + "lon": -66.13391, + "name": "Mamporal" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -12.567255, + "lon": -150.856887 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-16.4332°, 179.36451°)", + " Point B: (10.36556°, -66.13391°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -12.567255°", + " Longitude: -150.856887°", + "FINAL ANSWER: -12.567255, -150.856887" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 31.12586, + "lon": 75.47508, + "name": "Nakodar" + }, + "point_b": { + "lat": -1.45583, + "lon": -48.50444, + "name": "Belém" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 29.166317, + "lon": 5.205926 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (31.12586°, 75.47508°)", + " Point B: (-1.45583°, -48.50444°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 29.166317°", + " Longitude: 5.205926°", + "FINAL ANSWER: 29.166317, 5.205926" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 41.42973, + "lon": -97.36838, + "name": "Columbus" + }, + "point_b": { + "lat": -14.63126, + "lon": -69.44638, + "name": "La Rinconada" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 13.785149, + "lon": -81.601462 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (41.42973°, -97.36838°)", + " Point B: (-14.63126°, -69.44638°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 13.785149°", + " Longitude: -81.601462°", + "FINAL ANSWER: 13.785149, -81.601462" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -10.59333, + "lon": -36.94028, + "name": "Japaratuba" + }, + "point_b": { + "lat": -37.87822, + "lon": 175.4402, + "name": "Cambridge" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -36.291224, + "lon": -55.530413 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-10.59333°, -36.94028°)", + " Point B: (-37.87822°, 175.4402°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -36.291224°", + " Longitude: -55.530413°", + "FINAL ANSWER: -36.291224, -55.530413" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 32.93333, + "lon": 132.73333, + "name": "Sukumo" + }, + "point_b": { + "lat": 41.27954, + "lon": -72.8151, + "name": "Branford" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 73.257242, + "lon": -163.723247 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (32.93333°, 132.73333°)", + " Point B: (41.27954°, -72.8151°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 73.257242°", + " Longitude: -163.723247°", + "FINAL ANSWER: 73.257242, -163.723247" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 18.57677, + "lon": -72.22625, + "name": "Croix-des-Bouquets" + }, + "point_b": { + "lat": 3.86512, + "lon": 32.48212, + "name": "Pajok" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 12.043914, + "lon": 7.901058 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (18.57677°, -72.22625°)", + " Point B: (3.86512°, 32.48212°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 12.043914°", + " Longitude: 7.901058°", + "FINAL ANSWER: 12.043914, 7.901058" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 41.63976, + "lon": 2.35739, + "name": "Cardedeu" + }, + "point_b": { + "lat": 11.69917, + "lon": 0.50611, + "name": "Natiaboani" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 26.67241, + "lon": 1.30742 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (41.63976°, 2.35739°)", + " Point B: (11.69917°, 0.50611°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 26.672410°", + " Longitude: 1.307420°", + "FINAL ANSWER: 26.672410, 1.307420" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 10.83333, + "lon": 38.26667, + "name": "Mertule Maryam" + }, + "point_b": { + "lat": -25.67361, + "lon": -48.51111, + "name": "Pontal do Paraná" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 0.363748, + "lon": 17.711164 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (10.83333°, 38.26667°)", + " Point B: (-25.67361°, -48.51111°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 0.363748°", + " Longitude: 17.711164°", + "FINAL ANSWER: 0.363748, 17.711164" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 55.62868, + "lon": 37.8443, + "name": "Dzerzhinskiy" + }, + "point_b": { + "lat": -6.75472, + "lon": -51.08389, + "name": "Ourilândia do Norte" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 47.467418, + "lon": 1.433352 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (55.62868°, 37.8443°)", + " Point B: (-6.75472°, -51.08389°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 47.467418°", + " Longitude: 1.433352°", + "FINAL ANSWER: 47.467418, 1.433352" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 21.56128, + "lon": 74.21238, + "name": "Taloda" + }, + "point_b": { + "lat": -17.91796, + "lon": 19.77314, + "name": "Rundu" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 2.048295, + "lon": 46.656427 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (21.56128°, 74.21238°)", + " Point B: (-17.91796°, 19.77314°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 2.048295°", + " Longitude: 46.656427°", + "FINAL ANSWER: 2.048295, 46.656427" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 39.56667, + "lon": -0.33333, + "name": "Massamagrell" + }, + "point_b": { + "lat": 7.75537, + "lon": -0.98085, + "name": "Atebubu" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 15.708406, + "lon": -0.844749 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (39.56667°, -0.33333°)", + " Point B: (7.75537°, -0.98085°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 15.708406°", + " Longitude: -0.844749°", + "FINAL ANSWER: 15.708406, -0.844749" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -16.39899, + "lon": -71.53747, + "name": "Arequipa" + }, + "point_b": { + "lat": -29.33528, + "lon": -49.72694, + "name": "Torres" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -23.242491, + "lon": -61.160001 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-16.39899°, -71.53747°)", + " Point B: (-29.33528°, -49.72694°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -23.242491°", + " Longitude: -61.160001°", + "FINAL ANSWER: -23.242491, -61.160001" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 35.40611, + "lon": 129.16861, + "name": "Ungsang" + }, + "point_b": { + "lat": 2.67375, + "lon": 101.8721, + "name": "Bandar Sri Sendayan" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 27.678696, + "lon": 121.091089 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (35.40611°, 129.16861°)", + " Point B: (2.67375°, 101.8721°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 27.678696°", + " Longitude: 121.091089°", + "FINAL ANSWER: 27.678696, 121.091089" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 10.474, + "lon": -66.54241, + "name": "Guatire" + }, + "point_b": { + "lat": -6.80306, + "lon": -35.08056, + "name": "Rio Tinto" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 1.906838, + "lon": -50.732914 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (10.474°, -66.54241°)", + " Point B: (-6.80306°, -35.08056°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 1.906838°", + " Longitude: -50.732914°", + "FINAL ANSWER: 1.906838, -50.732914" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 37.11954, + "lon": 140.26211, + "name": "Shirakawa" + }, + "point_b": { + "lat": -5.91556, + "lon": -35.26278, + "name": "Parnamirim" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 67.313197, + "lon": -17.960686 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (37.11954°, 140.26211°)", + " Point B: (-5.91556°, -35.26278°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 67.313197°", + " Longitude: -17.960686°", + "FINAL ANSWER: 67.313197, -17.960686" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 39.13705, + "lon": -76.6983, + "name": "Severn" + }, + "point_b": { + "lat": -0.9516, + "lon": 122.7875, + "name": "Luwuk" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 58.746547, + "lon": 166.710249 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (39.13705°, -76.6983°)", + " Point B: (-0.9516°, 122.7875°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 58.746547°", + " Longitude: 166.710249°", + "FINAL ANSWER: 58.746547, 166.710249" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -27.1518, + "lon": -48.48941, + "name": "Bombinhas" + }, + "point_b": { + "lat": 41.4349, + "lon": 2.17883, + "name": "Porta" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 25.292423, + "lon": -13.597065 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-27.1518°, -48.48941°)", + " Point B: (41.4349°, 2.17883°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 25.292423°", + " Longitude: -13.597065°", + "FINAL ANSWER: 25.292423, -13.597065" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -20.88231, + "lon": 55.4504, + "name": "Saint-Denis" + }, + "point_b": { + "lat": -10.8258, + "lon": -65.3581, + "name": "Guayaramerín" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -29.875952, + "lon": -7.47283 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-20.88231°, 55.4504°)", + " Point B: (-10.8258°, -65.3581°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -29.875952°", + " Longitude: -7.472830°", + "FINAL ANSWER: -29.875952, -7.472830" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -28.55104, + "lon": -56.04125, + "name": "Santo Tomé" + }, + "point_b": { + "lat": -21.76417, + "lon": -43.35028, + "name": "Juiz de Fora" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -23.559113, + "lon": -46.392895 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-28.55104°, -56.04125°)", + " Point B: (-21.76417°, -43.35028°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -23.559113°", + " Longitude: -46.392895°", + "FINAL ANSWER: -23.559113, -46.392895" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 38.66311, + "lon": -90.57707, + "name": "Chesterfield" + }, + "point_b": { + "lat": 26.01856, + "lon": 89.98564, + "name": "Dhubri" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 83.662456, + "lon": 93.708435 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (38.66311°, -90.57707°)", + " Point B: (26.01856°, 89.98564°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 83.662456°", + " Longitude: 93.708435°", + "FINAL ANSWER: 83.662456, 93.708435" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 51.76338, + "lon": 7.8887, + "name": "Ahlen" + }, + "point_b": { + "lat": -30.29626, + "lon": 153.11351, + "name": "Coffs Harbour" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 52.618165, + "lon": 69.600646 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (51.76338°, 7.8887°)", + " Point B: (-30.29626°, 153.11351°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 52.618165°", + " Longitude: 69.600646°", + "FINAL ANSWER: 52.618165, 69.600646" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 42.29732, + "lon": -71.43701, + "name": "Framingham Center" + }, + "point_b": { + "lat": -21.00961, + "lon": 55.27134, + "name": "Saint-Paul" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 22.210941, + "lon": 4.91938 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (42.29732°, -71.43701°)", + " Point B: (-21.00961°, 55.27134°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 22.210941°", + " Longitude: 4.919380°", + "FINAL ANSWER: 22.210941, 4.919380" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 30.90316, + "lon": 29.55276, + "name": "Burj al ‘Arab" + }, + "point_b": { + "lat": 53.4115, + "lon": -2.83935, + "name": "Huyton" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 43.274657, + "lon": 16.352163 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (30.90316°, 29.55276°)", + " Point B: (53.4115°, -2.83935°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 43.274657°", + " Longitude: 16.352163°", + "FINAL ANSWER: 43.274657, 16.352163" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -4.23222, + "lon": -39.1925, + "name": "Caridade" + }, + "point_b": { + "lat": 5.31667, + "lon": 39.58333, + "name": "Negēlē" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -1.874712, + "lon": -19.489932 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-4.23222°, -39.1925°)", + " Point B: (5.31667°, 39.58333°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -1.874712°", + " Longitude: -19.489932°", + "FINAL ANSWER: -1.874712, -19.489932" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 53.44253, + "lon": -2.42323, + "name": "Irlam" + }, + "point_b": { + "lat": -12.1201, + "lon": -58.00274, + "name": "Brasnorte" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 39.448941, + "lon": -23.84476 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (53.44253°, -2.42323°)", + " Point B: (-12.1201°, -58.00274°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 39.448941°", + " Longitude: -23.844760°", + "FINAL ANSWER: 39.448941, -23.844760" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 35.92472, + "lon": 6.69528, + "name": "Aïn Kercha" + }, + "point_b": { + "lat": 41.74753, + "lon": -87.71116, + "name": "Ashburn" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 45.06926, + "lon": -12.981387 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (35.92472°, 6.69528°)", + " Point B: (41.74753°, -87.71116°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 45.069260°", + " Longitude: -12.981387°", + "FINAL ANSWER: 45.069260, -12.981387" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 25.93315, + "lon": -80.16255, + "name": "North Miami Beach" + }, + "point_b": { + "lat": 27.23517, + "lon": 94.10357, + "name": "North Lakhimpur" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 84.255815, + "lon": 0.492766 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (25.93315°, -80.16255°)", + " Point B: (27.23517°, 94.10357°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 84.255815°", + " Longitude: 0.492766°", + "FINAL ANSWER: 84.255815, 0.492766" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 8.74921, + "lon": 4.13113, + "name": "Igbeti" + }, + "point_b": { + "lat": 41.72449, + "lon": -81.24566, + "name": "Painesville" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 32.456483, + "lon": -31.224542 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (8.74921°, 4.13113°)", + " Point B: (41.72449°, -81.24566°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 32.456483°", + " Longitude: -31.224542°", + "FINAL ANSWER: 32.456483, -31.224542" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -28.28389, + "lon": -52.78639, + "name": "Carazinho" + }, + "point_b": { + "lat": 47.42977, + "lon": 19.21592, + "name": "Pestlőrinc" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -8.578009, + "lon": -36.676949 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-28.28389°, -52.78639°)", + " Point B: (47.42977°, 19.21592°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -8.578009°", + " Longitude: -36.676949°", + "FINAL ANSWER: -8.578009, -36.676949" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -17.63185, + "lon": -71.34108, + "name": "Ilo" + }, + "point_b": { + "lat": 14.064, + "lon": -3.07539, + "name": "Koro" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 6.221056, + "lon": -20.228741 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-17.63185°, -71.34108°)", + " Point B: (14.064°, -3.07539°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 6.221056°", + " Longitude: -20.228741°", + "FINAL ANSWER: 6.221056, -20.228741" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -19.33018, + "lon": 48.97791, + "name": "Vatomandry" + }, + "point_b": { + "lat": 41.4349, + "lon": 2.17883, + "name": "Porta" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -3.724287, + "lon": 38.509969 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-19.33018°, 48.97791°)", + " Point B: (41.4349°, 2.17883°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -3.724287°", + " Longitude: 38.509969°", + "FINAL ANSWER: -3.724287, 38.509969" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 40.73542, + "lon": 8.56771, + "name": "Monte Rosello" + }, + "point_b": { + "lat": 32.57286, + "lon": -6.01947, + "name": "El Ksiba" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 38.868966, + "lon": 4.622013 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (40.73542°, 8.56771°)", + " Point B: (32.57286°, -6.01947°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 38.868966°", + " Longitude: 4.622013°", + "FINAL ANSWER: 38.868966, 4.622013" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -17.39799, + "lon": -66.03825, + "name": "Sacaba" + }, + "point_b": { + "lat": 22.84412, + "lon": 82.19823, + "name": "Pasān" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 9.841719, + "lon": 4.575264 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-17.39799°, -66.03825°)", + " Point B: (22.84412°, 82.19823°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 9.841719°", + " Longitude: 4.575264°", + "FINAL ANSWER: 9.841719, 4.575264" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 33.35608, + "lon": 6.86319, + "name": "El Oued" + }, + "point_b": { + "lat": 52.02694, + "lon": -0.49567, + "name": "Ampthill" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 47.407386, + "lon": 1.810411 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (33.35608°, 6.86319°)", + " Point B: (52.02694°, -0.49567°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 47.407386°", + " Longitude: 1.810411°", + "FINAL ANSWER: 47.407386, 1.810411" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 51.88056, + "lon": 45.00609, + "name": "Atkarsk" + }, + "point_b": { + "lat": 51.80949, + "lon": 10.33821, + "name": "Clausthal-Zellerfeld" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 52.787171, + "lon": 18.867084 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (51.88056°, 45.00609°)", + " Point B: (51.80949°, 10.33821°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 52.787171°", + " Longitude: 18.867084°", + "FINAL ANSWER: 52.787171, 18.867084" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -0.50397, + "lon": 36.31845, + "name": "Gilgil" + }, + "point_b": { + "lat": 20.85829, + "lon": 92.29773, + "name": "Teknāf" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 16.67738, + "lon": 77.435036 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-0.50397°, 36.31845°)", + " Point B: (20.85829°, 92.29773°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 16.677380°", + " Longitude: 77.435036°", + "FINAL ANSWER: 16.677380, 77.435036" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 50.75104, + "lon": 33.47471, + "name": "Romny" + }, + "point_b": { + "lat": 58.53706, + "lon": 15.03649, + "name": "Motala" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 56.866389, + "lon": 20.331382 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (50.75104°, 33.47471°)", + " Point B: (58.53706°, 15.03649°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 56.866389°", + " Longitude: 20.331382°", + "FINAL ANSWER: 56.866389, 20.331382" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 11.33333, + "lon": 27.8, + "name": "Babanūsah" + }, + "point_b": { + "lat": 32.81612, + "lon": 73.88697, + "name": "Kharian" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 23.772214, + "lon": 48.969174 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (11.33333°, 27.8°)", + " Point B: (32.81612°, 73.88697°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 23.772214°", + " Longitude: 48.969174°", + "FINAL ANSWER: 23.772214, 48.969174" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 40.42378, + "lon": -3.56129, + "name": "Coslada" + }, + "point_b": { + "lat": 66.49897, + "lon": 25.68867, + "name": "Rovaniemi" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 54.269683, + "lon": 6.401875 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (40.42378°, -3.56129°)", + " Point B: (66.49897°, 25.68867°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 54.269683°", + " Longitude: 6.401875°", + "FINAL ANSWER: 54.269683, 6.401875" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 45.51314, + "lon": 9.14343, + "name": "Quarto Oggiaro" + }, + "point_b": { + "lat": -0.75, + "lon": 29.7, + "name": "Kihihi" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 34.252346, + "lon": 16.026167 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (45.51314°, 9.14343°)", + " Point B: (-0.75°, 29.7°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 34.252346°", + " Longitude: 16.026167°", + "FINAL ANSWER: 34.252346, 16.026167" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -37.57742, + "lon": 144.72607, + "name": "Sunbury" + }, + "point_b": { + "lat": 45.25008, + "lon": -74.13253, + "name": "Salaberry-de-Valleyfield" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 34.80728, + "lon": -122.038558 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-37.57742°, 144.72607°)", + " Point B: (45.25008°, -74.13253°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 34.807280°", + " Longitude: -122.038558°", + "FINAL ANSWER: 34.807280, -122.038558" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 30.10778, + "lon": 78.29255, + "name": "Rishīkesh" + }, + "point_b": { + "lat": 45.53792, + "lon": 9.18921, + "name": "Bresso" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 43.231945, + "lon": 47.883082 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (30.10778°, 78.29255°)", + " Point B: (45.53792°, 9.18921°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 43.231945°", + " Longitude: 47.883082°", + "FINAL ANSWER: 43.231945, 47.883082" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 36.72016, + "lon": -4.42034, + "name": "Málaga" + }, + "point_b": { + "lat": -37.87822, + "lon": 175.4402, + "name": "Cambridge" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -7.842625, + "lon": -0.567182 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (36.72016°, -4.42034°)", + " Point B: (-37.87822°, 175.4402°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -7.842625°", + " Longitude: -0.567182°", + "FINAL ANSWER: -7.842625, -0.567182" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 30.58333, + "lon": 114.26667, + "name": "Wuhan" + }, + "point_b": { + "lat": 20.30734, + "lon": -89.41809, + "name": "Oxkutzkab" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 47.459981, + "lon": -108.037473 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (30.58333°, 114.26667°)", + " Point B: (20.30734°, -89.41809°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 47.459981°", + " Longitude: -108.037473°", + "FINAL ANSWER: 47.459981, -108.037473" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -11.66278, + "lon": 39.55056, + "name": "Mueda" + }, + "point_b": { + "lat": 35.29778, + "lon": 126.78444, + "name": "Jangseong" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 2.331177, + "lon": 58.693597 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-11.66278°, 39.55056°)", + " Point B: (35.29778°, 126.78444°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 2.331177°", + " Longitude: 58.693597°", + "FINAL ANSWER: 2.331177, 58.693597" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 54.90973, + "lon": 64.4319, + "name": "Kurtamysh" + }, + "point_b": { + "lat": 33.37362, + "lon": -7.99462, + "name": "Bir Jdid" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 50.005882, + "lon": 20.521809 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (54.90973°, 64.4319°)", + " Point B: (33.37362°, -7.99462°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 50.005882°", + " Longitude: 20.521809°", + "FINAL ANSWER: 50.005882, 20.521809" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 41.5361, + "lon": -8.78201, + "name": "Esposende" + }, + "point_b": { + "lat": 39.3895, + "lon": 140.05813, + "name": "Yurihonjō" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 72.494722, + "lon": 68.918178 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (41.5361°, -8.78201°)", + " Point B: (39.3895°, 140.05813°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 72.494722°", + " Longitude: 68.918178°", + "FINAL ANSWER: 72.494722, 68.918178" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -36.9482, + "lon": 174.87019, + "name": "Otara" + }, + "point_b": { + "lat": 2.33468, + "lon": 37.99086, + "name": "Marsabit" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -20.378564, + "lon": 60.763069 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-36.9482°, 174.87019°)", + " Point B: (2.33468°, 37.99086°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -20.378564°", + " Longitude: 60.763069°", + "FINAL ANSWER: -20.378564, 60.763069" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 25.74167, + "lon": -100.30222, + "name": "San Nicolás de los Garza" + }, + "point_b": { + "lat": 39.20144, + "lon": -85.92138, + "name": "Columbus" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 36.000495, + "lon": -89.948021 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (25.74167°, -100.30222°)", + " Point B: (39.20144°, -85.92138°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 36.000495°", + " Longitude: -89.948021°", + "FINAL ANSWER: 36.000495, -89.948021" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 51.35478, + "lon": 11.98923, + "name": "Merseburg" + }, + "point_b": { + "lat": -34.02262, + "lon": 20.44171, + "name": "Swellendam" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 8.688887, + "lon": 16.810693 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (51.35478°, 11.98923°)", + " Point B: (-34.02262°, 20.44171°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 8.688887°", + " Longitude: 16.810693°", + "FINAL ANSWER: 8.688887, 16.810693" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 45.46005, + "lon": -73.57058, + "name": "Verdun" + }, + "point_b": { + "lat": 60.23355, + "lon": 25.09947, + "name": "Mellunkylä" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 55.8037, + "lon": -58.84933 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (45.46005°, -73.57058°)", + " Point B: (60.23355°, 25.09947°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 55.803700°", + " Longitude: -58.849330°", + "FINAL ANSWER: 55.803700, -58.849330" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 12.43527, + "lon": -86.87862, + "name": "León" + }, + "point_b": { + "lat": -15.50819, + "lon": 27.92441, + "name": "Nampundwe" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -10.46715, + "lon": -1.644494 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (12.43527°, -86.87862°)", + " Point B: (-15.50819°, 27.92441°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -10.467150°", + " Longitude: -1.644494°", + "FINAL ANSWER: -10.467150, -1.644494" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 43.8317, + "lon": 23.23793, + "name": "Lom" + }, + "point_b": { + "lat": -2.5964, + "lon": 140.6324, + "name": "Abepura" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 45.700535, + "lon": 62.736762 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (43.8317°, 23.23793°)", + " Point B: (-2.5964°, 140.6324°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 45.700535°", + " Longitude: 62.736762°", + "FINAL ANSWER: 45.700535, 62.736762" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -4.78944, + "lon": -40.06333, + "name": "Monsenhor Tabosa" + }, + "point_b": { + "lat": 41.63065, + "lon": 15.91876, + "name": "Manfredonia" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 20.61103, + "lon": -16.413191 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-4.78944°, -40.06333°)", + " Point B: (41.63065°, 15.91876°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 20.611030°", + " Longitude: -16.413191°", + "FINAL ANSWER: 20.611030, -16.413191" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -2.2933, + "lon": 29.1877, + "name": "Macuba" + }, + "point_b": { + "lat": 38.67902, + "lon": -9.1569, + "name": "Almada" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 29.356105, + "lon": 2.69058 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-2.2933°, 29.1877°)", + " Point B: (38.67902°, -9.1569°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 29.356105°", + " Longitude: 2.690580°", + "FINAL ANSWER: 29.356105, 2.690580" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -14.81909, + "lon": 14.53504, + "name": "Quipungo" + }, + "point_b": { + "lat": -25.97972, + "lon": -52.56778, + "name": "Coronel Vivida" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -24.041738, + "lon": -17.636022 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-14.81909°, 14.53504°)", + " Point B: (-25.97972°, -52.56778°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -24.041738°", + " Longitude: -17.636022°", + "FINAL ANSWER: -24.041738, -17.636022" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 30.08963, + "lon": 105.85665, + "name": "Tianjia" + }, + "point_b": { + "lat": 58.23544, + "lon": 92.48351, + "name": "Lesosibirsk" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 51.362947, + "lon": 97.277688 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (30.08963°, 105.85665°)", + " Point B: (58.23544°, 92.48351°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 51.362947°", + " Longitude: 97.277688°", + "FINAL ANSWER: 51.362947, 97.277688" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 14.6228, + "lon": 121.0897, + "name": "Calumpang" + }, + "point_b": { + "lat": 48.13392, + "lon": 11.3765, + "name": "Germering" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 45.713288, + "lon": 80.852551 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (14.6228°, 121.0897°)", + " Point B: (48.13392°, 11.3765°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 45.713288°", + " Longitude: 80.852551°", + "FINAL ANSWER: 45.713288, 80.852551" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 6.54584, + "lon": -0.76264, + "name": "Nkawkaw" + }, + "point_b": { + "lat": 45.01242, + "lon": 8.64379, + "name": "Valenza" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 35.463289, + "lon": 5.564728 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (6.54584°, -0.76264°)", + " Point B: (45.01242°, 8.64379°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 35.463289°", + " Longitude: 5.564728°", + "FINAL ANSWER: 35.463289, 5.564728" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -10.70833, + "lon": -38.18333, + "name": "Poço Verde" + }, + "point_b": { + "lat": -10.71667, + "lon": 38.8, + "name": "Masasi" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -12.843895, + "lon": -19.046033 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-10.70833°, -38.18333°)", + " Point B: (-10.71667°, 38.8°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -12.843895°", + " Longitude: -19.046033°", + "FINAL ANSWER: -12.843895, -19.046033" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 17.67152, + "lon": 75.91044, + "name": "Sholapur" + }, + "point_b": { + "lat": 52.54608, + "lon": 13.5013, + "name": "Alt-Hohenschönhausen" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 28.929714, + "lon": 65.346221 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (17.67152°, 75.91044°)", + " Point B: (52.54608°, 13.5013°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 28.929714°", + " Longitude: 65.346221°", + "FINAL ANSWER: 28.929714, 65.346221" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 4.91667, + "lon": -52.26667, + "name": "Rémire-Montjoly" + }, + "point_b": { + "lat": 14.97089, + "lon": 8.88786, + "name": "Tanout" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 11.509401, + "lon": -22.211476 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (4.91667°, -52.26667°)", + " Point B: (14.97089°, 8.88786°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 11.509401°", + " Longitude: -22.211476°", + "FINAL ANSWER: 11.509401, -22.211476" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 25.23831, + "lon": 86.73559, + "name": "Sultānganj" + }, + "point_b": { + "lat": -37.8, + "lon": 144.96667, + "name": "Carlton" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -23.250777, + "lon": 127.515719 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (25.23831°, 86.73559°)", + " Point B: (-37.8°, 144.96667°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -23.250777°", + " Longitude: 127.515719°", + "FINAL ANSWER: -23.250777, 127.515719" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -37.74981, + "lon": 144.9109, + "name": "Essendon" + }, + "point_b": { + "lat": 8.33015, + "lon": -71.75277, + "name": "Tovar" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -38.343735, + "lon": -124.798186 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-37.74981°, 144.9109°)", + " Point B: (8.33015°, -71.75277°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -38.343735°", + " Longitude: -124.798186°", + "FINAL ANSWER: -38.343735, -124.798186" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 18.80748, + "lon": -69.78431, + "name": "Monte Plata" + }, + "point_b": { + "lat": 44.88448, + "lon": 40.58893, + "name": "Kurganinsk" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 46.814487, + "lon": -26.284858 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (18.80748°, -69.78431°)", + " Point B: (44.88448°, 40.58893°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 46.814487°", + " Longitude: -26.284858°", + "FINAL ANSWER: 46.814487, -26.284858" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 34.76615, + "lon": 135.62759, + "name": "Neyagawa" + }, + "point_b": { + "lat": 11.78442, + "lon": 9.6069, + "name": "Kiyawa" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 30.061618, + "lon": 32.077198 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (34.76615°, 135.62759°)", + " Point B: (11.78442°, 9.6069°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 30.061618°", + " Longitude: 32.077198°", + "FINAL ANSWER: 30.061618, 32.077198" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 31.46116, + "lon": 74.10091, + "name": "Sharqpur Sharif" + }, + "point_b": { + "lat": 12.98456, + "lon": 80.1747, + "name": "Meenambakkam" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 22.250941, + "lon": 77.339802 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (31.46116°, 74.10091°)", + " Point B: (12.98456°, 80.1747°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 22.250941°", + " Longitude: 77.339802°", + "FINAL ANSWER: 22.250941, 77.339802" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 43.09722, + "lon": -89.50429, + "name": "Middleton" + }, + "point_b": { + "lat": 36.44788, + "lon": 8.4413, + "name": "Ghardimaou" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 46.379816, + "lon": -11.321871 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (43.09722°, -89.50429°)", + " Point B: (36.44788°, 8.4413°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 46.379816°", + " Longitude: -11.321871°", + "FINAL ANSWER: 46.379816, -11.321871" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 53.33333, + "lon": 8.48333, + "name": "Brake (Unterweser)" + }, + "point_b": { + "lat": 7.16008, + "lon": -6.30642, + "name": "Bédiala" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 30.442351, + "lon": -0.75921 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (53.33333°, 8.48333°)", + " Point B: (7.16008°, -6.30642°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 30.442351°", + " Longitude: -0.759210°", + "FINAL ANSWER: 30.442351, -0.759210" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 51.46839, + "lon": -0.36092, + "name": "Hounslow" + }, + "point_b": { + "lat": 37.59577, + "lon": -122.01913, + "name": "Union City" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 52.751384, + "lon": -104.71625 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (51.46839°, -0.36092°)", + " Point B: (37.59577°, -122.01913°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 52.751384°", + " Longitude: -104.716250°", + "FINAL ANSWER: 52.751384, -104.716250" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -1.25367, + "lon": 34.47596, + "name": "Sirari" + }, + "point_b": { + "lat": 12.28, + "lon": -14.22222, + "name": "Gabú" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 6.047544, + "lon": 10.423828 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-1.25367°, 34.47596°)", + " Point B: (12.28°, -14.22222°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 6.047544°", + " Longitude: 10.423828°", + "FINAL ANSWER: 6.047544, 10.423828" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 37.18447, + "lon": 128.46821, + "name": "Neietsu" + }, + "point_b": { + "lat": 9.15212, + "lon": 76.52338, + "name": "Krishnāpuram" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 17.620361, + "lon": 87.501536 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (37.18447°, 128.46821°)", + " Point B: (9.15212°, 76.52338°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 17.620361°", + " Longitude: 87.501536°", + "FINAL ANSWER: 17.620361, 87.501536" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 12.81028, + "lon": -16.22639, + "name": "Bignona" + }, + "point_b": { + "lat": 19.26755, + "lon": -99.61925, + "name": "San Francisco Cuaxusco" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 21.055297, + "lon": -57.095136 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (12.81028°, -16.22639°)", + " Point B: (19.26755°, -99.61925°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 21.055297°", + " Longitude: -57.095136°", + "FINAL ANSWER: 21.055297, -57.095136" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 39.29123, + "lon": 8.99879, + "name": "Assemini" + }, + "point_b": { + "lat": -20.07028, + "lon": -44.30167, + "name": "Igarapé" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 25.731821, + "lon": -7.498932 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (39.29123°, 8.99879°)", + " Point B: (-20.07028°, -44.30167°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 25.731821°", + " Longitude: -7.498932°", + "FINAL ANSWER: 25.731821, -7.498932" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 16.22564, + "lon": -61.38098, + "name": "Sainte-Anne" + }, + "point_b": { + "lat": 30.4427, + "lon": -97.77501, + "name": "Jollyville" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 24.418703, + "lon": -78.564878 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (16.22564°, -61.38098°)", + " Point B: (30.4427°, -97.77501°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 24.418703°", + " Longitude: -78.564878°", + "FINAL ANSWER: 24.418703, -78.564878" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -1.52361, + "lon": -46.8975, + "name": "Santa Luzia do Pará" + }, + "point_b": { + "lat": 35.36395, + "lon": -0.51279, + "name": "’Aïn el Berd" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 18.295982, + "lon": -26.194084 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-1.52361°, -46.8975°)", + " Point B: (35.36395°, -0.51279°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 18.295982°", + " Longitude: -26.194084°", + "FINAL ANSWER: 18.295982, -26.194084" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 38.77144, + "lon": -90.37095, + "name": "Hazelwood" + }, + "point_b": { + "lat": 43.88917, + "lon": 8.03933, + "name": "Imperia" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 53.362817, + "lon": -43.773349 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (38.77144°, -90.37095°)", + " Point B: (43.88917°, 8.03933°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 53.362817°", + " Longitude: -43.773349°", + "FINAL ANSWER: 53.362817, -43.773349" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 44.55, + "lon": 23.51667, + "name": "Filiaşi" + }, + "point_b": { + "lat": 1.67817, + "lon": -75.28466, + "name": "El Doncello" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 18.162303, + "lon": -57.833003 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (44.55°, 23.51667°)", + " Point B: (1.67817°, -75.28466°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 18.162303°", + " Longitude: -57.833003°", + "FINAL ANSWER: 18.162303, -57.833003" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 30.07994, + "lon": -95.41716, + "name": "Spring" + }, + "point_b": { + "lat": 58.23544, + "lon": 92.48351, + "name": "Lesosibirsk" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 75.423655, + "lon": -107.299805 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (30.07994°, -95.41716°)", + " Point B: (58.23544°, 92.48351°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 75.423655°", + " Longitude: -107.299805°", + "FINAL ANSWER: 75.423655, -107.299805" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 31.22452, + "lon": 75.77387, + "name": "Phagwāra" + }, + "point_b": { + "lat": 36.56041, + "lon": 4.85454, + "name": "Feraoun" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 36.592671, + "lon": 59.587935 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (31.22452°, 75.77387°)", + " Point B: (36.56041°, 4.85454°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 36.592671°", + " Longitude: 59.587935°", + "FINAL ANSWER: 36.592671, 59.587935" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 26.17035, + "lon": -98.05195, + "name": "Donna" + }, + "point_b": { + "lat": 48.84085, + "lon": 12.96068, + "name": "Deggendorf" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 41.483261, + "lon": -81.01446 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (26.17035°, -98.05195°)", + " Point B: (48.84085°, 12.96068°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 41.483261°", + " Longitude: -81.014460°", + "FINAL ANSWER: 41.483261, -81.014460" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 37.02534, + "lon": 138.25561, + "name": "Myoko" + }, + "point_b": { + "lat": 5.03347, + "lon": -6.15137, + "name": "Gaoulou" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 49.951444, + "lon": 47.102842 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (37.02534°, 138.25561°)", + " Point B: (5.03347°, -6.15137°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 49.951444°", + " Longitude: 47.102842°", + "FINAL ANSWER: 49.951444, 47.102842" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 27.0186, + "lon": 77.17636, + "name": "Weir" + }, + "point_b": { + "lat": -27.342, + "lon": 31.58, + "name": "Ncotshane" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 13.679924, + "lon": 65.129046 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (27.0186°, 77.17636°)", + " Point B: (-27.342°, 31.58°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 13.679924°", + " Longitude: 65.129046°", + "FINAL ANSWER: 13.679924, 65.129046" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -37.91806, + "lon": 145.03544, + "name": "Bentleigh" + }, + "point_b": { + "lat": 33.88835, + "lon": -118.30896, + "name": "Gardena" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -3.027647, + "lon": -164.997741 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-37.91806°, 145.03544°)", + " Point B: (33.88835°, -118.30896°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -3.027647°", + " Longitude: -164.997741°", + "FINAL ANSWER: -3.027647, -164.997741" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 11.3, + "lon": 39.68333, + "name": "Hāyk’" + }, + "point_b": { + "lat": -9.93333, + "lon": 35.33333, + "name": "Mahanje" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 5.99299, + "lon": 38.582767 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (11.3°, 39.68333°)", + " Point B: (-9.93333°, 35.33333°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 5.992990°", + " Longitude: 38.582767°", + "FINAL ANSWER: 5.992990, 38.582767" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 31.18248, + "lon": 35.69999, + "name": "Qīr Moāv" + }, + "point_b": { + "lat": -37.79117, + "lon": 144.81637, + "name": "Sunshine West" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -24.433393, + "lon": 112.322322 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (31.18248°, 35.69999°)", + " Point B: (-37.79117°, 144.81637°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -24.433393°", + " Longitude: 112.322322°", + "FINAL ANSWER: -24.433393, 112.322322" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 45.18497, + "lon": 15.80579, + "name": "Velika Kladuša" + }, + "point_b": { + "lat": 18.96506, + "lon": 79.47475, + "name": "Mandamarri" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 42.24616, + "lon": 35.59483 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (45.18497°, 15.80579°)", + " Point B: (18.96506°, 79.47475°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 42.246160°", + " Longitude: 35.594830°", + "FINAL ANSWER: 42.246160, 35.594830" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 27.23731, + "lon": 76.62243, + "name": "Rājgarh" + }, + "point_b": { + "lat": -7.25972, + "lon": -34.9075, + "name": "Conde" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 5.579502, + "lon": -9.849009 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (27.23731°, 76.62243°)", + " Point B: (-7.25972°, -34.9075°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 5.579502°", + " Longitude: -9.849009°", + "FINAL ANSWER: 5.579502, -9.849009" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 11.74859, + "lon": 75.57558, + "name": "Panniyannūr" + }, + "point_b": { + "lat": 25.04049, + "lon": 83.60749, + "name": "Bhabhua" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 18.436696, + "lon": 79.435671 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (11.74859°, 75.57558°)", + " Point B: (25.04049°, 83.60749°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 18.436696°", + " Longitude: 79.435671°", + "FINAL ANSWER: 18.436696, 79.435671" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 48.22544, + "lon": 16.30871, + "name": "Hernals" + }, + "point_b": { + "lat": 37.4063, + "lon": -1.58289, + "name": "Águilas" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 43.162892, + "lon": 6.571628 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (48.22544°, 16.30871°)", + " Point B: (37.4063°, -1.58289°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 43.162892°", + " Longitude: 6.571628°", + "FINAL ANSWER: 43.162892, 6.571628" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 9.88333, + "lon": 36.61667, + "name": "Āyana" + }, + "point_b": { + "lat": 39.24611, + "lon": -94.41912, + "name": "Liberty" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 46.849037, + "lon": -14.166108 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (9.88333°, 36.61667°)", + " Point B: (39.24611°, -94.41912°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 46.849037°", + " Longitude: -14.166108°", + "FINAL ANSWER: 46.849037, -14.166108" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 55.80202, + "lon": 37.67159, + "name": "Sokol’niki" + }, + "point_b": { + "lat": 9.14011, + "lon": 99.33311, + "name": "Surat Thani" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 36.179476, + "lon": 77.80565 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (55.80202°, 37.67159°)", + " Point B: (9.14011°, 99.33311°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 36.179476°", + " Longitude: 77.805650°", + "FINAL ANSWER: 36.179476, 77.805650" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -5.89222, + "lon": -42.63611, + "name": "Água Branca" + }, + "point_b": { + "lat": 35.98907, + "lon": 50.74512, + "name": "Shahr-e Jadīd-e Mehestan" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 8.19668, + "lon": -23.095111 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-5.89222°, -42.63611°)", + " Point B: (35.98907°, 50.74512°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 8.196680°", + " Longitude: -23.095111°", + "FINAL ANSWER: 8.196680, -23.095111" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 8.92901, + "lon": -75.02709, + "name": "San Benito Abad" + }, + "point_b": { + "lat": 29.98924, + "lon": 107.61521, + "name": "Shetan" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 65.060276, + "lon": 113.299524 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (8.92901°, -75.02709°)", + " Point B: (29.98924°, 107.61521°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 65.060276°", + " Longitude: 113.299524°", + "FINAL ANSWER: 65.060276, 113.299524" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 38.5503, + "lon": 44.9521, + "name": "Khowy" + }, + "point_b": { + "lat": 8.35362, + "lon": 77.1859, + "name": "Palugal" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 24.289914, + "lon": 63.005946 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (38.5503°, 44.9521°)", + " Point B: (8.35362°, 77.1859°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 24.289914°", + " Longitude: 63.005946°", + "FINAL ANSWER: 24.289914, 63.005946" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 20.98333, + "lon": 105.83333, + "name": "Bạch Mai" + }, + "point_b": { + "lat": 46.29914, + "lon": 30.65529, + "name": "Chornomors’k" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 39.837008, + "lon": 74.807081 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (20.98333°, 105.83333°)", + " Point B: (46.29914°, 30.65529°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 39.837008°", + " Longitude: 74.807081°", + "FINAL ANSWER: 39.837008, 74.807081" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -24.88333, + "lon": 28.28333, + "name": "Bela Bela" + }, + "point_b": { + "lat": 50.90861, + "lon": 4.67056, + "name": "Herent" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -5.824674, + "lon": 23.286696 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-24.88333°, 28.28333°)", + " Point B: (50.90861°, 4.67056°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -5.824674°", + " Longitude: 23.286696°", + "FINAL ANSWER: -5.824674, 23.286696" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -2.69583, + "lon": -44.82139, + "name": "São Bento" + }, + "point_b": { + "lat": 51.68072, + "lon": -0.39446, + "name": "North Watford" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 26.098262, + "lon": -28.066683 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-2.69583°, -44.82139°)", + " Point B: (51.68072°, -0.39446°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 26.098262°", + " Longitude: -28.066683°", + "FINAL ANSWER: 26.098262, -28.066683" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 7.97252, + "lon": 2.22176, + "name": "Glazoué" + }, + "point_b": { + "lat": 33.78942, + "lon": -7.15968, + "name": "Bouznika" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 20.944573, + "lon": -2.057937 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (7.97252°, 2.22176°)", + " Point B: (33.78942°, -7.15968°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 20.944573°", + " Longitude: -2.057937°", + "FINAL ANSWER: 20.944573, -2.057937" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 39.98928, + "lon": -75.24324, + "name": "Overbrook" + }, + "point_b": { + "lat": 43.66294, + "lon": -116.68736, + "name": "Caldwell" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 43.734278, + "lon": -95.343239 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (39.98928°, -75.24324°)", + " Point B: (43.66294°, -116.68736°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 43.734278°", + " Longitude: -95.343239°", + "FINAL ANSWER: 43.734278, -95.343239" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -7.88806, + "lon": 110.32889, + "name": "Bantul" + }, + "point_b": { + "lat": 28.83379, + "lon": 106.75535, + "name": "Fuhuan" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 19.658286, + "lon": 107.758289 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-7.88806°, 110.32889°)", + " Point B: (28.83379°, 106.75535°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 19.658286°", + " Longitude: 107.758289°", + "FINAL ANSWER: 19.658286, 107.758289" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -30.40001, + "lon": 27.70027, + "name": "Quthing" + }, + "point_b": { + "lat": 46.67361, + "lon": 28.05944, + "name": "Huşi" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 8.136839, + "lon": 27.859404 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-30.40001°, 27.70027°)", + " Point B: (46.67361°, 28.05944°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 8.136839°", + " Longitude: 27.859404°", + "FINAL ANSWER: 8.136839, 27.859404" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 36.71068, + "lon": -4.63297, + "name": "Cártama" + }, + "point_b": { + "lat": 6.41502, + "lon": 2.88132, + "name": "Badagry" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 14.01554, + "lon": 1.259822 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (36.71068°, -4.63297°)", + " Point B: (6.41502°, 2.88132°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 14.015540°", + " Longitude: 1.259822°", + "FINAL ANSWER: 14.015540, 1.259822" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 9.30143, + "lon": 13.39771, + "name": "Garoua" + }, + "point_b": { + "lat": 42.34447, + "lon": -88.04175, + "name": "Grayslake" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 24.489527, + "lon": -4.745946 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (9.30143°, 13.39771°)", + " Point B: (42.34447°, -88.04175°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 24.489527°", + " Longitude: -4.745946°", + "FINAL ANSWER: 24.489527, -4.745946" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -2.4421, + "lon": 28.9824, + "name": "Bushenge" + }, + "point_b": { + "lat": 51.04954, + "lon": 5.22606, + "name": "Beringen" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 11.187174, + "lon": 24.631878 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-2.4421°, 28.9824°)", + " Point B: (51.04954°, 5.22606°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 11.187174°", + " Longitude: 24.631878°", + "FINAL ANSWER: 11.187174, 24.631878" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 48.08829, + "lon": 9.23033, + "name": "Sigmaringen" + }, + "point_b": { + "lat": 57.35918, + "lon": 37.60806, + "name": "Kashin" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 53.56567, + "lon": 21.876421 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (48.08829°, 9.23033°)", + " Point B: (57.35918°, 37.60806°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 53.565670°", + " Longitude: 21.876421°", + "FINAL ANSWER: 53.565670, 21.876421" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 36.13333, + "lon": 139.7, + "name": "Kurihashi" + }, + "point_b": { + "lat": 22.72709, + "lon": -81.28963, + "name": "Pedro Betancourt" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 53.9419, + "lon": 169.810932 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (36.13333°, 139.7°)", + " Point B: (22.72709°, -81.28963°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 53.941900°", + " Longitude: 169.810932°", + "FINAL ANSWER: 53.941900, 169.810932" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 40.80028, + "lon": 19.91667, + "name": "Kuçovë" + }, + "point_b": { + "lat": -0.11306, + "lon": 31.85389, + "name": "Lukaya" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 10.17517, + "lon": 29.367429 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (40.80028°, 19.91667°)", + " Point B: (-0.11306°, 31.85389°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 10.175170°", + " Longitude: 29.367429°", + "FINAL ANSWER: 10.175170, 29.367429" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 5.48363, + "lon": 7.03325, + "name": "Owerri" + }, + "point_b": { + "lat": -38.95078, + "lon": -68.0592, + "name": "Neuquén" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -7.904671, + "lon": -8.53193 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (5.48363°, 7.03325°)", + " Point B: (-38.95078°, -68.0592°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -7.904671°", + " Longitude: -8.531930°", + "FINAL ANSWER: -7.904671, -8.531930" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 36.6, + "lon": 136.61667, + "name": "Kanazawa" + }, + "point_b": { + "lat": 49.78162, + "lon": 14.68697, + "name": "Benešov" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 51.949424, + "lon": 118.702343 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (36.6°, 136.61667°)", + " Point B: (49.78162°, 14.68697°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 51.949424°", + " Longitude: 118.702343°", + "FINAL ANSWER: 51.949424, 118.702343" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 21.63093, + "lon": 99.92676, + "name": "Kēng Tung" + }, + "point_b": { + "lat": 53.55, + "lon": -1.48333, + "name": "Barnsley" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 36.900535, + "lon": 85.380844 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (21.63093°, 99.92676°)", + " Point B: (53.55°, -1.48333°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 36.900535°", + " Longitude: 85.380844°", + "FINAL ANSWER: 36.900535, 85.380844" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 5.71667, + "lon": 116.4, + "name": "Tambunan" + }, + "point_b": { + "lat": 10.7, + "lon": 37.06667, + "name": "Burē" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 10.613663, + "lon": 77.031567 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (5.71667°, 116.4°)", + " Point B: (10.7°, 37.06667°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 10.613663°", + " Longitude: 77.031567°", + "FINAL ANSWER: 10.613663, 77.031567" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 41.91738, + "lon": 3.1631, + "name": "Palafrugell" + }, + "point_b": { + "lat": 39.04194, + "lon": 106.39583, + "name": "Dawukou" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 49.249325, + "lon": 85.046743 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (41.91738°, 3.1631°)", + " Point B: (39.04194°, 106.39583°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 49.249325°", + " Longitude: 85.046743°", + "FINAL ANSWER: 49.249325, 85.046743" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -5.08917, + "lon": -81.11444, + "name": "Paita" + }, + "point_b": { + "lat": 48.23656, + "lon": -79.02311, + "name": "Rouyn-Noranda" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 34.908259, + "lon": -79.753368 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-5.08917°, -81.11444°)", + " Point B: (48.23656°, -79.02311°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 34.908259°", + " Longitude: -79.753368°", + "FINAL ANSWER: 34.908259, -79.753368" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 17.70217, + "lon": 33.98638, + "name": "Atbara" + }, + "point_b": { + "lat": 8.03424, + "lon": 2.4866, + "name": "Savé" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 15.673499, + "lon": 25.870045 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (17.70217°, 33.98638°)", + " Point B: (8.03424°, 2.4866°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 15.673499°", + " Longitude: 25.870045°", + "FINAL ANSWER: 15.673499, 25.870045" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -23.27583, + "lon": -51.27833, + "name": "Cambé" + }, + "point_b": { + "lat": 6.4134, + "lon": 81.3346, + "name": "Kataragama" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -20.172806, + "lon": 20.143806 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-23.27583°, -51.27833°)", + " Point B: (6.4134°, 81.3346°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -20.172806°", + " Longitude: 20.143806°", + "FINAL ANSWER: -20.172806, 20.143806" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 68.79833, + "lon": 16.54165, + "name": "Harstad" + }, + "point_b": { + "lat": 35.23151, + "lon": 9.12321, + "name": "Sbeitla" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 60.454514, + "lon": 13.302751 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (68.79833°, 16.54165°)", + " Point B: (35.23151°, 9.12321°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 60.454514°", + " Longitude: 13.302751°", + "FINAL ANSWER: 60.454514, 13.302751" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 38.99915, + "lon": -3.36991, + "name": "Manzanares" + }, + "point_b": { + "lat": 31.34943, + "lon": 74.70271, + "name": "Bhikkiwind Uttār" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 42.196992, + "lon": 37.85425 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (38.99915°, -3.36991°)", + " Point B: (31.34943°, 74.70271°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 42.196992°", + " Longitude: 37.854250°", + "FINAL ANSWER: 42.196992, 37.854250" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 30.8248, + "lon": 30.81805, + "name": "Kafr az Zayyāt" + }, + "point_b": { + "lat": 10.05, + "lon": -5.33778, + "name": "Nambingué" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 26.437765, + "lon": 20.745641 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (30.8248°, 30.81805°)", + " Point B: (10.05°, -5.33778°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 26.437765°", + " Longitude: 20.745641°", + "FINAL ANSWER: 26.437765, 20.745641" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 33.80101, + "lon": 130.68422, + "name": "Inokura" + }, + "point_b": { + "lat": 6.98008, + "lon": 2.6649, + "name": "Pobé" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 25.842815, + "lon": 25.818395 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (33.80101°, 130.68422°)", + " Point B: (6.98008°, 2.6649°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 25.842815°", + " Longitude: 25.818395°", + "FINAL ANSWER: 25.842815, 25.818395" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -16.32667, + "lon": -48.95278, + "name": "Anápolis" + }, + "point_b": { + "lat": 47.79494, + "lon": 124.45773, + "name": "Fuyu" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 20.312758, + "lon": -43.583875 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-16.32667°, -48.95278°)", + " Point B: (47.79494°, 124.45773°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 20.312758°", + " Longitude: -43.583875°", + "FINAL ANSWER: 20.312758, -43.583875" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 14.0432, + "lon": -6.1067, + "name": "Siribala Coro" + }, + "point_b": { + "lat": 36.65038, + "lon": 10.59004, + "name": "Beni Khalled" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 31.196557, + "lon": 5.749842 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (14.0432°, -6.1067°)", + " Point B: (36.65038°, 10.59004°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 31.196557°", + " Longitude: 5.749842°", + "FINAL ANSWER: 31.196557, 5.749842" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 31.22323, + "lon": -85.39049, + "name": "Dothan" + }, + "point_b": { + "lat": 19.35529, + "lon": -99.06224, + "name": "Iztapalapa" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 25.447115, + "lon": -92.563659 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (31.22323°, -85.39049°)", + " Point B: (19.35529°, -99.06224°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 25.447115°", + " Longitude: -92.563659°", + "FINAL ANSWER: 25.447115, -92.563659" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -18.77861, + "lon": -46.4075, + "name": "Lagoa Formosa" + }, + "point_b": { + "lat": 33.88863, + "lon": -117.81311, + "name": "Yorba Linda" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 9.265841, + "lon": -79.409289 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-18.77861°, -46.4075°)", + " Point B: (33.88863°, -117.81311°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 9.265841°", + " Longitude: -79.409289°", + "FINAL ANSWER: 9.265841, -79.409289" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -6.55833, + "lon": -35.74167, + "name": "Araruna" + }, + "point_b": { + "lat": 34.09668, + "lon": -117.71978, + "name": "Claremont" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 27.879266, + "lon": -93.3055 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-6.55833°, -35.74167°)", + " Point B: (34.09668°, -117.71978°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 27.879266°", + " Longitude: -93.305500°", + "FINAL ANSWER: 27.879266, -93.305500" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -31.89578, + "lon": 115.76431, + "name": "Scarborough" + }, + "point_b": { + "lat": 50.9803, + "lon": 11.32903, + "name": "Weimar" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 37.107003, + "lon": 50.21876 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-31.89578°, 115.76431°)", + " Point B: (50.9803°, 11.32903°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 37.107003°", + " Longitude: 50.218760°", + "FINAL ANSWER: 37.107003, 50.218760" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 18.9378, + "lon": -103.96417, + "name": "Ciudad de Armería" + }, + "point_b": { + "lat": 26.61708, + "lon": -80.07231, + "name": "Lake Worth Beach" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 21.181991, + "lon": -98.246091 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (18.9378°, -103.96417°)", + " Point B: (26.61708°, -80.07231°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 21.181991°", + " Longitude: -98.246091°", + "FINAL ANSWER: 21.181991, -98.246091" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 22.86416, + "lon": 88.63701, + "name": "Ashoknagar Kalyangarh" + }, + "point_b": { + "lat": 53.41058, + "lon": -2.97794, + "name": "Liverpool" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 54.291155, + "lon": 28.070782 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (22.86416°, 88.63701°)", + " Point B: (53.41058°, -2.97794°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 54.291155°", + " Longitude: 28.070782°", + "FINAL ANSWER: 54.291155, 28.070782" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 33.04623, + "lon": -96.99417, + "name": "Lewisville" + }, + "point_b": { + "lat": 14.04138, + "lon": -88.93951, + "name": "Chalatenango" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 18.827692, + "lon": -90.752893 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (33.04623°, -96.99417°)", + " Point B: (14.04138°, -88.93951°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 18.827692°", + " Longitude: -90.752893°", + "FINAL ANSWER: 18.827692, -90.752893" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 25.56892, + "lon": 91.88313, + "name": "Shillong" + }, + "point_b": { + "lat": 6.52799, + "lon": 3.35411, + "name": "Mushin" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 25.591834, + "lon": 68.051132 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (25.56892°, 91.88313°)", + " Point B: (6.52799°, 3.35411°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 25.591834°", + " Longitude: 68.051132°", + "FINAL ANSWER: 25.591834, 68.051132" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -7.8685, + "lon": 111.462, + "name": "Ponorogo" + }, + "point_b": { + "lat": 40.79389, + "lon": -73.965, + "name": "Manhattan Valley" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 64.394533, + "lon": 128.278133 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-7.8685°, 111.462°)", + " Point B: (40.79389°, -73.965°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 64.394533°", + " Longitude: 128.278133°", + "FINAL ANSWER: 64.394533, 128.278133" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -32.16422, + "lon": 25.61918, + "name": "Cradock" + }, + "point_b": { + "lat": 33.9164, + "lon": -118.35257, + "name": "Hawthorne" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -17.715645, + "lon": -12.818714 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-32.16422°, 25.61918°)", + " Point B: (33.9164°, -118.35257°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -17.715645°", + " Longitude: -12.818714°", + "FINAL ANSWER: -17.715645, -12.818714" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 45.40008, + "lon": -71.89908, + "name": "Sherbrooke" + }, + "point_b": { + "lat": -34.18551, + "lon": 142.16251, + "name": "Mildura" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -9.259164, + "lon": 173.38957 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (45.40008°, -71.89908°)", + " Point B: (-34.18551°, 142.16251°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -9.259164°", + " Longitude: 173.389570°", + "FINAL ANSWER: -9.259164, 173.389570" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 51.21667, + "lon": 6.26667, + "name": "Schwalmtal" + }, + "point_b": { + "lat": 38.78393, + "lon": 63.88035, + "name": "Saýat" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 51.096337, + "lon": 22.812998 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (51.21667°, 6.26667°)", + " Point B: (38.78393°, 63.88035°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 51.096337°", + " Longitude: 22.812998°", + "FINAL ANSWER: 51.096337, 22.812998" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 4.603, + "lon": 9.0404, + "name": "Ekondo Titi" + }, + "point_b": { + "lat": -23.52719, + "lon": -46.61751, + "name": "Pari" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -17.629667, + "lon": -31.556428 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (4.603°, 9.0404°)", + " Point B: (-23.52719°, -46.61751°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -17.629667°", + " Longitude: -31.556428°", + "FINAL ANSWER: -17.629667, -31.556428" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 36.82098, + "lon": -76.36883, + "name": "Portsmouth Heights" + }, + "point_b": { + "lat": 40.98894, + "lon": 28.67582, + "name": "Yakuplu" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 52.966088, + "lon": -26.04001 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (36.82098°, -76.36883°)", + " Point B: (40.98894°, 28.67582°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 52.966088°", + " Longitude: -26.040010°", + "FINAL ANSWER: 52.966088, -26.040010" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 44.18073, + "lon": 28.63432, + "name": "Constanţa" + }, + "point_b": { + "lat": -12.77698, + "lon": 45.28234, + "name": "Labattoir" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 1.542891, + "lon": 41.783652 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (44.18073°, 28.63432°)", + " Point B: (-12.77698°, 45.28234°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 1.542891°", + " Longitude: 41.783652°", + "FINAL ANSWER: 1.542891, 41.783652" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -1.6558, + "lon": 37.37454, + "name": "Kinoi" + }, + "point_b": { + "lat": 40.14192, + "lon": 29.97932, + "name": "Bilecik" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 19.279579, + "lon": 34.170467 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-1.6558°, 37.37454°)", + " Point B: (40.14192°, 29.97932°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 19.279579°", + " Longitude: 34.170467°", + "FINAL ANSWER: 19.279579, 34.170467" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -21.4825, + "lon": -51.53278, + "name": "Dracena" + }, + "point_b": { + "lat": 55.90867, + "lon": 53.93437, + "name": "Agidel’" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 25.938779, + "lon": -16.863023 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-21.4825°, -51.53278°)", + " Point B: (55.90867°, 53.93437°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 25.938779°", + " Longitude: -16.863023°", + "FINAL ANSWER: 25.938779, -16.863023" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 36.54722, + "lon": 4.68611, + "name": "Seddouk" + }, + "point_b": { + "lat": 11.17151, + "lon": 75.80611, + "name": "Beypore" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 20.528486, + "lon": 60.947609 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (36.54722°, 4.68611°)", + " Point B: (11.17151°, 75.80611°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 20.528486°", + " Longitude: 60.947609°", + "FINAL ANSWER: 20.528486, 60.947609" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 42.73722, + "lon": 124.72222, + "name": "Xifeng" + }, + "point_b": { + "lat": 12.91667, + "lon": -14.16667, + "name": "Diaoubé" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 36.111008, + "lon": 3.680088 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (42.73722°, 124.72222°)", + " Point B: (12.91667°, -14.16667°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 36.111008°", + " Longitude: 3.680088°", + "FINAL ANSWER: 36.111008, 3.680088" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -4.23246, + "lon": -44.78164, + "name": "Bacabal" + }, + "point_b": { + "lat": 51.12753, + "lon": 16.96186, + "name": "Osiedle Kosmonautów" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 26.597507, + "lon": -21.655379 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-4.23246°, -44.78164°)", + " Point B: (51.12753°, 16.96186°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 26.597507°", + " Longitude: -21.655379°", + "FINAL ANSWER: 26.597507, -21.655379" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 52.92815, + "lon": 12.80311, + "name": "Neuruppin" + }, + "point_b": { + "lat": 9.33754, + "lon": -66.25282, + "name": "Chaguaramas" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 37.524314, + "lon": -37.996385 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (52.92815°, 12.80311°)", + " Point B: (9.33754°, -66.25282°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 37.524314°", + " Longitude: -37.996385°", + "FINAL ANSWER: 37.524314, -37.996385" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 25.70816, + "lon": -80.407, + "name": "Kendale Lakes" + }, + "point_b": { + "lat": 23.43305, + "lon": 84.67992, + "name": "Lohārdagā" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 53.443057, + "lon": 69.248376 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (25.70816°, -80.407°)", + " Point B: (23.43305°, 84.67992°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 53.443057°", + " Longitude: 69.248376°", + "FINAL ANSWER: 53.443057, 69.248376" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 22.7984, + "lon": 114.46716, + "name": "Danshui" + }, + "point_b": { + "lat": 51.10286, + "lon": 17.03006, + "name": "Wrocław" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 48.097257, + "lon": 77.939297 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (22.7984°, 114.46716°)", + " Point B: (51.10286°, 17.03006°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 48.097257°", + " Longitude: 77.939297°", + "FINAL ANSWER: 48.097257, 77.939297" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -3.12873, + "lon": -58.15501, + "name": "Urucurituba" + }, + "point_b": { + "lat": -27.25806, + "lon": -49.93389, + "name": "Pouso Redondo" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -9.184833, + "lon": -56.252405 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-3.12873°, -58.15501°)", + " Point B: (-27.25806°, -49.93389°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -9.184833°", + " Longitude: -56.252405°", + "FINAL ANSWER: -9.184833, -56.252405" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 30.36742, + "lon": 30.50871, + "name": "Madīnat as Sādāt" + }, + "point_b": { + "lat": -25.06597, + "lon": -130.10147, + "name": "Adamstown" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 30.345932, + "lon": -16.805208 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (30.36742°, 30.50871°)", + " Point B: (-25.06597°, -130.10147°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 30.345932°", + " Longitude: -16.805208°", + "FINAL ANSWER: 30.345932, -16.805208" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 18.04041, + "lon": 74.18719, + "name": "Lonand" + }, + "point_b": { + "lat": -1.8, + "lon": -53.48, + "name": "Prainha" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 9.321561, + "lon": -23.845133 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (18.04041°, 74.18719°)", + " Point B: (-1.8°, -53.48°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 9.321561°", + " Longitude: -23.845133°", + "FINAL ANSWER: 9.321561, -23.845133" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 51.50896, + "lon": -0.3713, + "name": "Southall" + }, + "point_b": { + "lat": 35.46522, + "lon": -6.03415, + "name": "Asilah" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 47.52632, + "lon": -2.098807 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (51.50896°, -0.3713°)", + " Point B: (35.46522°, -6.03415°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 47.526320°", + " Longitude: -2.098807°", + "FINAL ANSWER: 47.526320, -2.098807" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 28.19377, + "lon": 115.7836, + "name": "Jianguang" + }, + "point_b": { + "lat": -15.83403, + "lon": -67.56586, + "name": "Caranavi" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 24.856002, + "lon": -77.444027 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (28.19377°, 115.7836°)", + " Point B: (-15.83403°, -67.56586°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 24.856002°", + " Longitude: -77.444027°", + "FINAL ANSWER: 24.856002, -77.444027" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 8.76962, + "lon": -70.11086, + "name": "Barrancas" + }, + "point_b": { + "lat": 3.19916, + "lon": 101.64983, + "name": "Taman Petaling" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 40.597239, + "lon": -40.317132 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (8.76962°, -70.11086°)", + " Point B: (3.19916°, 101.64983°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 40.597239°", + " Longitude: -40.317132°", + "FINAL ANSWER: 40.597239, -40.317132" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 28.03811, + "lon": 79.12668, + "name": "Budaun" + }, + "point_b": { + "lat": 40.982, + "lon": 28.6399, + "name": "Beylikdüzü" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 37.220845, + "lon": 55.989305 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (28.03811°, 79.12668°)", + " Point B: (40.982°, 28.6399°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 37.220845°", + " Longitude: 55.989305°", + "FINAL ANSWER: 37.220845, 55.989305" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 33.86845, + "lon": 57.42885, + "name": "Boshrūyeh" + }, + "point_b": { + "lat": 13.2, + "lon": 34.16667, + "name": "Ad Dindar" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 29.065088, + "lon": 50.843202 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (33.86845°, 57.42885°)", + " Point B: (13.2°, 34.16667°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 29.065088°", + " Longitude: 50.843202°", + "FINAL ANSWER: 29.065088, 50.843202" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 12.24661, + "lon": -1.58402, + "name": "Zinguédéssé" + }, + "point_b": { + "lat": 51.14236, + "lon": 3.1368, + "name": "Zedelgem" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 31.715196, + "lon": 0.261475 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (12.24661°, -1.58402°)", + " Point B: (51.14236°, 3.1368°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 31.715196°", + " Longitude: 0.261475°", + "FINAL ANSWER: 31.715196, 0.261475" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -15.96528, + "lon": -54.96833, + "name": "Jaciara" + }, + "point_b": { + "lat": 10.65, + "lon": 76.53333, + "name": "Alattūr" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -6.446296, + "lon": 12.17875 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-15.96528°, -54.96833°)", + " Point B: (10.65°, 76.53333°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -6.446296°", + " Longitude: 12.178750°", + "FINAL ANSWER: -6.446296, 12.178750" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 20.45, + "lon": 106.34002, + "name": "Thái Bình" + }, + "point_b": { + "lat": 9.27345, + "lon": 24.41701, + "name": "Kafia Kingi" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 21.213955, + "lon": 85.137215 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (20.45°, 106.34002°)", + " Point B: (9.27345°, 24.41701°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 21.213955°", + " Longitude: 85.137215°", + "FINAL ANSWER: 21.213955, 85.137215" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 51.86333, + "lon": 4.3625, + "name": "Hoogvliet" + }, + "point_b": { + "lat": 12.8924, + "lon": 80.08079, + "name": "Vandalūr" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 38.350125, + "lon": 52.114578 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (51.86333°, 4.3625°)", + " Point B: (12.8924°, 80.08079°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 38.350125°", + " Longitude: 52.114578°", + "FINAL ANSWER: 38.350125, 52.114578" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -32.74976, + "lon": -70.72584, + "name": "San Felipe" + }, + "point_b": { + "lat": -53.78773, + "lon": -67.70975, + "name": "Río Grande" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -48.536401, + "lon": -68.687795 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-32.74976°, -70.72584°)", + " Point B: (-53.78773°, -67.70975°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -48.536401°", + " Longitude: -68.687795°", + "FINAL ANSWER: -48.536401, -68.687795" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 40.94652, + "lon": -124.10062, + "name": "McKinleyville" + }, + "point_b": { + "lat": 17.44781, + "lon": 78.52633, + "name": "Malkajgiri" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 44.783759, + "lon": 91.712638 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (40.94652°, -124.10062°)", + " Point B: (17.44781°, 78.52633°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 44.783759°", + " Longitude: 91.712638°", + "FINAL ANSWER: 44.783759, 91.712638" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 42.06642, + "lon": -87.93729, + "name": "Mount Prospect" + }, + "point_b": { + "lat": 51.19188, + "lon": 5.11662, + "name": "Mol" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 51.304889, + "lon": -70.509711 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (42.06642°, -87.93729°)", + " Point B: (51.19188°, 5.11662°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 51.304889°", + " Longitude: -70.509711°", + "FINAL ANSWER: 51.304889, -70.509711" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -13.83333, + "lon": -171.76666, + "name": "Apia" + }, + "point_b": { + "lat": 10.49093, + "lon": 107.27014, + "name": "Thị Trấn Đất Đỏ" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 4.414673, + "lon": 127.52609 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-13.83333°, -171.76666°)", + " Point B: (10.49093°, 107.27014°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 4.414673°", + " Longitude: 127.526090°", + "FINAL ANSWER: 4.414673, 127.526090" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 33.44001, + "lon": -112.05805, + "name": "Central City" + }, + "point_b": { + "lat": 50.66829, + "lon": 4.61443, + "name": "Louvain-la-Neuve" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 60.160126, + "lon": -26.476664 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (33.44001°, -112.05805°)", + " Point B: (50.66829°, 4.61443°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 60.160126°", + " Longitude: -26.476664°", + "FINAL ANSWER: 60.160126, -26.476664" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 34.03612, + "lon": -117.99118, + "name": "Avocado Heights" + }, + "point_b": { + "lat": 43.10247, + "lon": 128.90848, + "name": "Antu" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 55.223801, + "lon": -169.074765 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (34.03612°, -117.99118°)", + " Point B: (43.10247°, 128.90848°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 55.223801°", + " Longitude: -169.074765°", + "FINAL ANSWER: 55.223801, -169.074765" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -17.93285, + "lon": 25.83066, + "name": "Victoria Falls" + }, + "point_b": { + "lat": 41.95392, + "lon": -87.67895, + "name": "North Center" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 1.601673, + "lon": 2.969263 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-17.93285°, 25.83066°)", + " Point B: (41.95392°, -87.67895°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 1.601673°", + " Longitude: 2.969263°", + "FINAL ANSWER: 1.601673, 2.969263" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -24.53333, + "lon": 32.98333, + "name": "Chokwé" + }, + "point_b": { + "lat": 11.41667, + "lon": 37.16667, + "name": "Mer’āwī" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -6.562658, + "lon": 35.153053 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-24.53333°, 32.98333°)", + " Point B: (11.41667°, 37.16667°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -6.562658°", + " Longitude: 35.153053°", + "FINAL ANSWER: -6.562658, 35.153053" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 39.91956, + "lon": -75.16475, + "name": "Lower Moyamensing" + }, + "point_b": { + "lat": -37.89138, + "lon": 144.62368, + "name": "Wyndham Vale" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -20.698075, + "lon": -176.948142 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (39.91956°, -75.16475°)", + " Point B: (-37.89138°, 144.62368°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -20.698075°", + " Longitude: -176.948142°", + "FINAL ANSWER: -20.698075, -176.948142" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 37.48412, + "lon": 13.98542, + "name": "San Cataldo" + }, + "point_b": { + "lat": 11.09246, + "lon": 77.31225, + "name": "Andipalayam" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 33.954123, + "lon": 32.669097 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (37.48412°, 13.98542°)", + " Point B: (11.09246°, 77.31225°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 33.954123°", + " Longitude: 32.669097°", + "FINAL ANSWER: 33.954123, 32.669097" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -22.55941, + "lon": 17.08323, + "name": "Windhoek" + }, + "point_b": { + "lat": 3.8682, + "lon": 102.5862, + "name": "Kampung Perak" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -4.668494, + "lon": 82.469239 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-22.55941°, 17.08323°)", + " Point B: (3.8682°, 102.5862°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -4.668494°", + " Longitude: 82.469239°", + "FINAL ANSWER: -4.668494, 82.469239" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -3.63333, + "lon": 32.18333, + "name": "Masumbwe" + }, + "point_b": { + "lat": 22.22819, + "lon": -102.32216, + "name": "Rincón de Romos" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 11.184876, + "lon": 2.4949 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-3.63333°, 32.18333°)", + " Point B: (22.22819°, -102.32216°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 11.184876°", + " Longitude: 2.494900°", + "FINAL ANSWER: 11.184876, 2.494900" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 29.1872, + "lon": -82.14009, + "name": "Ocala" + }, + "point_b": { + "lat": 35.43515, + "lon": 139.4256, + "name": "Ayase" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 49.173204, + "lon": -104.213958 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (29.1872°, -82.14009°)", + " Point B: (35.43515°, 139.4256°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 49.173204°", + " Longitude: -104.213958°", + "FINAL ANSWER: 49.173204, -104.213958" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 50.73385, + "lon": 4.23454, + "name": "Halle" + }, + "point_b": { + "lat": 36.83111, + "lon": 9.92417, + "name": "Jedeïda" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 40.330977, + "lon": 8.733192 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (50.73385°, 4.23454°)", + " Point B: (36.83111°, 9.92417°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 40.330977°", + " Longitude: 8.733192°", + "FINAL ANSWER: 40.330977, 8.733192" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -27.22426, + "lon": 153.02075, + "name": "North Lakes" + }, + "point_b": { + "lat": -28.16678, + "lon": 30.23371, + "name": "Dundee" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -47.630036, + "lon": 92.080817 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-27.22426°, 153.02075°)", + " Point B: (-28.16678°, 30.23371°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -47.630036°", + " Longitude: 92.080817°", + "FINAL ANSWER: -47.630036, 92.080817" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 42.24954, + "lon": -71.06616, + "name": "Milton" + }, + "point_b": { + "lat": -32.88946, + "lon": -68.84582, + "name": "Mendoza" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -14.104828, + "lon": -69.410398 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (42.24954°, -71.06616°)", + " Point B: (-32.88946°, -68.84582°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -14.104828°", + " Longitude: -69.410398°", + "FINAL ANSWER: -14.104828, -69.410398" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -16.91667, + "lon": 49.58333, + "name": "Soanierana Ivongo" + }, + "point_b": { + "lat": 33.5806, + "lon": -112.23738, + "name": "Peoria" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 40.401742, + "lon": -7.976918 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-16.91667°, 49.58333°)", + " Point B: (33.5806°, -112.23738°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 40.401742°", + " Longitude: -7.976918°", + "FINAL ANSWER: 40.401742, -7.976918" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 6.54368, + "lon": -7.4935, + "name": "Guiglo" + }, + "point_b": { + "lat": 59.32667, + "lon": 14.52386, + "name": "Karlskoga" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 33.371208, + "lon": -0.063111 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (6.54368°, -7.4935°)", + " Point B: (59.32667°, 14.52386°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 33.371208°", + " Longitude: -0.063111°", + "FINAL ANSWER: 33.371208, -0.063111" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 18.11675, + "lon": 76.75279, + "name": "Nilanga" + }, + "point_b": { + "lat": 22.53511, + "lon": 91.91919, + "name": "Raojān" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 21.556853, + "lon": 88.045996 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (18.11675°, 76.75279°)", + " Point B: (22.53511°, 91.91919°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 21.556853°", + " Longitude: 88.045996°", + "FINAL ANSWER: 21.556853, 88.045996" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 35.82159, + "lon": 51.64444, + "name": "Lavāsān" + }, + "point_b": { + "lat": -17.81667, + "lon": -63.05, + "name": "Cotoca" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -0.868232, + "lon": -37.825638 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (35.82159°, 51.64444°)", + " Point B: (-17.81667°, -63.05°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -0.868232°", + " Longitude: -37.825638°", + "FINAL ANSWER: -0.868232, -37.825638" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 25.48694, + "lon": 119.19834, + "name": "Jiangkou" + }, + "point_b": { + "lat": 33.45643, + "lon": 49.45646, + "name": "Aznā" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 35.381884, + "lon": 67.556296 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (25.48694°, 119.19834°)", + " Point B: (33.45643°, 49.45646°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 35.381884°", + " Longitude: 67.556296°", + "FINAL ANSWER: 35.381884, 67.556296" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 45.7125, + "lon": 16.07556, + "name": "Velika Gorica" + }, + "point_b": { + "lat": 6.78634, + "lon": -7.39338, + "name": "Fengolo" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 16.808092, + "lon": -2.818806 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (45.7125°, 16.07556°)", + " Point B: (6.78634°, -7.39338°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 16.808092°", + " Longitude: -2.818806°", + "FINAL ANSWER: 16.808092, -2.818806" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 18.54685, + "lon": -70.50692, + "name": "San José de Ocoa" + }, + "point_b": { + "lat": 26.90403, + "lon": 83.98087, + "name": "Padrauna" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 61.987965, + "lon": -0.960711 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (18.54685°, -70.50692°)", + " Point B: (26.90403°, 83.98087°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 61.987965°", + " Longitude: -0.960711°", + "FINAL ANSWER: 61.987965, -0.960711" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 53.14362, + "lon": 0.3363, + "name": "Skegness" + }, + "point_b": { + "lat": 53.62072, + "lon": 10.68748, + "name": "Mölln" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 53.34658, + "lon": 2.898982 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (53.14362°, 0.3363°)", + " Point B: (53.62072°, 10.68748°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 53.346580°", + " Longitude: 2.898982°", + "FINAL ANSWER: 53.346580, 2.898982" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -31.88775, + "lon": 115.9099, + "name": "Morley" + }, + "point_b": { + "lat": 25.94167, + "lon": 83.56111, + "name": "Mau" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -17.665099, + "lon": 106.906127 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-31.88775°, 115.9099°)", + " Point B: (25.94167°, 83.56111°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -17.665099°", + " Longitude: 106.906127°", + "FINAL ANSWER: -17.665099, 106.906127" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 27.70169, + "lon": 85.3206, + "name": "Kathmandu" + }, + "point_b": { + "lat": 31.36876, + "lon": 108.24215, + "name": "Gaoqiao" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 30.831498, + "lon": 102.365871 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (27.70169°, 85.3206°)", + " Point B: (31.36876°, 108.24215°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 30.831498°", + " Longitude: 102.365871°", + "FINAL ANSWER: 30.831498, 102.365871" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 24.4982, + "lon": 93.98126, + "name": "Kakching" + }, + "point_b": { + "lat": 10.60768, + "lon": -72.97901, + "name": "Villanueva" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 69.252132, + "lon": -8.130435 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (24.4982°, 93.98126°)", + " Point B: (10.60768°, -72.97901°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 69.252132°", + " Longitude: -8.130435°", + "FINAL ANSWER: 69.252132, -8.130435" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 40.28533, + "lon": 141.62875, + "name": "Ōno" + }, + "point_b": { + "lat": -6.05255, + "lon": 26.9143, + "name": "Kabalo" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 29.214197, + "lon": 72.645831 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (40.28533°, 141.62875°)", + " Point B: (-6.05255°, 26.9143°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 29.214197°", + " Longitude: 72.645831°", + "FINAL ANSWER: 29.214197, 72.645831" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 46.05007, + "lon": -73.46586, + "name": "Saint-Charles-Borromée" + }, + "point_b": { + "lat": -38.97736, + "lon": -67.82714, + "name": "Allen" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -17.722777, + "lon": -69.322209 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (46.05007°, -73.46586°)", + " Point B: (-38.97736°, -67.82714°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -17.722777°", + " Longitude: -69.322209°", + "FINAL ANSWER: -17.722777, -69.322209" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 33.54225, + "lon": -117.78311, + "name": "Laguna Beach" + }, + "point_b": { + "lat": 11.19152, + "lon": 40.01675, + "name": "Batī" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 40.157732, + "lon": 23.020426 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (33.54225°, -117.78311°)", + " Point B: (11.19152°, 40.01675°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 40.157732°", + " Longitude: 23.020426°", + "FINAL ANSWER: 40.157732, 23.020426" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 42.5334, + "lon": 70.3496, + "name": "Turar Ryskulov" + }, + "point_b": { + "lat": 36.56463, + "lon": 3.5933, + "name": "Lakhdaria" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 41.716393, + "lon": 18.48018 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (42.5334°, 70.3496°)", + " Point B: (36.56463°, 3.5933°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 41.716393°", + " Longitude: 18.480180°", + "FINAL ANSWER: 41.716393, 18.480180" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 17.69915, + "lon": 74.16252, + "name": "Koregaon" + }, + "point_b": { + "lat": -24.54528, + "lon": -52.98778, + "name": "Ubiratã" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -19.003737, + "lon": -18.267347 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (17.69915°, 74.16252°)", + " Point B: (-24.54528°, -52.98778°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -19.003737°", + " Longitude: -18.267347°", + "FINAL ANSWER: -19.003737, -18.267347" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -8.80778, + "lon": -39.82556, + "name": "Santa Maria da Boa Vista" + }, + "point_b": { + "lat": -36.75818, + "lon": 144.28024, + "name": "Bendigo" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -42.239531, + "lon": -43.255631 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-8.80778°, -39.82556°)", + " Point B: (-36.75818°, 144.28024°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -42.239531°", + " Longitude: -43.255631°", + "FINAL ANSWER: -42.239531, -43.255631" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 12.6, + "lon": 37.46667, + "name": "Gonder" + }, + "point_b": { + "lat": 51.83167, + "lon": 4.6875, + "name": "Papendrecht" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 33.240065, + "lon": 24.856023 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (12.6°, 37.46667°)", + " Point B: (51.83167°, 4.6875°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 33.240065°", + " Longitude: 24.856023°", + "FINAL ANSWER: 33.240065, 24.856023" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 1.21456, + "lon": -77.27846, + "name": "Pasto" + }, + "point_b": { + "lat": 9.67954, + "lon": 39.53262, + "name": "Debre Birhan" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 11.452949, + "lon": 10.032902 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (1.21456°, -77.27846°)", + " Point B: (9.67954°, 39.53262°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 11.452949°", + " Longitude: 10.032902°", + "FINAL ANSWER: 11.452949, 10.032902" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 39.90929, + "lon": -74.15486, + "name": "Bayville" + }, + "point_b": { + "lat": 26.62535, + "lon": -81.6248, + "name": "Lehigh Acres" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 36.632949, + "lon": -76.251209 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (39.90929°, -74.15486°)", + " Point B: (26.62535°, -81.6248°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 36.632949°", + " Longitude: -76.251209°", + "FINAL ANSWER: 36.632949, -76.251209" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 41.95503, + "lon": -87.94007, + "name": "Bensenville" + }, + "point_b": { + "lat": 13.07, + "lon": 80.24083, + "name": "Chetput" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 72.069519, + "lon": 48.49546 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (41.95503°, -87.94007°)", + " Point B: (13.07°, 80.24083°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 72.069519°", + " Longitude: 48.495460°", + "FINAL ANSWER: 72.069519, 48.495460" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 41.50633, + "lon": -5.74456, + "name": "Zamora" + }, + "point_b": { + "lat": 26.19698, + "lon": 127.72591, + "name": "Kanegusuku" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 56.923124, + "lon": 24.958378 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (41.50633°, -5.74456°)", + " Point B: (26.19698°, 127.72591°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 56.923124°", + " Longitude: 24.958378°", + "FINAL ANSWER: 56.923124, 24.958378" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 48.70291, + "lon": 2.41357, + "name": "Vigneux-sur-Seine" + }, + "point_b": { + "lat": 28.6167, + "lon": 77.33207, + "name": "Gharroli" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 48.996075, + "lon": 25.021183 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (48.70291°, 2.41357°)", + " Point B: (28.6167°, 77.33207°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 48.996075°", + " Longitude: 25.021183°", + "FINAL ANSWER: 48.996075, 25.021183" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 37.04308, + "lon": -100.921, + "name": "Liberal" + }, + "point_b": { + "lat": 6.03131, + "lon": -75.43333, + "name": "La Ceja" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 22.023537, + "lon": -86.758623 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (37.04308°, -100.921°)", + " Point B: (6.03131°, -75.43333°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 22.023537°", + " Longitude: -86.758623°", + "FINAL ANSWER: 22.023537, -86.758623" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -5.70729, + "lon": -78.80785, + "name": "Jaén" + }, + "point_b": { + "lat": 18.90135, + "lon": -97.63833, + "name": "Palmarito Tochapan" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 6.686246, + "lon": -87.983429 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-5.70729°, -78.80785°)", + " Point B: (18.90135°, -97.63833°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 6.686246°", + " Longitude: -87.983429°", + "FINAL ANSWER: 6.686246, -87.983429" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 5.63638, + "lon": 100.84517, + "name": "Kampung Kupang" + }, + "point_b": { + "lat": -14.85195, + "lon": -66.74954, + "name": "San Borja" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -19.24967, + "lon": 67.519749 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (5.63638°, 100.84517°)", + " Point B: (-14.85195°, -66.74954°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -19.249670°", + " Longitude: 67.519749°", + "FINAL ANSWER: -19.249670, 67.519749" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 37.3675, + "lon": 126.94694, + "name": "Gunpo" + }, + "point_b": { + "lat": -10.58333, + "lon": 35.4, + "name": "Maposeni" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 18.744332, + "lon": 74.965299 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (37.3675°, 126.94694°)", + " Point B: (-10.58333°, 35.4°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 18.744332°", + " Longitude: 74.965299°", + "FINAL ANSWER: 18.744332, 74.965299" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 20.38983, + "lon": 78.09027, + "name": "Lohāra" + }, + "point_b": { + "lat": 48.22697, + "lon": 11.47573, + "name": "Karlsfeld" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 45.38167, + "lon": 32.878426 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (20.38983°, 78.09027°)", + " Point B: (48.22697°, 11.47573°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 45.381670°", + " Longitude: 32.878426°", + "FINAL ANSWER: 45.381670, 32.878426" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 40.55851, + "lon": 17.80774, + "name": "Mesagne" + }, + "point_b": { + "lat": 15.2, + "lon": 101.13333, + "name": "Chai Badan" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 26.268122, + "lon": 84.845931 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (40.55851°, 17.80774°)", + " Point B: (15.2°, 101.13333°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 26.268122°", + " Longitude: 84.845931°", + "FINAL ANSWER: 26.268122, 84.845931" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -2.19616, + "lon": -79.88621, + "name": "Guayaquil" + }, + "point_b": { + "lat": 29.68403, + "lon": 106.61486, + "name": "Huixing" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 65.401653, + "lon": 127.352247 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-2.19616°, -79.88621°)", + " Point B: (29.68403°, 106.61486°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 65.401653°", + " Longitude: 127.352247°", + "FINAL ANSWER: 65.401653, 127.352247" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -37.9, + "lon": 144.66667, + "name": "Werribee" + }, + "point_b": { + "lat": 42.77361, + "lon": -81.18038, + "name": "St. Thomas" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 29.233988, + "lon": -123.396251 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-37.9°, 144.66667°)", + " Point B: (42.77361°, -81.18038°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 29.233988°", + " Longitude: -123.396251°", + "FINAL ANSWER: 29.233988, -123.396251" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 41.68921, + "lon": 2.48965, + "name": "Sant Celoni" + }, + "point_b": { + "lat": 36.54569, + "lon": 4.05712, + "name": "Tizi-n-Tleta" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 39.12007, + "lon": 3.302013 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (41.68921°, 2.48965°)", + " Point B: (36.54569°, 4.05712°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 39.120070°", + " Longitude: 3.302013°", + "FINAL ANSWER: 39.120070, 3.302013" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 55.63826, + "lon": 109.32709, + "name": "Severobaykal’sk" + }, + "point_b": { + "lat": 50.53439, + "lon": 36.68462, + "name": "Razumnoye" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 58.791702, + "lon": 70.508377 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (55.63826°, 109.32709°)", + " Point B: (50.53439°, 36.68462°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 58.791702°", + " Longitude: 70.508377°", + "FINAL ANSWER: 58.791702, 70.508377" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 40.9558, + "lon": 14.27201, + "name": "Frattaminore" + }, + "point_b": { + "lat": 31.76212, + "lon": -95.63079, + "name": "Palestine" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 44.600533, + "lon": -74.830341 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (40.9558°, 14.27201°)", + " Point B: (31.76212°, -95.63079°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 44.600533°", + " Longitude: -74.830341°", + "FINAL ANSWER: 44.600533, -74.830341" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -41.13827, + "lon": 175.0502, + "name": "Upper Hutt" + }, + "point_b": { + "lat": 56.17527, + "lon": 36.97082, + "name": "Solnechnogorsk" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -12.078464, + "lon": 148.355954 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-41.13827°, 175.0502°)", + " Point B: (56.17527°, 36.97082°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -12.078464°", + " Longitude: 148.355954°", + "FINAL ANSWER: -12.078464, 148.355954" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -29.26737, + "lon": 26.72595, + "name": "Botshabelo" + }, + "point_b": { + "lat": 35.14953, + "lon": -90.04898, + "name": "Memphis" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 23.32004, + "lon": -56.021629 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-29.26737°, 26.72595°)", + " Point B: (35.14953°, -90.04898°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 23.320040°", + " Longitude: -56.021629°", + "FINAL ANSWER: 23.320040, -56.021629" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 52.40786, + "lon": 13.22514, + "name": "Kleinmachnow" + }, + "point_b": { + "lat": 52.085, + "lon": 4.88333, + "name": "Woerden" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 52.31996, + "lon": 9.039033 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (52.40786°, 13.22514°)", + " Point B: (52.085°, 4.88333°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 52.319960°", + " Longitude: 9.039033°", + "FINAL ANSWER: 52.319960, 9.039033" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 48.0021, + "lon": 0.20251, + "name": "Le Mans" + }, + "point_b": { + "lat": -25.5036, + "lon": -54.65067, + "name": "Ciudad del Este" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 31.24727, + "lon": -18.75954 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (48.0021°, 0.20251°)", + " Point B: (-25.5036°, -54.65067°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 31.247270°", + " Longitude: -18.759540°", + "FINAL ANSWER: 31.247270, -18.759540" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 51.67873, + "lon": 6.15895, + "name": "Goch" + }, + "point_b": { + "lat": 24.656, + "lon": 68.837, + "name": "Badin" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 42.434676, + "lon": 44.058689 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (51.67873°, 6.15895°)", + " Point B: (24.656°, 68.837°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 42.434676°", + " Longitude: 44.058689°", + "FINAL ANSWER: 42.434676, 44.058689" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 9.54189, + "lon": 76.34236, + "name": "Komalapuram" + }, + "point_b": { + "lat": 64.571, + "lon": 30.57667, + "name": "Kostomuksha" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 52.784391, + "lon": 51.507895 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (9.54189°, 76.34236°)", + " Point B: (64.571°, 30.57667°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 52.784391°", + " Longitude: 51.507895°", + "FINAL ANSWER: 52.784391, 51.507895" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -33.75881, + "lon": 150.99292, + "name": "Baulkham Hills" + }, + "point_b": { + "lat": 44.74471, + "lon": -0.68194, + "name": "Cestas" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -7.545561, + "lon": 119.817486 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-33.75881°, 150.99292°)", + " Point B: (44.74471°, -0.68194°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -7.545561°", + " Longitude: 119.817486°", + "FINAL ANSWER: -7.545561, 119.817486" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -39.64355, + "lon": -72.33269, + "name": "Panguipulli" + }, + "point_b": { + "lat": -13.62015, + "lon": 29.3939, + "name": "Mkushi" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -38.186868, + "lon": -13.364845 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-39.64355°, -72.33269°)", + " Point B: (-13.62015°, 29.3939°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -38.186868°", + " Longitude: -13.364845°", + "FINAL ANSWER: -38.186868, -13.364845" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 26.26841, + "lon": 73.00594, + "name": "Jodhpur" + }, + "point_b": { + "lat": 25.0321, + "lon": -111.66256, + "name": "Ciudad Constitución" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 56.93637, + "lon": -116.878143 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (26.26841°, 73.00594°)", + " Point B: (25.0321°, -111.66256°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 56.936370°", + " Longitude: -116.878143°", + "FINAL ANSWER: 56.936370, -116.878143" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 40.62333, + "lon": 49.55861, + "name": "Hacı Zeynalabdin" + }, + "point_b": { + "lat": 13.04603, + "lon": 121.46205, + "name": "Pinamalayan" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 38.068038, + "lon": 71.30866 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (40.62333°, 49.55861°)", + " Point B: (13.04603°, 121.46205°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 38.068038°", + " Longitude: 71.308660°", + "FINAL ANSWER: 38.068038, 71.308660" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -21.3777, + "lon": 55.61691, + "name": "Saint-Joseph" + }, + "point_b": { + "lat": -22.46889, + "lon": -44.44667, + "name": "Resende" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -29.652904, + "lon": -20.46378 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-21.3777°, 55.61691°)", + " Point B: (-22.46889°, -44.44667°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -29.652904°", + " Longitude: -20.463780°", + "FINAL ANSWER: -29.652904, -20.463780" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -1.165, + "lon": 15.97, + "name": "Oyo" + }, + "point_b": { + "lat": -7.11799, + "lon": 39.20782, + "name": "Mkuranga" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -2.710204, + "lon": 21.749966 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-1.165°, 15.97°)", + " Point B: (-7.11799°, 39.20782°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -2.710204°", + " Longitude: 21.749966°", + "FINAL ANSWER: -2.710204, 21.749966" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -21.09083, + "lon": -45.09139, + "name": "Perdões" + }, + "point_b": { + "lat": 11.31004, + "lon": 106.09828, + "name": "Tây Ninh" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -25.591216, + "lon": -4.188418 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-21.09083°, -45.09139°)", + " Point B: (11.31004°, 106.09828°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -25.591216°", + " Longitude: -4.188418°", + "FINAL ANSWER: -25.591216, -4.188418" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -23.065, + "lon": -54.19056, + "name": "Naviraí" + }, + "point_b": { + "lat": 22.33023, + "lon": 114.15945, + "name": "Sham Shui Po" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 12.372223, + "lon": 70.912443 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-23.065°, -54.19056°)", + " Point B: (22.33023°, 114.15945°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 12.372223°", + " Longitude: 70.912443°", + "FINAL ANSWER: 12.372223, 70.912443" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 33.86726, + "lon": -112.14682, + "name": "Anthem" + }, + "point_b": { + "lat": -25.44613, + "lon": -56.43928, + "name": "Coronel Oviedo" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 4.758761, + "lon": -83.024064 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (33.86726°, -112.14682°)", + " Point B: (-25.44613°, -56.43928°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 4.758761°", + " Longitude: -83.024064°", + "FINAL ANSWER: 4.758761, -83.024064" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 22.60291, + "lon": 88.27751, + "name": "Bankra" + }, + "point_b": { + "lat": 27.2872, + "lon": 68.50623, + "name": "Ranipur" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 25.274264, + "lon": 78.581829 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (22.60291°, 88.27751°)", + " Point B: (27.2872°, 68.50623°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 25.274264°", + " Longitude: 78.581829°", + "FINAL ANSWER: 25.274264, 78.581829" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 13.41778, + "lon": -16.66667, + "name": "Faji Kunda" + }, + "point_b": { + "lat": 8.97054, + "lon": 37.76117, + "name": "Guder" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 11.056067, + "lon": 24.34894 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (13.41778°, -16.66667°)", + " Point B: (8.97054°, 37.76117°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 11.056067°", + " Longitude: 24.348940°", + "FINAL ANSWER: 11.056067, 24.348940" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 1.7541, + "lon": 103.2798, + "name": "Kawasan Penempatan Ulu Sungai Benut" + }, + "point_b": { + "lat": 51.49777, + "lon": 44.47678, + "name": "Kalininsk" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 29.707939, + "lon": 81.339522 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (1.7541°, 103.2798°)", + " Point B: (51.49777°, 44.47678°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 29.707939°", + " Longitude: 81.339522°", + "FINAL ANSWER: 29.707939, 81.339522" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -10.73333, + "lon": -37.49333, + "name": "Campo do Brito" + }, + "point_b": { + "lat": 50.64336, + "lon": 7.2278, + "name": "Bad Honnef" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 36.763046, + "lon": -9.13739 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-10.73333°, -37.49333°)", + " Point B: (50.64336°, 7.2278°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 36.763046°", + " Longitude: -9.137390°", + "FINAL ANSWER: 36.763046, -9.137390" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 26.82649, + "lon": -109.64206, + "name": "Huatabampo" + }, + "point_b": { + "lat": 12.79163, + "lon": 78.71644, + "name": "Ambur" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 46.730944, + "lon": 88.323282 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (26.82649°, -109.64206°)", + " Point B: (12.79163°, 78.71644°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 46.730944°", + " Longitude: 88.323282°", + "FINAL ANSWER: 46.730944, 88.323282" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 35.3108, + "lon": 139.81877, + "name": "Futtsu" + }, + "point_b": { + "lat": 12.98456, + "lon": 80.1747, + "name": "Meenambakkam" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 32.363721, + "lon": 122.739713 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (35.3108°, 139.81877°)", + " Point B: (12.98456°, 80.1747°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 32.363721°", + " Longitude: 122.739713°", + "FINAL ANSWER: 32.363721, 122.739713" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 9.73586, + "lon": -75.52626, + "name": "San Onofre" + }, + "point_b": { + "lat": 26.03033, + "lon": 119.59739, + "name": "Tantou" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 56.266181, + "lon": 144.973034 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (9.73586°, -75.52626°)", + " Point B: (26.03033°, 119.59739°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 56.266181°", + " Longitude: 144.973034°", + "FINAL ANSWER: 56.266181, 144.973034" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 50.5752, + "lon": 19.32461, + "name": "Myszków" + }, + "point_b": { + "lat": 20.3306, + "lon": 74.24467, + "name": "Chāndor" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 38.606757, + "lon": 52.495182 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (50.5752°, 19.32461°)", + " Point B: (20.3306°, 74.24467°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 38.606757°", + " Longitude: 52.495182°", + "FINAL ANSWER: 38.606757, 52.495182" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 45.256, + "lon": 131.11637, + "name": "Jidong" + }, + "point_b": { + "lat": -23.83322, + "lon": 30.16351, + "name": "Tzaneen" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 34.374176, + "lon": 96.380668 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (45.256°, 131.11637°)", + " Point B: (-23.83322°, 30.16351°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 34.374176°", + " Longitude: 96.380668°", + "FINAL ANSWER: 34.374176, 96.380668" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 2.14838, + "lon": 27.99466, + "name": "Wamba" + }, + "point_b": { + "lat": 44.83061, + "lon": -0.52675, + "name": "Floirac" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 34.763411, + "lon": 8.895895 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (2.14838°, 27.99466°)", + " Point B: (44.83061°, -0.52675°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 34.763411°", + " Longitude: 8.895895°", + "FINAL ANSWER: 34.763411, 8.895895" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 31.99289, + "lon": 44.92552, + "name": "Ad Dīwānīyah" + }, + "point_b": { + "lat": 25.3604, + "lon": 60.3995, + "name": "Konārak" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 27.178709, + "lon": 56.713693 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (31.99289°, 44.92552°)", + " Point B: (25.3604°, 60.3995°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 27.178709°", + " Longitude: 56.713693°", + "FINAL ANSWER: 27.178709, 56.713693" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 5.35113, + "lon": -0.62313, + "name": "Winneba" + }, + "point_b": { + "lat": -0.60467, + "lon": 30.64851, + "name": "Mbarara" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 2.464317, + "lon": 15.047263 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (5.35113°, -0.62313°)", + " Point B: (-0.60467°, 30.64851°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 2.464317°", + " Longitude: 15.047263°", + "FINAL ANSWER: 2.464317, 15.047263" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 63.78977, + "lon": 74.52301, + "name": "Muravlenko" + }, + "point_b": { + "lat": -32.0671, + "lon": -60.64267, + "name": "Diamante" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 58.562664, + "lon": -0.652591 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (63.78977°, 74.52301°)", + " Point B: (-32.0671°, -60.64267°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 58.562664°", + " Longitude: -0.652591°", + "FINAL ANSWER: 58.562664, -0.652591" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 16.79183, + "lon": -62.21058, + "name": "Brades" + }, + "point_b": { + "lat": 33.90331, + "lon": -5.36868, + "name": "Sabaa Aiyoun" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 32.019929, + "lon": -21.147409 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (16.79183°, -62.21058°)", + " Point B: (33.90331°, -5.36868°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 32.019929°", + " Longitude: -21.147409°", + "FINAL ANSWER: 32.019929, -21.147409" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 7.82719, + "lon": 6.07502, + "name": "Kabba" + }, + "point_b": { + "lat": 6.76229, + "lon": -6.8638, + "name": "Zoukougbeu" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 7.340981, + "lon": -0.402119 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (7.82719°, 6.07502°)", + " Point B: (6.76229°, -6.8638°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 7.340981°", + " Longitude: -0.402119°", + "FINAL ANSWER: 7.340981, -0.402119" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -16.70806, + "lon": -49.09306, + "name": "Senador Canedo" + }, + "point_b": { + "lat": 13.03299, + "lon": 8.32351, + "name": "Daura" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -9.704296, + "lon": -34.290962 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-16.70806°, -49.09306°)", + " Point B: (13.03299°, 8.32351°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -9.704296°", + " Longitude: -34.290962°", + "FINAL ANSWER: -9.704296, -34.290962" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 26.41667, + "lon": 101.01667, + "name": "Renhe" + }, + "point_b": { + "lat": -26.22861, + "lon": -52.67056, + "name": "Pato Branco" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -16.269608, + "lon": -11.892459 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (26.41667°, 101.01667°)", + " Point B: (-26.22861°, -52.67056°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -16.269608°", + " Longitude: -11.892459°", + "FINAL ANSWER: -16.269608, -11.892459" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 44.66885, + "lon": -90.1718, + "name": "Marshfield" + }, + "point_b": { + "lat": -24.42, + "lon": -53.52139, + "name": "Assis Chateaubriand" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -6.954579, + "lon": -61.825401 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (44.66885°, -90.1718°)", + " Point B: (-24.42°, -53.52139°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -6.954579°", + " Longitude: -61.825401°", + "FINAL ANSWER: -6.954579, -61.825401" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 35.31558, + "lon": 139.31625, + "name": "Ōiso" + }, + "point_b": { + "lat": 59.92335, + "lon": 32.33966, + "name": "Volkhov" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 49.11214, + "lon": 126.003645 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (35.31558°, 139.31625°)", + " Point B: (59.92335°, 32.33966°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 49.112140°", + " Longitude: 126.003645°", + "FINAL ANSWER: 49.112140, 126.003645" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -17.78629, + "lon": -63.18117, + "name": "Santa Cruz de la Sierra" + }, + "point_b": { + "lat": -36.93754, + "lon": 174.65584, + "name": "Titirangi" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -34.931901, + "lon": -84.714352 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-17.78629°, -63.18117°)", + " Point B: (-36.93754°, 174.65584°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -34.931901°", + " Longitude: -84.714352°", + "FINAL ANSWER: -34.931901, -84.714352" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 39.07039, + "lon": -76.54524, + "name": "Severna Park" + }, + "point_b": { + "lat": 31.80437, + "lon": 44.4893, + "name": "Al Mishkhāb" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 46.927231, + "lon": 22.490776 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (39.07039°, -76.54524°)", + " Point B: (31.80437°, 44.4893°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 46.927231°", + " Longitude: 22.490776°", + "FINAL ANSWER: 46.927231, 22.490776" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -23.26917, + "lon": -51.04806, + "name": "Ibiporã" + }, + "point_b": { + "lat": 36.24624, + "lon": 139.07204, + "name": "Fujioka" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 60.491561, + "lon": -167.94255 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-23.26917°, -51.04806°)", + " Point B: (36.24624°, 139.07204°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 60.491561°", + " Longitude: -167.942550°", + "FINAL ANSWER: 60.491561, -167.942550" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -4.18396, + "lon": 13.2859, + "name": "Nkayi" + }, + "point_b": { + "lat": -7.2036, + "lon": 146.64014, + "name": "Bulolo" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -10.901878, + "lon": 45.924301 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-4.18396°, 13.2859°)", + " Point B: (-7.2036°, 146.64014°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -10.901878°", + " Longitude: 45.924301°", + "FINAL ANSWER: -10.901878, 45.924301" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 46.92119, + "lon": 26.92646, + "name": "Roman" + }, + "point_b": { + "lat": 15.35116, + "lon": 121.00393, + "name": "Peñaranda" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 29.457477, + "lon": 105.00475 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (46.92119°, 26.92646°)", + " Point B: (15.35116°, 121.00393°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 29.457477°", + " Longitude: 105.004750°", + "FINAL ANSWER: 29.457477, 105.004750" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 11.48333, + "lon": 37.58333, + "name": "T’īs Isat" + }, + "point_b": { + "lat": 51.60794, + "lon": 4.7915, + "name": "Hoge Vucht" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 42.517498, + "lon": 16.420152 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (11.48333°, 37.58333°)", + " Point B: (51.60794°, 4.7915°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 42.517498°", + " Longitude: 16.420152°", + "FINAL ANSWER: 42.517498, 16.420152" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 38.5503, + "lon": 44.9521, + "name": "Khowy" + }, + "point_b": { + "lat": -34.58333, + "lon": -58.38333, + "name": "Retiro" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 3.194306, + "lon": -8.576516 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (38.5503°, 44.9521°)", + " Point B: (-34.58333°, -58.38333°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 3.194306°", + " Longitude: -8.576516°", + "FINAL ANSWER: 3.194306, -8.576516" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 32.58986, + "lon": -96.85695, + "name": "DeSoto" + }, + "point_b": { + "lat": -36.9482, + "lon": 174.87019, + "name": "Otara" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -3.034022, + "lon": -139.525106 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (32.58986°, -96.85695°)", + " Point B: (-36.9482°, 174.87019°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -3.034022°", + " Longitude: -139.525106°", + "FINAL ANSWER: -3.034022, -139.525106" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 30.58123, + "lon": 107.68064, + "name": "Helin" + }, + "point_b": { + "lat": 32.68325, + "lon": 51.60158, + "name": "Rehnān" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 34.622472, + "lon": 65.605222 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (30.58123°, 107.68064°)", + " Point B: (32.68325°, 51.60158°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 34.622472°", + " Longitude: 65.605222°", + "FINAL ANSWER: 34.622472, 65.605222" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 50.99687, + "lon": 8.11062, + "name": "Hilchenbach" + }, + "point_b": { + "lat": 43.56491, + "lon": 27.83138, + "name": "Dobrich" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 47.703485, + "lon": 18.671429 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (50.99687°, 8.11062°)", + " Point B: (43.56491°, 27.83138°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 47.703485°", + " Longitude: 18.671429°", + "FINAL ANSWER: 47.703485, 18.671429" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -8.515, + "lon": -41.005, + "name": "Afrânio" + }, + "point_b": { + "lat": 35.53333, + "lon": 135.1, + "name": "Yotsutsuji" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 29.377596, + "lon": -36.091761 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-8.515°, -41.005°)", + " Point B: (35.53333°, 135.1°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 29.377596°", + " Longitude: -36.091761°", + "FINAL ANSWER: 29.377596, -36.091761" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 40.46396, + "lon": -3.63625, + "name": "Canillas" + }, + "point_b": { + "lat": 51.37992, + "lon": -0.24445, + "name": "Worcester Park" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 48.660887, + "lon": -1.226457 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (40.46396°, -3.63625°)", + " Point B: (51.37992°, -0.24445°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 48.660887°", + " Longitude: -1.226457°", + "FINAL ANSWER: 48.660887, -1.226457" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 10.24752, + "lon": -68.76966, + "name": "Boraure" + }, + "point_b": { + "lat": -6.63784, + "lon": 38.35396, + "name": "Chalinze" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 3.036778, + "lon": -14.844885 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (10.24752°, -68.76966°)", + " Point B: (-6.63784°, 38.35396°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 3.036778°", + " Longitude: -14.844885°", + "FINAL ANSWER: 3.036778, -14.844885" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 43.30667, + "lon": 128.51139, + "name": "Dashitou" + }, + "point_b": { + "lat": 15.02995, + "lon": -91.14876, + "name": "Santa Cruz del Quiché" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 56.882309, + "lon": -140.018919 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (43.30667°, 128.51139°)", + " Point B: (15.02995°, -91.14876°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 56.882309°", + " Longitude: -140.018919°", + "FINAL ANSWER: 56.882309, -140.018919" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 28.84122, + "lon": 112.35505, + "name": "Qionghu" + }, + "point_b": { + "lat": -33.96109, + "lon": 25.61494, + "name": "Port Elizabeth" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 13.521474, + "lon": 89.979141 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (28.84122°, 112.35505°)", + " Point B: (-33.96109°, 25.61494°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 13.521474°", + " Longitude: 89.979141°", + "FINAL ANSWER: 13.521474, 89.979141" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 41.27621, + "lon": -72.86843, + "name": "East Haven" + }, + "point_b": { + "lat": 12.4386, + "lon": -2.03279, + "name": "Kindi" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 22.796032, + "lon": -16.032149 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (41.27621°, -72.86843°)", + " Point B: (12.4386°, -2.03279°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 22.796032°", + " Longitude: -16.032149°", + "FINAL ANSWER: 22.796032, -16.032149" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 48.84232, + "lon": 9.23028, + "name": "Stuttgart Mühlhausen" + }, + "point_b": { + "lat": -36.90694, + "lon": 174.68704, + "name": "New Lynn" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 33.318572, + "lon": 129.215471 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (48.84232°, 9.23028°)", + " Point B: (-36.90694°, 174.68704°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 33.318572°", + " Longitude: 129.215471°", + "FINAL ANSWER: 33.318572, 129.215471" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 29.57991, + "lon": 71.75213, + "name": "Dhanot" + }, + "point_b": { + "lat": 50.23271, + "lon": 12.87117, + "name": "Karlovy Vary" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 37.287343, + "lon": 60.640258 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (29.57991°, 71.75213°)", + " Point B: (50.23271°, 12.87117°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 37.287343°", + " Longitude: 60.640258°", + "FINAL ANSWER: 37.287343, 60.640258" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 35.74045, + "lon": 139.63136, + "name": "Nukui" + }, + "point_b": { + "lat": 47.8974, + "lon": -122.18154, + "name": "Eastmont" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 46.681968, + "lon": 157.546214 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (35.74045°, 139.63136°)", + " Point B: (47.8974°, -122.18154°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 46.681968°", + " Longitude: 157.546214°", + "FINAL ANSWER: 46.681968, 157.546214" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -1.74639, + "lon": -47.05944, + "name": "Capitão Poço" + }, + "point_b": { + "lat": -3.31987, + "lon": 114.59075, + "name": "Banjarmasin" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -15.506975, + "lon": 33.550148 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-1.74639°, -47.05944°)", + " Point B: (-3.31987°, 114.59075°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -15.506975°", + " Longitude: 33.550148°", + "FINAL ANSWER: -15.506975, 33.550148" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -12.69056, + "lon": -43.18417, + "name": "Paratinga" + }, + "point_b": { + "lat": 43.30727, + "lon": 124.33371, + "name": "Lishu" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 71.852872, + "lon": 75.114184 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-12.69056°, -43.18417°)", + " Point B: (43.30727°, 124.33371°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 71.852872°", + " Longitude: 75.114184°", + "FINAL ANSWER: 71.852872, 75.114184" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 18.51957, + "lon": -88.30397, + "name": "Chetumal" + }, + "point_b": { + "lat": 49.443, + "lon": 7.77161, + "name": "Kaiserslautern" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 44.627241, + "lon": -51.979836 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (18.51957°, -88.30397°)", + " Point B: (49.443°, 7.77161°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 44.627241°", + " Longitude: -51.979836°", + "FINAL ANSWER: 44.627241, -51.979836" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 27.91855, + "lon": -15.43433, + "name": "Ingenio" + }, + "point_b": { + "lat": 41.19203, + "lon": -8.54118, + "name": "Baguim do Monte" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 34.603447, + "lon": -12.264272 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (27.91855°, -15.43433°)", + " Point B: (41.19203°, -8.54118°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 34.603447°", + " Longitude: -12.264272°", + "FINAL ANSWER: 34.603447, -12.264272" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -17.89194, + "lon": -39.37194, + "name": "Nova Viçosa" + }, + "point_b": { + "lat": 11.58528, + "lon": 122.75111, + "name": "Roxas City" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -4.976213, + "lon": 85.703436 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-17.89194°, -39.37194°)", + " Point B: (11.58528°, 122.75111°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -4.976213°", + " Longitude: 85.703436°", + "FINAL ANSWER: -4.976213, 85.703436" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 1.74016, + "lon": 98.78117, + "name": "Sibolga" + }, + "point_b": { + "lat": 40.4842, + "lon": -88.99369, + "name": "Bloomington" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 35.577347, + "lon": 104.801448 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (1.74016°, 98.78117°)", + " Point B: (40.4842°, -88.99369°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 35.577347°", + " Longitude: 104.801448°", + "FINAL ANSWER: 35.577347, 104.801448" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 45.80397, + "lon": 15.16886, + "name": "Novo Mesto" + }, + "point_b": { + "lat": 30.54197, + "lon": 107.57518, + "name": "Yinping" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 41.227057, + "lon": 90.313377 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (45.80397°, 15.16886°)", + " Point B: (30.54197°, 107.57518°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 41.227057°", + " Longitude: 90.313377°", + "FINAL ANSWER: 41.227057, 90.313377" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -7.1502, + "lon": 111.8817, + "name": "Bojonegoro" + }, + "point_b": { + "lat": 22.06046, + "lon": 88.10975, + "name": "Haldia" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 7.616383, + "lon": 100.406927 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-7.1502°, 111.8817°)", + " Point B: (22.06046°, 88.10975°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 7.616383°", + " Longitude: 100.406927°", + "FINAL ANSWER: 7.616383, 100.406927" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 10.86225, + "lon": 0.20762, + "name": "Dapaong" + }, + "point_b": { + "lat": 38.90122, + "lon": -77.26526, + "name": "Vienna" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 36.817171, + "lon": -54.080015 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (10.86225°, 0.20762°)", + " Point B: (38.90122°, -77.26526°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 36.817171°", + " Longitude: -54.080015°", + "FINAL ANSWER: 36.817171, -54.080015" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 21.61951, + "lon": 39.69659, + "name": "Al Jumūm" + }, + "point_b": { + "lat": -21.53667, + "lon": -49.85806, + "name": "Promissão" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -11.589909, + "lon": -26.62421 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (21.61951°, 39.69659°)", + " Point B: (-21.53667°, -49.85806°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -11.589909°", + " Longitude: -26.624210°", + "FINAL ANSWER: -11.589909, -26.624210" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 52.51732, + "lon": 13.58871, + "name": "Kaulsdorf" + }, + "point_b": { + "lat": 40.41896, + "lon": -80.58952, + "name": "Weirton" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 57.752132, + "lon": -11.794979 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (52.51732°, 13.58871°)", + " Point B: (40.41896°, -80.58952°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 57.752132°", + " Longitude: -11.794979°", + "FINAL ANSWER: 57.752132, -11.794979" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -0.55085, + "lon": 166.9252, + "name": "Yaren" + }, + "point_b": { + "lat": 25.69893, + "lon": 32.6421, + "name": "Luxor" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 29.677876, + "lon": 106.816635 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-0.55085°, 166.9252°)", + " Point B: (25.69893°, 32.6421°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 29.677876°", + " Longitude: 106.816635°", + "FINAL ANSWER: 29.677876, 106.816635" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 40.38333, + "lon": -3.61667, + "name": "Vallecas" + }, + "point_b": { + "lat": -11.79667, + "lon": -49.52889, + "name": "Formoso do Araguaia" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 28.524566, + "lon": -18.15527 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (40.38333°, -3.61667°)", + " Point B: (-11.79667°, -49.52889°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 28.524566°", + " Longitude: -18.155270°", + "FINAL ANSWER: 28.524566, -18.155270" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 55.73333, + "lon": 37.66667, + "name": "Taganskiy" + }, + "point_b": { + "lat": -12.58946, + "lon": -69.19948, + "name": "Puerto Maldonado" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 31.9665, + "lon": -35.651452 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (55.73333°, 37.66667°)", + " Point B: (-12.58946°, -69.19948°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 31.966500°", + " Longitude: -35.651452°", + "FINAL ANSWER: 31.966500, -35.651452" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 36.55528, + "lon": 2.79028, + "name": "Oued el Alleug" + }, + "point_b": { + "lat": 36.61033, + "lon": -88.31476, + "name": "Murray" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 43.91079, + "lon": -18.08714 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (36.55528°, 2.79028°)", + " Point B: (36.61033°, -88.31476°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 43.910790°", + " Longitude: -18.087140°", + "FINAL ANSWER: 43.910790, -18.087140" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 7.4698, + "lon": 80.6217, + "name": "Matale" + }, + "point_b": { + "lat": -3.83778, + "lon": -50.6375, + "name": "Pacajá" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 0.330033, + "lon": -18.034001 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (7.4698°, 80.6217°)", + " Point B: (-3.83778°, -50.6375°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 0.330033°", + " Longitude: -18.034001°", + "FINAL ANSWER: 0.330033, -18.034001" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 40.46001, + "lon": 39.47176, + "name": "Gümüşhane" + }, + "point_b": { + "lat": -34.424, + "lon": 150.89345, + "name": "Wollongong" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -16.105002, + "lon": 122.093714 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (40.46001°, 39.47176°)", + " Point B: (-34.424°, 150.89345°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -16.105002°", + " Longitude: 122.093714°", + "FINAL ANSWER: -16.105002, 122.093714" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 5.48956, + "lon": 6.00407, + "name": "Ughelli" + }, + "point_b": { + "lat": -17.06667, + "lon": 15.73333, + "name": "Ondjiva" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -0.160024, + "lon": 8.386436 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (5.48956°, 6.00407°)", + " Point B: (-17.06667°, 15.73333°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -0.160024°", + " Longitude: 8.386436°", + "FINAL ANSWER: -0.160024, 8.386436" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -36.12179, + "lon": 146.88809, + "name": "Wodonga" + }, + "point_b": { + "lat": 53.33333, + "lon": 8.48333, + "name": "Brake (Unterweser)" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 21.626479, + "lon": 99.223902 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-36.12179°, 146.88809°)", + " Point B: (53.33333°, 8.48333°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 21.626479°", + " Longitude: 99.223902°", + "FINAL ANSWER: 21.626479, 99.223902" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -37.74124, + "lon": 144.73631, + "name": "Caroline Springs" + }, + "point_b": { + "lat": -17.5976, + "lon": -44.73367, + "name": "Várzea da Palma" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -76.672625, + "lon": -81.648098 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-37.74124°, 144.73631°)", + " Point B: (-17.5976°, -44.73367°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -76.672625°", + " Longitude: -81.648098°", + "FINAL ANSWER: -76.672625, -81.648098" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 10.22677, + "lon": -67.33122, + "name": "La Victoria" + }, + "point_b": { + "lat": 16.61667, + "lon": 74.40442, + "name": "Hupari" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 36.038339, + "lon": 1.337642 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (10.22677°, -67.33122°)", + " Point B: (16.61667°, 74.40442°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 36.038339°", + " Longitude: 1.337642°", + "FINAL ANSWER: 36.038339, 1.337642" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 47.24878, + "lon": 6.01815, + "name": "Besançon" + }, + "point_b": { + "lat": -3.96426, + "lon": 39.5498, + "name": "Mazeras" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 22.475779, + "lon": 26.062829 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (47.24878°, 6.01815°)", + " Point B: (-3.96426°, 39.5498°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 22.475779°", + " Longitude: 26.062829°", + "FINAL ANSWER: 22.475779, 26.062829" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 36.67176, + "lon": 4.19176, + "name": "Tizi Rached" + }, + "point_b": { + "lat": 56.39733, + "lon": 38.71404, + "name": "Aleksandrov" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 47.804526, + "lon": 18.190816 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (36.67176°, 4.19176°)", + " Point B: (56.39733°, 38.71404°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 47.804526°", + " Longitude: 18.190816°", + "FINAL ANSWER: 47.804526, 18.190816" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 11.10983, + "lon": 77.98883, + "name": "Pottanūr" + }, + "point_b": { + "lat": 48.82586, + "lon": 2.3508, + "name": "Maison Blanche" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 24.14536, + "lon": 64.839409 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (11.10983°, 77.98883°)", + " Point B: (48.82586°, 2.3508°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 24.145360°", + " Longitude: 64.839409°", + "FINAL ANSWER: 24.145360, 64.839409" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 40.23645, + "lon": -83.36714, + "name": "Marysville" + }, + "point_b": { + "lat": 11.73333, + "lon": 38.46667, + "name": "Nefas Mewch’a" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 48.62989, + "lon": -48.044184 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (40.23645°, -83.36714°)", + " Point B: (11.73333°, 38.46667°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 48.629890°", + " Longitude: -48.044184°", + "FINAL ANSWER: 48.629890, -48.044184" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -33.08338, + "lon": -68.47312, + "name": "San Martín" + }, + "point_b": { + "lat": 38.0176, + "lon": 12.53617, + "name": "Trapani" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 21.942372, + "lon": -11.061307 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-33.08338°, -68.47312°)", + " Point B: (38.0176°, 12.53617°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 21.942372°", + " Longitude: -11.061307°", + "FINAL ANSWER: 21.942372, -11.061307" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 40.92538, + "lon": -74.27654, + "name": "Wayne" + }, + "point_b": { + "lat": 34.21334, + "lon": -118.57203, + "name": "Winnetka" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 40.899866, + "lon": -85.98255 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (40.92538°, -74.27654°)", + " Point B: (34.21334°, -118.57203°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 40.899866°", + " Longitude: -85.982550°", + "FINAL ANSWER: 40.899866, -85.982550" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 7.43636, + "lon": 5.45925, + "name": "Emure-Ekiti" + }, + "point_b": { + "lat": -6.7475, + "lon": -51.16111, + "name": "Tucumã" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 0.391222, + "lon": -22.874013 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (7.43636°, 5.45925°)", + " Point B: (-6.7475°, -51.16111°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 0.391222°", + " Longitude: -22.874013°", + "FINAL ANSWER: 0.391222, -22.874013" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -18.07051, + "lon": 178.51313, + "name": "Nasinu" + }, + "point_b": { + "lat": -3.10056, + "lon": -45.03361, + "name": "Matinha" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -26.935162, + "lon": -146.901374 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-18.07051°, 178.51313°)", + " Point B: (-3.10056°, -45.03361°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -26.935162°", + " Longitude: -146.901374°", + "FINAL ANSWER: -26.935162, -146.901374" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 39.9036, + "lon": 8.59257, + "name": "Oristano" + }, + "point_b": { + "lat": -18.76969, + "lon": 46.04653, + "name": "Tsiroanomandidy" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 11.136387, + "lon": 29.355121 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (39.9036°, 8.59257°)", + " Point B: (-18.76969°, 46.04653°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 11.136387°", + " Longitude: 29.355121°", + "FINAL ANSWER: 11.136387, 29.355121" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 32.72541, + "lon": -97.32085, + "name": "Fort Worth" + }, + "point_b": { + "lat": 39.68442, + "lon": 106.81583, + "name": "Wuhai" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 62.833221, + "lon": 126.777197 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (32.72541°, -97.32085°)", + " Point B: (39.68442°, 106.81583°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 62.833221°", + " Longitude: 126.777197°", + "FINAL ANSWER: 62.833221, 126.777197" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -3.55592, + "lon": -80.44258, + "name": "Tumbes" + }, + "point_b": { + "lat": -27.04346, + "lon": -55.22698, + "name": "Jardín América" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -15.658182, + "lon": -68.56355 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-3.55592°, -80.44258°)", + " Point B: (-27.04346°, -55.22698°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -15.658182°", + " Longitude: -68.563550°", + "FINAL ANSWER: -15.658182, -68.563550" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 23.31667, + "lon": 58.01667, + "name": "Sufālat Samā’il" + }, + "point_b": { + "lat": 48.93564, + "lon": 2.35387, + "name": "Saint-Denis" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 31.879469, + "lon": 47.602601 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (23.31667°, 58.01667°)", + " Point B: (48.93564°, 2.35387°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 31.879469°", + " Longitude: 47.602601°", + "FINAL ANSWER: 31.879469, 47.602601" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 55.78438, + "lon": -4.10007, + "name": "High Blantyre" + }, + "point_b": { + "lat": 49.37511, + "lon": 35.45493, + "name": "Berestyn" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 54.237216, + "lon": 17.184721 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (55.78438°, -4.10007°)", + " Point B: (49.37511°, 35.45493°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 54.237216°", + " Longitude: 17.184721°", + "FINAL ANSWER: 54.237216, 17.184721" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 14.0683, + "lon": 121.3256, + "name": "San Pablo" + }, + "point_b": { + "lat": -32.92953, + "lon": 151.7801, + "name": "Newcastle" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 2.167822, + "lon": 128.432319 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (14.0683°, 121.3256°)", + " Point B: (-32.92953°, 151.7801°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 2.167822°", + " Longitude: 128.432319°", + "FINAL ANSWER: 2.167822, 128.432319" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 31.22078, + "lon": 74.25483, + "name": "Raja Jang" + }, + "point_b": { + "lat": 25.31258, + "lon": 86.48888, + "name": "Jamālpur" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 26.889028, + "lon": 83.556214 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (31.22078°, 74.25483°)", + " Point B: (25.31258°, 86.48888°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 26.889028°", + " Longitude: 83.556214°", + "FINAL ANSWER: 26.889028, 83.556214" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 33.50476, + "lon": 133.44475, + "name": "Tosa" + }, + "point_b": { + "lat": -3.38193, + "lon": 29.36142, + "name": "Bujumbura" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 10.880875, + "lon": 51.083924 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (33.50476°, 133.44475°)", + " Point B: (-3.38193°, 29.36142°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 10.880875°", + " Longitude: 51.083924°", + "FINAL ANSWER: 10.880875, 51.083924" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 33.55808, + "lon": -7.48647, + "name": "Tit Mellil" + }, + "point_b": { + "lat": 13.98534, + "lon": 74.55531, + "name": "Bhatkal" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 30.222221, + "lon": 37.315667 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (33.55808°, -7.48647°)", + " Point B: (13.98534°, 74.55531°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 30.222221°", + " Longitude: 37.315667°", + "FINAL ANSWER: 30.222221, 37.315667" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -33.9209, + "lon": 151.12506, + "name": "Earlwood" + }, + "point_b": { + "lat": 10.61712, + "lon": -75.15146, + "name": "Luruaco" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -9.378426, + "lon": -101.477368 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-33.9209°, 151.12506°)", + " Point B: (10.61712°, -75.15146°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -9.378426°", + " Longitude: -101.477368°", + "FINAL ANSWER: -9.378426, -101.477368" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 5.26667, + "lon": -73.91667, + "name": "La Mesa" + }, + "point_b": { + "lat": 10.60516, + "lon": 123.0417, + "name": "Murcia" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 34.182275, + "lon": 157.372567 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (5.26667°, -73.91667°)", + " Point B: (10.60516°, 123.0417°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 34.182275°", + " Longitude: 157.372567°", + "FINAL ANSWER: 34.182275, 157.372567" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -33.88834, + "lon": 151.12274, + "name": "Ashfield" + }, + "point_b": { + "lat": 34.86158, + "lon": -1.33935, + "name": "Mansoûra" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 2.043168, + "lon": 76.249909 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-33.88834°, 151.12274°)", + " Point B: (34.86158°, -1.33935°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 2.043168°", + " Longitude: 76.249909°", + "FINAL ANSWER: 2.043168, 76.249909" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -24.2957, + "lon": 28.11415, + "name": "Vaalwater" + }, + "point_b": { + "lat": 22.20789, + "lon": 70.38343, + "name": "Kālāvad" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -1.119163, + "lon": 49.422196 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-24.2957°, 28.11415°)", + " Point B: (22.20789°, 70.38343°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -1.119163°", + " Longitude: 49.422196°", + "FINAL ANSWER: -1.119163, 49.422196" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 40.48116, + "lon": -3.69659, + "name": "La Paz" + }, + "point_b": { + "lat": 36.30078, + "lon": -119.78291, + "name": "Lemoore" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 52.383275, + "lon": -28.84254 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (40.48116°, -3.69659°)", + " Point B: (36.30078°, -119.78291°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 52.383275°", + " Longitude: -28.842540°", + "FINAL ANSWER: 52.383275, -28.842540" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 40.44286, + "lon": -3.65346, + "name": "San Pascual" + }, + "point_b": { + "lat": 42.32652, + "lon": -122.87559, + "name": "Medford" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 55.14262, + "lon": -98.919559 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (40.44286°, -3.65346°)", + " Point B: (42.32652°, -122.87559°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 55.142620°", + " Longitude: -98.919559°", + "FINAL ANSWER: 55.142620, -98.919559" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -24.73611, + "lon": -48.12278, + "name": "Cajati" + }, + "point_b": { + "lat": 50.22362, + "lon": 120.17092, + "name": "E’erguna" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 74.94527, + "lon": 45.270065 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-24.73611°, -48.12278°)", + " Point B: (50.22362°, 120.17092°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 74.945270°", + " Longitude: 45.270065°", + "FINAL ANSWER: 74.945270, 45.270065" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 6.88922, + "lon": -7.51952, + "name": "Diourouzon" + }, + "point_b": { + "lat": -37.88214, + "lon": 144.98215, + "name": "Elwood" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -46.589912, + "lon": 43.712297 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (6.88922°, -7.51952°)", + " Point B: (-37.88214°, 144.98215°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -46.589912°", + " Longitude: 43.712297°", + "FINAL ANSWER: -46.589912, 43.712297" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -11.68472, + "lon": -41.76889, + "name": "Canarana" + }, + "point_b": { + "lat": 32.46098, + "lon": -84.98771, + "name": "Columbus" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 22.217207, + "lon": -72.450654 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-11.68472°, -41.76889°)", + " Point B: (32.46098°, -84.98771°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 22.217207°", + " Longitude: -72.450654°", + "FINAL ANSWER: 22.217207, -72.450654" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 21.05447, + "lon": 86.5156, + "name": "Bhadrak" + }, + "point_b": { + "lat": 29.26778, + "lon": 120.22528, + "name": "Dongyang" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 26.141557, + "lon": 102.78503 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (21.05447°, 86.5156°)", + " Point B: (29.26778°, 120.22528°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 26.141557°", + " Longitude: 102.785030°", + "FINAL ANSWER: 26.141557, 102.785030" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 6.33815, + "lon": 5.62575, + "name": "Benin City" + }, + "point_b": { + "lat": 19.67798, + "lon": 97.20975, + "name": "Loikaw" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 20.608355, + "lon": 73.416059 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (6.33815°, 5.62575°)", + " Point B: (19.67798°, 97.20975°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 20.608355°", + " Longitude: 73.416059°", + "FINAL ANSWER: 20.608355, 73.416059" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 9.5928, + "lon": -5.19449, + "name": "Ferkessédougou" + }, + "point_b": { + "lat": 26.45, + "lon": 99.15, + "name": "Yingpan" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 30.143003, + "lon": 71.484167 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (9.5928°, -5.19449°)", + " Point B: (26.45°, 99.15°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 30.143003°", + " Longitude: 71.484167°", + "FINAL ANSWER: 30.143003, 71.484167" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 51.7175, + "lon": 9.18596, + "name": "Brakel" + }, + "point_b": { + "lat": 51.39717, + "lon": 0.17321, + "name": "Swanley" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 51.643689, + "lon": 4.663683 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (51.7175°, 9.18596°)", + " Point B: (51.39717°, 0.17321°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 51.643689°", + " Longitude: 4.663683°", + "FINAL ANSWER: 51.643689, 4.663683" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 2.61028, + "lon": -60.5975, + "name": "Cantá" + }, + "point_b": { + "lat": 30.96187, + "lon": 108.24327, + "name": "Nanmen" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 36.994077, + "lon": -48.311097 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (2.61028°, -60.5975°)", + " Point B: (30.96187°, 108.24327°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 36.994077°", + " Longitude: -48.311097°", + "FINAL ANSWER: 36.994077, -48.311097" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -21.97722, + "lon": -44.9325, + "name": "Caxambu" + }, + "point_b": { + "lat": 16.77348, + "lon": -3.00742, + "name": "Timbuktu" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -12.591708, + "lon": -33.875716 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-21.97722°, -44.9325°)", + " Point B: (16.77348°, -3.00742°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -12.591708°", + " Longitude: -33.875716°", + "FINAL ANSWER: -12.591708, -33.875716" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 28.92313, + "lon": -13.66579, + "name": "Puerto del Carmen" + }, + "point_b": { + "lat": 27.05524, + "lon": 79.9188, + "name": "Kannauj" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 37.819825, + "lon": 33.654965 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (28.92313°, -13.66579°)", + " Point B: (27.05524°, 79.9188°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 37.819825°", + " Longitude: 33.654965°", + "FINAL ANSWER: 37.819825, 33.654965" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -37.60075, + "lon": 145.09555, + "name": "Mernda" + }, + "point_b": { + "lat": 6.65175, + "lon": -4.20406, + "name": "Bongouanou" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -52.459969, + "lon": 99.772654 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-37.60075°, 145.09555°)", + " Point B: (6.65175°, -4.20406°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -52.459969°", + " Longitude: 99.772654°", + "FINAL ANSWER: -52.459969, 99.772654" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 12.07244, + "lon": 106.42078, + "name": "Snuol" + }, + "point_b": { + "lat": 22.24126, + "lon": -80.3911, + "name": "Palmira" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 47.417589, + "lon": 116.062248 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (12.07244°, 106.42078°)", + " Point B: (22.24126°, -80.3911°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 47.417589°", + " Longitude: 116.062248°", + "FINAL ANSWER: 47.417589, 116.062248" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -37.75819, + "lon": 145.00583, + "name": "Thornbury" + }, + "point_b": { + "lat": 19.64745, + "lon": -102.04897, + "name": "Paracho de Verduzco" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -15.964616, + "lon": -151.018499 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-37.75819°, 145.00583°)", + " Point B: (19.64745°, -102.04897°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -15.964616°", + " Longitude: -151.018499°", + "FINAL ANSWER: -15.964616, -151.018499" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 31.93221, + "lon": 35.04416, + "name": "Modiin Ilit" + }, + "point_b": { + "lat": 43.79773, + "lon": 81.52435, + "name": "Arewusitang" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 36.547405, + "lon": 45.103253 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (31.93221°, 35.04416°)", + " Point B: (43.79773°, 81.52435°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 36.547405°", + " Longitude: 45.103253°", + "FINAL ANSWER: 36.547405, 45.103253" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 45.54558, + "lon": 126.95191, + "name": "Acheng" + }, + "point_b": { + "lat": 30.22409, + "lon": -92.01984, + "name": "Lafayette" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 50.872277, + "lon": -108.682635 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (45.54558°, 126.95191°)", + " Point B: (30.22409°, -92.01984°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 50.872277°", + " Longitude: -108.682635°", + "FINAL ANSWER: 50.872277, -108.682635" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 37.97451, + "lon": 140.77202, + "name": "Kakuda" + }, + "point_b": { + "lat": 3.53944, + "lon": -76.30361, + "name": "Palmira" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 28.33882, + "lon": -96.771128 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (37.97451°, 140.77202°)", + " Point B: (3.53944°, -76.30361°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 28.338820°", + " Longitude: -96.771128°", + "FINAL ANSWER: 28.338820, -96.771128" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 32.29016, + "lon": 72.28182, + "name": "Jauharabad" + }, + "point_b": { + "lat": 50.51987, + "lon": 22.13968, + "name": "Nisko" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 44.167925, + "lon": 50.997244 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (32.29016°, 72.28182°)", + " Point B: (50.51987°, 22.13968°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 44.167925°", + " Longitude: 50.997244°", + "FINAL ANSWER: 44.167925, 50.997244" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -4.94028, + "lon": -37.97583, + "name": "Russas" + }, + "point_b": { + "lat": 18.85364, + "lon": -97.06229, + "name": "Ixtaczoquitlán" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 13.885262, + "lon": -81.520221 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-4.94028°, -37.97583°)", + " Point B: (18.85364°, -97.06229°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 13.885262°", + " Longitude: -81.520221°", + "FINAL ANSWER: 13.885262, -81.520221" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 47.3737, + "lon": -68.32512, + "name": "Edmundston" + }, + "point_b": { + "lat": 31.54351, + "lon": -8.76275, + "name": "Chichaoua" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 46.639061, + "lon": -50.957191 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (47.3737°, -68.32512°)", + " Point B: (31.54351°, -8.76275°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 46.639061°", + " Longitude: -50.957191°", + "FINAL ANSWER: 46.639061, -50.957191" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 38.10705, + "lon": 127.70632, + "name": "Hwacheon" + }, + "point_b": { + "lat": 0.29123, + "lon": 9.50465, + "name": "Owendo" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 41.49028, + "lon": 91.377249 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (38.10705°, 127.70632°)", + " Point B: (0.29123°, 9.50465°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 41.490280°", + " Longitude: 91.377249°", + "FINAL ANSWER: 41.490280, 91.377249" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 37.97476, + "lon": -87.55585, + "name": "Evansville" + }, + "point_b": { + "lat": 1.86391, + "lon": 9.76582, + "name": "Bata" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 28.535009, + "lon": -31.24706 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (37.97476°, -87.55585°)", + " Point B: (1.86391°, 9.76582°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 28.535009°", + " Longitude: -31.247060°", + "FINAL ANSWER: 28.535009, -31.247060" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 50.81667, + "lon": 8.1, + "name": "Wilnsdorf" + }, + "point_b": { + "lat": 38.01657, + "lon": 114.15328, + "name": "Siwei" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 50.22337, + "lon": 96.455299 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (50.81667°, 8.1°)", + " Point B: (38.01657°, 114.15328°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 50.223370°", + " Longitude: 96.455299°", + "FINAL ANSWER: 50.223370, 96.455299" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -22.92389, + "lon": -45.46167, + "name": "Pindamonhangaba" + }, + "point_b": { + "lat": 32.79335, + "lon": 12.48845, + "name": "Şabrātah" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 19.853161, + "lon": -4.034088 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-22.92389°, -45.46167°)", + " Point B: (32.79335°, 12.48845°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 19.853161°", + " Longitude: -4.034088°", + "FINAL ANSWER: 19.853161, -4.034088" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 40.49631, + "lon": -3.71957, + "name": "Mirasierra" + }, + "point_b": { + "lat": -21.2766, + "lon": 55.51766, + "name": "Le Tampon" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 11.003354, + "lon": 29.194356 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (40.49631°, -3.71957°)", + " Point B: (-21.2766°, 55.51766°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 11.003354°", + " Longitude: 29.194356°", + "FINAL ANSWER: 11.003354, 29.194356" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 41.63526, + "lon": -70.92701, + "name": "New Bedford" + }, + "point_b": { + "lat": -5.85746, + "lon": 144.23058, + "name": "Mount Hagen" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 20.849705, + "lon": 164.191474 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (41.63526°, -70.92701°)", + " Point B: (-5.85746°, 144.23058°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 20.849705°", + " Longitude: 164.191474°", + "FINAL ANSWER: 20.849705, 164.191474" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -10.22306, + "lon": -54.97972, + "name": "Peixoto de Azevedo" + }, + "point_b": { + "lat": 51.16734, + "lon": 4.39513, + "name": "Wilrijk" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 23.09089, + "lon": -32.493362 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-10.22306°, -54.97972°)", + " Point B: (51.16734°, 4.39513°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 23.090890°", + " Longitude: -32.493362°", + "FINAL ANSWER: 23.090890, -32.493362" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -46.4, + "lon": 168.35, + "name": "Invercargill" + }, + "point_b": { + "lat": 6.08838, + "lon": 100.39167, + "name": "Kampung Alor Mengkudu" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -9.062139, + "lon": 113.33602 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-46.4°, 168.35°)", + " Point B: (6.08838°, 100.39167°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -9.062139°", + " Longitude: 113.336020°", + "FINAL ANSWER: -9.062139, 113.336020" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 12.86273, + "lon": -7.55985, + "name": "Koulikoro" + }, + "point_b": { + "lat": 20.23031, + "lon": -99.21396, + "name": "Mixquiahuala de Juarez" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 23.087311, + "lon": -52.258992 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (12.86273°, -7.55985°)", + " Point B: (20.23031°, -99.21396°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 23.087311°", + " Longitude: -52.258992°", + "FINAL ANSWER: 23.087311, -52.258992" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 30.58176, + "lon": 66.99406, + "name": "Pishin" + }, + "point_b": { + "lat": 31.93155, + "lon": 12.25291, + "name": "Zintan" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 33.206632, + "lon": 53.704627 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (30.58176°, 66.99406°)", + " Point B: (31.93155°, 12.25291°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 33.206632°", + " Longitude: 53.704627°", + "FINAL ANSWER: 33.206632, 53.704627" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -9.34917, + "lon": 34.77167, + "name": "Njombe" + }, + "point_b": { + "lat": 39.30286, + "lon": 9.20283, + "name": "Sinnai" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 3.006939, + "lon": 29.229723 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-9.34917°, 34.77167°)", + " Point B: (39.30286°, 9.20283°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 3.006939°", + " Longitude: 29.229723°", + "FINAL ANSWER: 3.006939, 29.229723" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 33.32351, + "lon": 130.44218, + "name": "Nakatsukuma" + }, + "point_b": { + "lat": 40.97056, + "lon": 35.66222, + "name": "Havza" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 42.894224, + "lon": 110.935205 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (33.32351°, 130.44218°)", + " Point B: (40.97056°, 35.66222°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 42.894224°", + " Longitude: 110.935205°", + "FINAL ANSWER: 42.894224, 110.935205" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 39.91789, + "lon": -75.22796, + "name": "Elmwood" + }, + "point_b": { + "lat": -5.05, + "lon": 38.61667, + "name": "Maramba" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 13.187474, + "lon": 17.414152 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (39.91789°, -75.22796°)", + " Point B: (-5.05°, 38.61667°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 13.187474°", + " Longitude: 17.414152°", + "FINAL ANSWER: 13.187474, 17.414152" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 43.84635, + "lon": -91.24819, + "name": "North La Crosse" + }, + "point_b": { + "lat": 5.93876, + "lon": -6.59826, + "name": "Yabayo" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 19.688035, + "lon": -22.250391 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (43.84635°, -91.24819°)", + " Point B: (5.93876°, -6.59826°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 19.688035°", + " Longitude: -22.250391°", + "FINAL ANSWER: 19.688035, -22.250391" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 40.65829, + "lon": 22.89712, + "name": "Meneméni" + }, + "point_b": { + "lat": 23.9196, + "lon": 115.7801, + "name": "Hedong" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 42.385267, + "lon": 74.92242 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (40.65829°, 22.89712°)", + " Point B: (23.9196°, 115.7801°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 42.385267°", + " Longitude: 74.922420°", + "FINAL ANSWER: 42.385267, 74.922420" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 6.54584, + "lon": -0.76264, + "name": "Nkawkaw" + }, + "point_b": { + "lat": 44.05207, + "lon": -123.08675, + "name": "Eugene" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 43.25377, + "lon": -45.67565 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (6.54584°, -0.76264°)", + " Point B: (44.05207°, -123.08675°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 43.253770°", + " Longitude: -45.675650°", + "FINAL ANSWER: 43.253770, -45.675650" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -23.08639, + "lon": -46.95056, + "name": "Louveira" + }, + "point_b": { + "lat": -27.49325, + "lon": 153.05826, + "name": "Coorparoo" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -51.231713, + "lon": -65.140464 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-23.08639°, -46.95056°)", + " Point B: (-27.49325°, 153.05826°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -51.231713°", + " Longitude: -65.140464°", + "FINAL ANSWER: -51.231713, -65.140464" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 27.03766, + "lon": 14.42832, + "name": "Sabha" + }, + "point_b": { + "lat": 24.34478, + "lon": 124.15717, + "name": "Ishigaki" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 36.769499, + "lon": 40.064444 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (27.03766°, 14.42832°)", + " Point B: (24.34478°, 124.15717°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 36.769499°", + " Longitude: 40.064444°", + "FINAL ANSWER: 36.769499, 40.064444" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 33.66946, + "lon": -117.82311, + "name": "Irvine" + }, + "point_b": { + "lat": 14.02188, + "lon": 100.17183, + "name": "Bang Len" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 52.967045, + "lon": 158.640752 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (33.66946°, -117.82311°)", + " Point B: (14.02188°, 100.17183°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 52.967045°", + " Longitude: 158.640752°", + "FINAL ANSWER: 52.967045, 158.640752" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 53.62744, + "lon": 21.81253, + "name": "Pisz" + }, + "point_b": { + "lat": 24.04372, + "lon": 78.33014, + "name": "Khurai" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 49.246912, + "lon": 41.182488 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (53.62744°, 21.81253°)", + " Point B: (24.04372°, 78.33014°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 49.246912°", + " Longitude: 41.182488°", + "FINAL ANSWER: 49.246912, 41.182488" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -22.665, + "lon": -45.00944, + "name": "Cachoeira Paulista" + }, + "point_b": { + "lat": 48.9482, + "lon": 2.19169, + "name": "Sartrouville" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 14.256916, + "lon": -25.617447 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-22.665°, -45.00944°)", + " Point B: (48.9482°, 2.19169°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 14.256916°", + " Longitude: -25.617447°", + "FINAL ANSWER: 14.256916, -25.617447" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 3.207, + "lon": 101.727, + "name": "Setapak" + }, + "point_b": { + "lat": -7.05, + "lon": 109.55, + "name": "Buaran" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -4.490612, + "lon": 107.58146 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (3.207°, 101.727°)", + " Point B: (-7.05°, 109.55°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -4.490612°", + " Longitude: 107.581460°", + "FINAL ANSWER: -4.490612, 107.581460" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 35.35693, + "lon": 138.99759, + "name": "Oyama" + }, + "point_b": { + "lat": 9.9938, + "lon": -84.12742, + "name": "San Francisco" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 49.513264, + "lon": 175.079116 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (35.35693°, 138.99759°)", + " Point B: (9.9938°, -84.12742°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 49.513264°", + " Longitude: 175.079116°", + "FINAL ANSWER: 49.513264, 175.079116" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 30.82796, + "lon": 30.53552, + "name": "Ad Dilinjāt" + }, + "point_b": { + "lat": 4.42295, + "lon": -7.3528, + "name": "Tabou" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 25.042513, + "lon": 19.821096 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (30.82796°, 30.53552°)", + " Point B: (4.42295°, -7.3528°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 25.042513°", + " Longitude: 19.821096°", + "FINAL ANSWER: 25.042513, 19.821096" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 47.39724, + "lon": 8.61872, + "name": "Dübendorf" + }, + "point_b": { + "lat": 50.20745, + "lon": 19.16668, + "name": "Mysłowice" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 48.188449, + "lon": 11.143477 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (47.39724°, 8.61872°)", + " Point B: (50.20745°, 19.16668°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 48.188449°", + " Longitude: 11.143477°", + "FINAL ANSWER: 48.188449, 11.143477" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 45.50128, + "lon": 9.02681, + "name": "Cornaredo" + }, + "point_b": { + "lat": 10.49222, + "lon": 0.99972, + "name": "Cobly" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 28.053458, + "lon": 4.33924 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (45.50128°, 9.02681°)", + " Point B: (10.49222°, 0.99972°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 28.053458°", + " Longitude: 4.339240°", + "FINAL ANSWER: 28.053458, 4.339240" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 1.01572, + "lon": 35.00622, + "name": "Kitale" + }, + "point_b": { + "lat": 53.20278, + "lon": -6.09833, + "name": "Bray" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 14.91262, + "lon": 27.909215 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (1.01572°, 35.00622°)", + " Point B: (53.20278°, -6.09833°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 14.912620°", + " Longitude: 27.909215°", + "FINAL ANSWER: 14.912620, 27.909215" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 50.23139, + "lon": 106.20778, + "name": "Sühbaatar" + }, + "point_b": { + "lat": 31.03443, + "lon": 121.22326, + "name": "Songjiang" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 45.631767, + "lon": 110.869116 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (50.23139°, 106.20778°)", + " Point B: (31.03443°, 121.22326°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 45.631767°", + " Longitude: 110.869116°", + "FINAL ANSWER: 45.631767, 110.869116" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 22.48301, + "lon": 86.71793, + "name": "Chākuliā" + }, + "point_b": { + "lat": -7.0868, + "lon": 110.9158, + "name": "Purwodadi" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 7.870591, + "lon": 99.255028 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (22.48301°, 86.71793°)", + " Point B: (-7.0868°, 110.9158°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 7.870591°", + " Longitude: 99.255028°", + "FINAL ANSWER: 7.870591, 99.255028" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 45.43099, + "lon": 9.11093, + "name": "Corsico" + }, + "point_b": { + "lat": 55.86515, + "lon": -4.25763, + "name": "Glasgow" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 53.408686, + "lon": -0.322066 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (45.43099°, 9.11093°)", + " Point B: (55.86515°, -4.25763°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 53.408686°", + " Longitude: -0.322066°", + "FINAL ANSWER: 53.408686, -0.322066" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -23.37278, + "lon": -48.18417, + "name": "Guareí" + }, + "point_b": { + "lat": 32.60907, + "lon": 35.2892, + "name": "Afula" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -9.128536, + "lon": -27.591241 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-23.37278��, -48.18417°)", + " Point B: (32.60907°, 35.2892°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -9.128536°", + " Longitude: -27.591241°", + "FINAL ANSWER: -9.128536, -27.591241" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 50.81481, + "lon": 6.79387, + "name": "Erftstadt" + }, + "point_b": { + "lat": 38.61713, + "lon": -121.32828, + "name": "Carmichael" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 63.743891, + "lon": -21.971234 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (50.81481°, 6.79387°)", + " Point B: (38.61713°, -121.32828°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 63.743891°", + " Longitude: -21.971234°", + "FINAL ANSWER: 63.743891, -21.971234" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 16.79944, + "lon": -93.27219, + "name": "Berriozábal" + }, + "point_b": { + "lat": 50.82709, + "lon": 6.9747, + "name": "Wesseling" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 32.38567, + "lon": -77.993697 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (16.79944°, -93.27219°)", + " Point B: (50.82709°, 6.9747°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 32.385670°", + " Longitude: -77.993697°", + "FINAL ANSWER: 32.385670, -77.993697" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 27.23818, + "lon": 111.46214, + "name": "Shaoyang" + }, + "point_b": { + "lat": 31.08351, + "lon": -97.65974, + "name": "Harker Heights" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 65.689535, + "lon": -177.223362 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (27.23818°, 111.46214°)", + " Point B: (31.08351°, -97.65974°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 65.689535°", + " Longitude: -177.223362°", + "FINAL ANSWER: 65.689535, -177.223362" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 7.1127, + "lon": 5.1159, + "name": "Idanre" + }, + "point_b": { + "lat": 4.89035, + "lon": 114.94006, + "name": "Bandar Seri Begawan" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 10.364237, + "lon": 60.194292 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (7.1127°, 5.1159°)", + " Point B: (4.89035°, 114.94006°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat��)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 10.364237°", + " Longitude: 60.194292°", + "FINAL ANSWER: 10.364237, 60.194292" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 50.91667, + "lon": 8.1, + "name": "Netphen" + }, + "point_b": { + "lat": 36.83917, + "lon": 36.23025, + "name": "Dörtyol" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 44.736966, + "lon": 23.86891 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (50.91667°, 8.1°)", + " Point B: (36.83917°, 36.23025°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 44.736966°", + " Longitude: 23.868910°", + "FINAL ANSWER: 44.736966, 23.868910" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -18.13021, + "lon": 30.14074, + "name": "Chegutu" + }, + "point_b": { + "lat": 37.123, + "lon": -120.26018, + "name": "Chowchilla" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 31.86616, + "lon": -26.72591 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-18.13021°, 30.14074°)", + " Point B: (37.123°, -120.26018°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 31.866160°", + " Longitude: -26.725910°", + "FINAL ANSWER: 31.866160, -26.725910" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 18.79931, + "lon": 110.3841, + "name": "Wanning" + }, + "point_b": { + "lat": 34.15778, + "lon": -118.63842, + "name": "Calabasas" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 48.311034, + "lon": -150.218123 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (18.79931°, 110.3841°)", + " Point B: (34.15778°, -118.63842°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 48.311034°", + " Longitude: -150.218123°", + "FINAL ANSWER: 48.311034, -150.218123" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 50.26526, + "lon": -5.05436, + "name": "Truro" + }, + "point_b": { + "lat": 23.21494, + "lon": 81.53204, + "name": "Burhar" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 50.913142, + "lon": 22.749956 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (50.26526°, -5.05436°)", + " Point B: (23.21494°, 81.53204°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 50.913142°", + " Longitude: 22.749956°", + "FINAL ANSWER: 50.913142, 22.749956" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 9.96837, + "lon": -5.14882, + "name": "Ouangolodougou" + }, + "point_b": { + "lat": -33.79798, + "lon": 151.28826, + "name": "Manly" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -43.75325, + "lon": 50.956073 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (9.96837°, -5.14882°)", + " Point B: (-33.79798°, 151.28826°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -43.753250°", + " Longitude: 50.956073°", + "FINAL ANSWER: -43.753250, 50.956073" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 48.338, + "lon": 38.40239, + "name": "Debaltseve" + }, + "point_b": { + "lat": -24.86028, + "lon": -54.33278, + "name": "Santa Helena" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 35.578153, + "lon": 5.174492 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (48.338°, 38.40239°)", + " Point B: (-24.86028°, -54.33278°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 35.578153°", + " Longitude: 5.174492°", + "FINAL ANSWER: 35.578153, 5.174492" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 52.30273, + "lon": -0.69446, + "name": "Wellingborough" + }, + "point_b": { + "lat": 7.10769, + "lon": -7.55207, + "name": "Logoualé" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 41.043701, + "lon": -3.184739 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (52.30273°, -0.69446°)", + " Point B: (7.10769°, -7.55207°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 41.043701°", + " Longitude: -3.184739°", + "FINAL ANSWER: 41.043701, -3.184739" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 51.63333, + "lon": -0.2, + "name": "Totteridge" + }, + "point_b": { + "lat": 43.80306, + "lon": 143.89083, + "name": "Kitami" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 68.123585, + "lon": 22.958173 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (51.63333°, -0.2°)", + " Point B: (43.80306°, 143.89083°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 68.123585°", + " Longitude: 22.958173°", + "FINAL ANSWER: 68.123585, 22.958173" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 49.24991, + "lon": 8.51257, + "name": "Waghäusel" + }, + "point_b": { + "lat": 43.58508, + "lon": 5.00268, + "name": "Miramas" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 46.430883, + "lon": 6.666364 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (49.24991°, 8.51257°)", + " Point B: (43.58508°, 5.00268°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 46.430883°", + " Longitude: 6.666364°", + "FINAL ANSWER: 46.430883, 6.666364" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 19.48698, + "lon": -99.18594, + "name": "Azcapotzalco" + }, + "point_b": { + "lat": 51.53083, + "lon": 4.46528, + "name": "Roosendaal" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 35.219125, + "lon": -83.878156 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (19.48698°, -99.18594°)", + " Point B: (51.53083°, 4.46528°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 35.219125°", + " Longitude: -83.878156°", + "FINAL ANSWER: 35.219125, -83.878156" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 12.57758, + "lon": -87.02705, + "name": "Chichigalpa" + }, + "point_b": { + "lat": -37.76667, + "lon": 144.91667, + "name": "Moonee Ponds" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -38.565363, + "lon": -174.207539 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (12.57758°, -87.02705°)", + " Point B: (-37.76667°, 144.91667°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -38.565363°", + " Longitude: -174.207539°", + "FINAL ANSWER: -38.565363, -174.207539" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 48.20849, + "lon": 16.37208, + "name": "Vienna" + }, + "point_b": { + "lat": 44.4599, + "lon": 39.73005, + "name": "Apsheronsk" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 47.729055, + "lon": 22.488521 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (48.20849°, 16.37208°)", + " Point B: (44.4599°, 39.73005°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 47.729055°", + " Longitude: 22.488521°", + "FINAL ANSWER: 47.729055, 22.488521" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 37.94007, + "lon": 22.9513, + "name": "Kórinthos" + }, + "point_b": { + "lat": 55.87329, + "lon": -3.1051, + "name": "Bonnyrigg" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 47.629667, + "lon": 12.157898 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (37.94007°, 22.9513°)", + " Point B: (55.87329°, -3.1051°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 47.629667°", + " Longitude: 12.157898°", + "FINAL ANSWER: 47.629667, 12.157898" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 33.74002, + "lon": -116.93891, + "name": "East Hemet" + }, + "point_b": { + "lat": -33.89743, + "lon": 150.93446, + "name": "Cabramatta" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -18.372995, + "lon": 176.257497 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (33.74002°, -116.93891°)", + " Point B: (-33.89743°, 150.93446°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -18.372995°", + " Longitude: 176.257497°", + "FINAL ANSWER: -18.372995, 176.257497" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 48.79954, + "lon": 9.06316, + "name": "Gerlingen" + }, + "point_b": { + "lat": 14.5594, + "lon": 121.0258, + "name": "Bel Air" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 32.193353, + "lon": 104.478979 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (48.79954°, 9.06316°)", + " Point B: (14.5594°, 121.0258°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 32.193353°", + " Longitude: 104.478979°", + "FINAL ANSWER: 32.193353, 104.478979" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 50.72136, + "lon": 10.44386, + "name": "Schmalkalden" + }, + "point_b": { + "lat": 55.86661, + "lon": 48.35931, + "name": "Volzhsk" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 55.751605, + "lon": 38.151319 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (50.72136°, 10.44386°)", + " Point B: (55.86661°, 48.35931°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 55.751605°", + " Longitude: 38.151319°", + "FINAL ANSWER: 55.751605, 38.151319" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 37.94203, + "lon": 23.64619, + "name": "Piraeus" + }, + "point_b": { + "lat": 40.50677, + "lon": -74.26542, + "name": "Perth Amboy" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 47.085533, + "lon": 2.665221 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (37.94203°, 23.64619°)", + " Point B: (40.50677°, -74.26542°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 47.085533°", + " Longitude: 2.665221°", + "FINAL ANSWER: 47.085533, 2.665221" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 38.47318, + "lon": -77.99666, + "name": "Culpeper" + }, + "point_b": { + "lat": 36.29333, + "lon": 3.67319, + "name": "Aïn Bessem" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 43.791439, + "lon": -58.378214 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (38.47318°, -77.99666°)", + " Point B: (36.29333°, 3.67319°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 43.791439°", + " Longitude: -58.378214°", + "FINAL ANSWER: 43.791439, -58.378214" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 39.29034, + "lon": -84.50411, + "name": "Forest Park" + }, + "point_b": { + "lat": -40.95972, + "lon": 175.6575, + "name": "Masterton" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -23.111231, + "lon": -155.182665 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (39.29034°, -84.50411°)", + " Point B: (-40.95972°, 175.6575°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -23.111231°", + " Longitude: -155.182665°", + "FINAL ANSWER: -23.111231, -155.182665" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -37.99116, + "lon": 145.17385, + "name": "Keysborough" + }, + "point_b": { + "lat": -16.66663, + "lon": -48.61252, + "name": "Silvânia" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -46.550073, + "lon": -58.348168 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-37.99116°, 145.17385°)", + " Point B: (-16.66663°, -48.61252°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -46.550073°", + " Longitude: -58.348168°", + "FINAL ANSWER: -46.550073, -58.348168" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 16.01667, + "lon": 103.95, + "name": "Ban Selaphum" + }, + "point_b": { + "lat": 53.18333, + "lon": 8.0, + "name": "Bad Zwischenahn" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 53.393779, + "lon": 42.08431 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (16.01667°, 103.95°)", + " Point B: (53.18333°, 8.0°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 53.393779°", + " Longitude: 42.084310°", + "FINAL ANSWER: 53.393779, 42.084310" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 39.9475, + "lon": 127.87111, + "name": "Samho-rodongjagu" + }, + "point_b": { + "lat": 9.42958, + "lon": -64.46428, + "name": "Anaco" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 40.847015, + "lon": -73.071595 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (39.9475°, 127.87111°)", + " Point B: (9.42958°, -64.46428°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 40.847015°", + " Longitude: -73.071595°", + "FINAL ANSWER: 40.847015, -73.071595" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 23.01797, + "lon": 113.74866, + "name": "Dongguan" + }, + "point_b": { + "lat": 52.31394, + "lon": 9.9682, + "name": "Sehnde" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 56.230088, + "lon": 43.884699 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (23.01797°, 113.74866°)", + " Point B: (52.31394°, 9.9682°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 56.230088°", + " Longitude: 43.884699°", + "FINAL ANSWER: 56.230088, 43.884699" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 29.90565, + "lon": 107.63853, + "name": "Huwei" + }, + "point_b": { + "lat": 32.76272, + "lon": 21.75506, + "name": "Al Bayḑā’" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 39.74673, + "lon": 65.506294 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (29.90565°, 107.63853°)", + " Point B: (32.76272°, 21.75506°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 39.746730°", + " Longitude: 65.506294°", + "FINAL ANSWER: 39.746730, 65.506294" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 7.70156, + "lon": -72.35551, + "name": "Rubio" + }, + "point_b": { + "lat": 49.54637, + "lon": 30.87407, + "name": "Bohuslav" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 40.362239, + "lon": -35.496757 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (7.70156°, -72.35551°)", + " Point B: (49.54637°, 30.87407°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 40.362239°", + " Longitude: -35.496757°", + "FINAL ANSWER: 40.362239, -35.496757" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -19.55778, + "lon": -44.08139, + "name": "Matozinhos" + }, + "point_b": { + "lat": 45.18333, + "lon": 124.81667, + "name": "Fuyu" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 17.056968, + "lon": -33.019486 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-19.55778°, -44.08139°)", + " Point B: (45.18333°, 124.81667°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 17.056968°", + " Longitude: -33.019486°", + "FINAL ANSWER: 17.056968, -33.019486" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 26.46517, + "lon": 79.50918, + "name": "Auraiya" + }, + "point_b": { + "lat": 43.73899, + "lon": -79.22124, + "name": "Scarborough Village" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 73.193709, + "lon": 29.765076 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (26.46517°, 79.50918°)", + " Point B: (43.73899°, -79.22124°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 73.193709°", + " Longitude: 29.765076°", + "FINAL ANSWER: 73.193709, 29.765076" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 34.05168, + "lon": -117.9684, + "name": "West Puente Valley" + }, + "point_b": { + "lat": 60.0122, + "lon": 30.20897, + "name": "Untolovo" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 75.598141, + "lon": -8.341107 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (34.05168°, -117.9684°)", + " Point B: (60.0122°, 30.20897°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 75.598141°", + " Longitude: -8.341107°", + "FINAL ANSWER: 75.598141, -8.341107" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -4.23116, + "lon": -69.93858, + "name": "Tabatinga" + }, + "point_b": { + "lat": 41.84123, + "lon": 60.39268, + "name": "Gurlan" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 37.732414, + "lon": -22.146797 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-4.23116°, -69.93858°)", + " Point B: (41.84123°, 60.39268°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 37.732414°", + " Longitude: -22.146797°", + "FINAL ANSWER: 37.732414, -22.146797" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -0.826, + "lon": -52.506, + "name": "Laranjal do Jari" + }, + "point_b": { + "lat": 42.20704, + "lon": -71.68562, + "name": "Grafton" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 20.952388, + "lon": -60.654728 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-0.826°, -52.506°)", + " Point B: (42.20704°, -71.68562°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 20.952388°", + " Longitude: -60.654728°", + "FINAL ANSWER: 20.952388, -60.654728" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 29.65, + "lon": 91.1, + "name": "Lhasa" + }, + "point_b": { + "lat": 34.35417, + "lon": -119.05927, + "name": "Santa Paula" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 53.016895, + "lon": 110.887769 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (29.65°, 91.1°)", + " Point B: (34.35417°, -119.05927°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 53.016895°", + " Longitude: 110.887769°", + "FINAL ANSWER: 53.016895, 110.887769" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 51.84034, + "lon": 16.57494, + "name": "Leszno" + }, + "point_b": { + "lat": 6.59651, + "lon": 3.34205, + "name": "Ikeja" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 29.372882, + "lon": 8.409909 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (51.84034°, 16.57494°)", + " Point B: (6.59651°, 3.34205°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 29.372882°", + " Longitude: 8.409909°", + "FINAL ANSWER: 29.372882, 8.409909" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 14.18175, + "lon": 103.51761, + "name": "Samraong" + }, + "point_b": { + "lat": 34.1064, + "lon": -117.37032, + "name": "Rialto" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 36.165657, + "lon": 125.506641 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (14.18175°, 103.51761°)", + " Point B: (34.1064°, -117.37032°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 36.165657°", + " Longitude: 125.506641°", + "FINAL ANSWER: 36.165657, 125.506641" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 12.04888, + "lon": 24.88069, + "name": "Nyala" + }, + "point_b": { + "lat": 45.58005, + "lon": 9.27246, + "name": "Monza" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 20.571643, + "lon": 21.811314 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (12.04888°, 24.88069°)", + " Point B: (45.58005°, 9.27246°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 20.571643°", + " Longitude: 21.811314°", + "FINAL ANSWER: 20.571643, 21.811314" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 12.06667, + "lon": -2.23333, + "name": "Sabou" + }, + "point_b": { + "lat": 21.8787, + "lon": 95.97965, + "name": "Sagaing" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 24.985561, + "lon": 45.140453 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (12.06667°, -2.23333°)", + " Point B: (21.8787°, 95.97965°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 24.985561°", + " Longitude: 45.140453°", + "FINAL ANSWER: 24.985561, 45.140453" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 0.48829, + "lon": 42.78535, + "name": "Jilib" + }, + "point_b": { + "lat": 11.53495, + "lon": 106.88324, + "name": "Đồng Xoài" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 3.93426, + "lon": 58.565217 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (0.48829°, 42.78535°)", + " Point B: (11.53495°, 106.88324°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 3.934260°", + " Longitude: 58.565217°", + "FINAL ANSWER: 3.934260, 58.565217" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 39.64176, + "lon": -77.71999, + "name": "Hagerstown" + }, + "point_b": { + "lat": 29.99883, + "lon": -95.26216, + "name": "Humble" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 32.634745, + "lon": -91.254364 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (39.64176°, -77.71999°)", + " Point B: (29.99883°, -95.26216°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 32.634745°", + " Longitude: -91.254364°", + "FINAL ANSWER: 32.634745, -91.254364" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 12.99826, + "lon": 8.90991, + "name": "Magaria" + }, + "point_b": { + "lat": 44.60868, + "lon": -79.42068, + "name": "Orillia" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 26.160307, + "lon": -7.034539 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (12.99826°, 8.90991°)", + " Point B: (44.60868°, -79.42068°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 26.160307°", + " Longitude: -7.034539°", + "FINAL ANSWER: 26.160307, -7.034539" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 36.59245, + "lon": 127.29223, + "name": "Sejong" + }, + "point_b": { + "lat": 44.20221, + "lon": -88.4465, + "name": "Menasha" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 56.653493, + "lon": 144.807373 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (36.59245°, 127.29223°)", + " Point B: (44.20221°, -88.4465°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 56.653493°", + " Longitude: 144.807373°", + "FINAL ANSWER: 56.653493, 144.807373" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 28.45433, + "lon": 104.71498, + "name": "Xunchang" + }, + "point_b": { + "lat": 29.07441, + "lon": 31.09785, + "name": "Banī Suwayf" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 32.788385, + "lon": 86.981145 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (28.45433°, 104.71498°)", + " Point B: (29.07441°, 31.09785°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 32.788385°", + " Longitude: 86.981145°", + "FINAL ANSWER: 32.788385, 86.981145" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 5.80865, + "lon": 8.08098, + "name": "Ugep" + }, + "point_b": { + "lat": 34.40731, + "lon": -2.89732, + "name": "Taourirt" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 13.012361, + "lon": 5.665814 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (5.80865°, 8.08098°)", + " Point B: (34.40731°, -2.89732°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 13.012361°", + " Longitude: 5.665814°", + "FINAL ANSWER: 13.012361, 5.665814" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 40.3935, + "lon": -3.71196, + "name": "Comillas" + }, + "point_b": { + "lat": 39.83665, + "lon": -105.0372, + "name": "Westminster" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 49.24046, + "lon": -83.125738 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (40.3935°, -3.71196°)", + " Point B: (39.83665°, -105.0372°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 49.240460°", + " Longitude: -83.125738°", + "FINAL ANSWER: 49.240460, -83.125738" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 46.17185, + "lon": 1.87166, + "name": "Guéret" + }, + "point_b": { + "lat": 3.11667, + "lon": 101.68333, + "name": "Seputeh" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 19.972004, + "lon": 84.712469 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (46.17185°, 1.87166°)", + " Point B: (3.11667°, 101.68333°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 19.972004°", + " Longitude: 84.712469°", + "FINAL ANSWER: 19.972004, 84.712469" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 30.90711, + "lon": 32.02341, + "name": "Munsha‘at Abū ‘Umar" + }, + "point_b": { + "lat": 39.10638, + "lon": 27.66925, + "name": "Kırkağaç" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 37.071741, + "lon": 28.843226 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (30.90711°, 32.02341°)", + " Point B: (39.10638°, 27.66925°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 37.071741°", + " Longitude: 28.843226°", + "FINAL ANSWER: 37.071741, 28.843226" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 12.91667, + "lon": -14.16667, + "name": "Diaoubé" + }, + "point_b": { + "lat": 40.15552, + "lon": 26.41271, + "name": "Çanakkale" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 28.00724, + "lon": 3.561858 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (12.91667°, -14.16667°)", + " Point B: (40.15552°, 26.41271°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 28.007240°", + " Longitude: 3.561858°", + "FINAL ANSWER: 28.007240, 3.561858" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 4.48178, + "lon": 118.61119, + "name": "Semporna" + }, + "point_b": { + "lat": -17.01037, + "lon": -46.00851, + "name": "Brasilândia de Minas" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -21.135065, + "lon": 87.140511 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (4.48178°, 118.61119°)", + " Point B: (-17.01037°, -46.00851°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -21.135065°", + " Longitude: 87.140511°", + "FINAL ANSWER: -21.135065, 87.140511" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 39.34364, + "lon": 42.09918, + "name": "Karaçoban" + }, + "point_b": { + "lat": 25.01579, + "lon": 83.03294, + "name": "Ahraura" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 33.875211, + "lon": 64.256828 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (39.34364°, 42.09918°)", + " Point B: (25.01579°, 83.03294°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 33.875211°", + " Longitude: 64.256828°", + "FINAL ANSWER: 33.875211, 64.256828" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 23.07939, + "lon": -82.3769, + "name": "Naranjito" + }, + "point_b": { + "lat": 15.68618, + "lon": -93.20938, + "name": "Pijijiapan" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 17.592269, + "lon": -90.590657 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (23.07939°, -82.3769°)", + " Point B: (15.68618°, -93.20938°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 17.592269°", + " Longitude: -90.590657°", + "FINAL ANSWER: 17.592269, -90.590657" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 41.05237, + "lon": 14.33334, + "name": "San Nicola la Strada" + }, + "point_b": { + "lat": 45.64498, + "lon": 11.29886, + "name": "Valdagno" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 43.35869, + "lon": 12.873544 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (41.05237°, 14.33334°)", + " Point B: (45.64498°, 11.29886°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 43.358690°", + " Longitude: 12.873544°", + "FINAL ANSWER: 43.358690, 12.873544" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 47.50564, + "lon": 8.72413, + "name": "Winterthur" + }, + "point_b": { + "lat": 9.25025, + "lon": 0.78213, + "name": "Bassar" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 18.848815, + "lon": 2.302028 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (47.50564°, 8.72413°)", + " Point B: (9.25025°, 0.78213°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 18.848815°", + " Longitude: 2.302028°", + "FINAL ANSWER: 18.848815, 2.302028" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 28.3548, + "lon": -16.37268, + "name": "Candelaria" + }, + "point_b": { + "lat": -27.53221, + "lon": 153.22889, + "name": "Alexandra Hills" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 4.525406, + "lon": 70.824391 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (28.3548°, -16.37268°)", + " Point B: (-27.53221°, 153.22889°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 4.525406°", + " Longitude: 70.824391°", + "FINAL ANSWER: 4.525406, 70.824391" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 27.27359, + "lon": 76.98613, + "name": "Kherli" + }, + "point_b": { + "lat": 33.55, + "lon": 133.53333, + "name": "Kochi" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 31.197019, + "lon": 90.169246 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (27.27359°, 76.98613°)", + " Point B: (33.55°, 133.53333°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 31.197019°", + " Longitude: 90.169246°", + "FINAL ANSWER: 31.197019, 90.169246" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 9.96278, + "lon": 42.49278, + "name": "Ārabī" + }, + "point_b": { + "lat": -36.88333, + "lon": 174.7, + "name": "Avondale" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -40.553123, + "lon": 133.157019 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (9.96278°, 42.49278°)", + " Point B: (-36.88333°, 174.7°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -40.553123°", + " Longitude: 133.157019°", + "FINAL ANSWER: -40.553123, 133.157019" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 48.793, + "lon": 132.92033, + "name": "Birobidzhan" + }, + "point_b": { + "lat": 42.81424, + "lon": -73.93957, + "name": "Schenectady" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 76.967121, + "lon": -137.833599 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (48.793°, 132.92033°)", + " Point B: (42.81424°, -73.93957°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 76.967121°", + " Longitude: -137.833599°", + "FINAL ANSWER: 76.967121, -137.833599" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -19.26639, + "lon": 146.80569, + "name": "Townsville" + }, + "point_b": { + "lat": 52.41471, + "lon": 31.31429, + "name": "Dobrush" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 4.539645, + "lon": 127.999362 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-19.26639°, 146.80569°)", + " Point B: (52.41471°, 31.31429°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 4.539645°", + " Longitude: 127.999362°", + "FINAL ANSWER: 4.539645, 127.999362" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 53.17477, + "lon": 5.42244, + "name": "Harlingen" + }, + "point_b": { + "lat": 55.73321, + "lon": 38.46458, + "name": "Fryazevo" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 55.956292, + "lon": 29.922491 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (53.17477°, 5.42244°)", + " Point B: (55.73321°, 38.46458°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 55.956292°", + " Longitude: 29.922491°", + "FINAL ANSWER: 55.956292, 29.922491" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -8.0875, + "lon": -37.64306, + "name": "Custódia" + }, + "point_b": { + "lat": 17.39455, + "lon": 78.59047, + "name": "Pīrzādagūda" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 0.379905, + "lon": -9.458668 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-8.0875°, -37.64306°)", + " Point B: (17.39455°, 78.59047°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 0.379905°", + " Longitude: -9.458668°", + "FINAL ANSWER: 0.379905, -9.458668" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 59.19554, + "lon": 17.62525, + "name": "Södertälje" + }, + "point_b": { + "lat": 30.93976, + "lon": 30.81338, + "name": "Basyūn" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 38.118126, + "lon": 28.59395 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (59.19554°, 17.62525°)", + " Point B: (30.93976°, 30.81338°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 38.118126°", + " Longitude: 28.593950°", + "FINAL ANSWER: 38.118126, 28.593950" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -32.02957, + "lon": -61.22097, + "name": "Gálvez" + }, + "point_b": { + "lat": 37.84221, + "lon": 23.77651, + "name": "Voúla" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 3.936979, + "lon": -20.583411 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-32.02957°, -61.22097°)", + " Point B: (37.84221°, 23.77651°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 3.936979°", + " Longitude: -20.583411°", + "FINAL ANSWER: 3.936979, -20.583411" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 9.92866, + "lon": -69.6201, + "name": "Quíbor" + }, + "point_b": { + "lat": 8.3404, + "lon": 17.7663, + "name": "Moïssala" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 12.537437, + "lon": -25.804898 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (9.92866°, -69.6201°)", + " Point B: (8.3404°, 17.7663°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 12.537437°", + " Longitude: -25.804898°", + "FINAL ANSWER: 12.537437, -25.804898" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 37.06667, + "lon": 138.88333, + "name": "Muikamachi" + }, + "point_b": { + "lat": 27.44805, + "lon": 67.79654, + "name": "Warah" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 37.779223, + "lon": 101.167332 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (37.06667°, 138.88333°)", + " Point B: (27.44805°, 67.79654°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 37.779223°", + " Longitude: 101.167332°", + "FINAL ANSWER: 37.779223, 101.167332" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 25.85643, + "lon": 87.53836, + "name": "Kasba" + }, + "point_b": { + "lat": 25.12163, + "lon": 62.32541, + "name": "Gwadar" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 26.036321, + "lon": 74.892712 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (25.85643°, 87.53836°)", + " Point B: (25.12163°, 62.32541°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 26.036321°", + " Longitude: 74.892712°", + "FINAL ANSWER: 26.036321, 74.892712" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -26.81358, + "lon": 27.81695, + "name": "Sasolburg" + }, + "point_b": { + "lat": 40.65501, + "lon": 29.27693, + "name": "Yalova" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 6.921268, + "lon": 28.487767 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-26.81358°, 27.81695°)", + " Point B: (40.65501°, 29.27693°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 6.921268°", + " Longitude: 28.487767°", + "FINAL ANSWER: 6.921268, 28.487767" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 33.88835, + "lon": -118.30896, + "name": "Gardena" + }, + "point_b": { + "lat": 54.32435, + "lon": 18.60269, + "name": "Ujeścisko-Łostowice" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 52.542767, + "lon": -104.615884 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (33.88835°, -118.30896°)", + " Point B: (54.32435°, 18.60269°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 52.542767°", + " Longitude: -104.615884°", + "FINAL ANSWER: 52.542767, -104.615884" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 50.73583, + "lon": -1.78129, + "name": "Christchurch" + }, + "point_b": { + "lat": 35.47988, + "lon": -79.1803, + "name": "Sanford" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 43.941709, + "lon": -64.69958 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (50.73583°, -1.78129°)", + " Point B: (35.47988°, -79.1803°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 43.941709°", + " Longitude: -64.699580°", + "FINAL ANSWER: 43.941709, -64.699580" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 40.49874, + "lon": 22.92617, + "name": "Peraía" + }, + "point_b": { + "lat": 11.84692, + "lon": 13.15712, + "name": "Maiduguri" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 33.406558, + "lon": 19.950137 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (40.49874°, 22.92617°)", + " Point B: (11.84692°, 13.15712°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 33.406558°", + " Longitude: 19.950137°", + "FINAL ANSWER: 33.406558, 19.950137" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -3.20778, + "lon": -43.40361, + "name": "Urbano Santos" + }, + "point_b": { + "lat": 52.66384, + "lon": 41.88915, + "name": "Rasskazovo" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 14.578264, + "lon": -29.619839 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-3.20778°, -43.40361°)", + " Point B: (52.66384°, 41.88915°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 14.578264°", + " Longitude: -29.619839°", + "FINAL ANSWER: 14.578264, -29.619839" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 19.84799, + "lon": -71.64604, + "name": "San Fernando de Monte Cristi" + }, + "point_b": { + "lat": 25.94121, + "lon": -81.71842, + "name": "Marco Island" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 24.479467, + "lon": -79.11323 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (19.84799°, -71.64604°)", + " Point B: (25.94121°, -81.71842°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 24.479467°", + " Longitude: -79.113230°", + "FINAL ANSWER: 24.479467, -79.113230" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 46.63333, + "lon": 27.73333, + "name": "Vaslui" + }, + "point_b": { + "lat": -37.83634, + "lon": 144.65952, + "name": "Tarneit" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 8.313062, + "lon": 92.688193 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (46.63333°, 27.73333°)", + " Point B: (-37.83634°, 144.65952°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 8.313062°", + " Longitude: 92.688193°", + "FINAL ANSWER: 8.313062, 92.688193" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 0.87136, + "lon": -77.64027, + "name": "Pupiales" + }, + "point_b": { + "lat": 25.67325, + "lon": -100.45813, + "name": "Santa Catarina" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 13.52939, + "lon": -88.449544 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (0.87136°, -77.64027°)", + " Point B: (25.67325°, -100.45813°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 13.529390°", + " Longitude: -88.449544°", + "FINAL ANSWER: 13.529390, -88.449544" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 56.10921, + "lon": 94.58698, + "name": "Zelenogorsk" + }, + "point_b": { + "lat": 42.46037, + "lon": -71.34895, + "name": "Concord" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 75.534738, + "lon": 80.058654 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (56.10921°, 94.58698°)", + " Point B: (42.46037°, -71.34895°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 75.534738°", + " Longitude: 80.058654°", + "FINAL ANSWER: 75.534738, 80.058654" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 41.51431, + "lon": -7.98942, + "name": "Cabeceiras de Basto" + }, + "point_b": { + "lat": -18.03028, + "lon": -40.15056, + "name": "Pedro Canário" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 27.1401, + "lon": -18.215982 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (41.51431°, -7.98942°)", + " Point B: (-18.03028°, -40.15056°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 27.140100°", + " Longitude: -18.215982°", + "FINAL ANSWER: 27.140100, -18.215982" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 31.21735, + "lon": 72.99621, + "name": "Dijkot" + }, + "point_b": { + "lat": 48.48333, + "lon": -123.31667, + "name": "Gordon Head" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 77.216419, + "lon": 113.358284 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (31.21735°, 72.99621°)", + " Point B: (48.48333°, -123.31667°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 77.216419°", + " Longitude: 113.358284°", + "FINAL ANSWER: 77.216419, 113.358284" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -28.17827, + "lon": 30.14702, + "name": "Glencoe" + }, + "point_b": { + "lat": 45.17869, + "lon": 5.71479, + "name": "Grenoble" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 8.691684, + "lon": 19.311435 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-28.17827°, 30.14702°)", + " Point B: (45.17869°, 5.71479°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 8.691684°", + " Longitude: 19.311435°", + "FINAL ANSWER: 8.691684, 19.311435" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -0.24849, + "lon": 35.73194, + "name": "Molo" + }, + "point_b": { + "lat": 43.8317, + "lon": 23.23793, + "name": "Lom" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 21.906371, + "lon": 30.499969 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-0.24849°, 35.73194°)", + " Point B: (43.8317°, 23.23793°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 21.906371°", + " Longitude: 30.499969°", + "FINAL ANSWER: 21.906371, 30.499969" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 5.85475, + "lon": 6.85944, + "name": "Ihiala" + }, + "point_b": { + "lat": -10.12528, + "lon": -36.66194, + "name": "Igreja Nova" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -2.298923, + "lon": -14.781557 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (5.85475°, 6.85944°)", + " Point B: (-10.12528°, -36.66194°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -2.298923°", + " Longitude: -14.781557°", + "FINAL ANSWER: -2.298923, -14.781557" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 21.8422, + "lon": -78.76034, + "name": "Ciego de Ávila" + }, + "point_b": { + "lat": 42.0953, + "lon": -87.93757, + "name": "Prospect Heights" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 32.050395, + "lon": -82.836381 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (21.8422°, -78.76034°)", + " Point B: (42.0953°, -87.93757°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 32.050395°", + " Longitude: -82.836381°", + "FINAL ANSWER: 32.050395, -82.836381" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -22.08659, + "lon": -65.59422, + "name": "Villazón" + }, + "point_b": { + "lat": 30.6687, + "lon": 30.07391, + "name": "An Nūbārīyah" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -8.509061, + "lon": -42.01323 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-22.08659°, -65.59422°)", + " Point B: (30.6687°, 30.07391°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -8.509061°", + " Longitude: -42.013230°", + "FINAL ANSWER: -8.509061, -42.013230" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 48.90654, + "lon": 2.33339, + "name": "Saint-Ouen" + }, + "point_b": { + "lat": -1.24908, + "lon": -78.61675, + "name": "Ambato" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 29.759653, + "lon": -48.143665 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (48.90654°, 2.33339°)", + " Point B: (-1.24908°, -78.61675°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 29.759653°", + " Longitude: -48.143665°", + "FINAL ANSWER: 29.759653, -48.143665" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 33.5018, + "lon": -81.96512, + "name": "North Augusta" + }, + "point_b": { + "lat": 51.06314, + "lon": -0.32757, + "name": "Horsham" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 50.026718, + "lon": -48.063977 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (33.5018°, -81.96512°)", + " Point B: (51.06314°, -0.32757°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 50.026718°", + " Longitude: -48.063977°", + "FINAL ANSWER: 50.026718, -48.063977" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -11.47512, + "lon": 16.96496, + "name": "Nharêa" + }, + "point_b": { + "lat": 52.26896, + "lon": 20.98644, + "name": "Żoliborz" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 20.407834, + "lon": 18.510645 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-11.47512°, 16.96496°)", + " Point B: (52.26896°, 20.98644°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 20.407834°", + " Longitude: 18.510645°", + "FINAL ANSWER: 20.407834, 18.510645" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 31.45191, + "lon": 74.92777, + "name": "Tarn Taran" + }, + "point_b": { + "lat": 37.59577, + "lon": -122.01913, + "name": "Union City" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 57.455258, + "lon": 86.95567 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (31.45191°, 74.92777°)", + " Point B: (37.59577°, -122.01913°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 57.455258°", + " Longitude: 86.955670°", + "FINAL ANSWER: 57.455258, 86.955670" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 51.54649, + "lon": 6.59525, + "name": "Rheinberg" + }, + "point_b": { + "lat": 9.0661, + "lon": -79.42577, + "name": "Pedregal" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 38.024405, + "lon": -48.38096 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (51.54649°, 6.59525°)", + " Point B: (9.0661°, -79.42577°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 38.024405°", + " Longitude: -48.380960°", + "FINAL ANSWER: 38.024405, -48.380960" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 7.77917, + "lon": -68.22373, + "name": "Achaguas" + }, + "point_b": { + "lat": 7.57127, + "lon": -1.7087, + "name": "Nkoranza" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 9.155112, + "lon": -34.957028 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (7.77917°, -68.22373°)", + " Point B: (7.57127°, -1.7087°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 9.155112°", + " Longitude: -34.957028°", + "FINAL ANSWER: 9.155112, -34.957028" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -38.11531, + "lon": 145.29814, + "name": "Cranbourne East" + }, + "point_b": { + "lat": 6.49611, + "lon": 3.38778, + "name": "Makoko" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -39.434944, + "lon": 55.744651 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-38.11531°, 145.29814°)", + " Point B: (6.49611°, 3.38778°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -39.434944°", + " Longitude: 55.744651°", + "FINAL ANSWER: -39.434944, 55.744651" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -11.95972, + "lon": -40.16806, + "name": "Baixa Grande" + }, + "point_b": { + "lat": 33.23333, + "lon": 130.3, + "name": "Saga" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 64.954615, + "lon": 91.990698 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-11.95972°, -40.16806°)", + " Point B: (33.23333°, 130.3°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 64.954615°", + " Longitude: 91.990698°", + "FINAL ANSWER: 64.954615, 91.990698" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 15.21233, + "lon": 145.7545, + "name": "Saipan" + }, + "point_b": { + "lat": 41.00367, + "lon": -80.34701, + "name": "New Castle" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 52.666272, + "lon": -163.330274 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (15.21233°, 145.7545°)", + " Point B: (41.00367°, -80.34701°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 52.666272°", + " Longitude: -163.330274°", + "FINAL ANSWER: 52.666272, -163.330274" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 28.10545, + "lon": -82.52594, + "name": "Greater Northdale" + }, + "point_b": { + "lat": -25.699, + "lon": 27.47475, + "name": "Marikana" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 16.975773, + "lon": -52.697048 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (28.10545°, -82.52594°)", + " Point B: (-25.699°, 27.47475°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 16.975773°", + " Longitude: -52.697048°", + "FINAL ANSWER: 16.975773, -52.697048" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 36.4009, + "lon": 47.1133, + "name": "Takāb" + }, + "point_b": { + "lat": 13.884, + "lon": 122.2604, + "name": "Lopez" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 30.568114, + "lon": 88.79828 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (36.4009°, 47.1133°)", + " Point B: (13.884°, 122.2604°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 30.568114°", + " Longitude: 88.798280°", + "FINAL ANSWER: 30.568114, 88.798280" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 51.87113, + "lon": 0.15868, + "name": "Bishops Stortford" + }, + "point_b": { + "lat": 35.74381, + "lon": -0.7693, + "name": "’Aïn el Turk" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 43.808391, + "lon": -0.368366 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (51.87113°, 0.15868°)", + " Point B: (35.74381°, -0.7693°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 43.808391°", + " Longitude: -0.368366°", + "FINAL ANSWER: 43.808391, -0.368366" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 19.04222, + "lon": -98.11889, + "name": "Casa Blanca" + }, + "point_b": { + "lat": 42.19454, + "lon": -71.83563, + "name": "Auburn" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 25.272049, + "lon": -92.64971 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (19.04222°, -98.11889°)", + " Point B: (42.19454°, -71.83563°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 25.272049°", + " Longitude: -92.649710°", + "FINAL ANSWER: 25.272049, -92.649710" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -43.11819, + "lon": -73.61661, + "name": "Quellón" + }, + "point_b": { + "lat": 22.9464, + "lon": 113.35769, + "name": "Shiqiao" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -15.714254, + "lon": 122.822051 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-43.11819°, -73.61661°)", + " Point B: (22.9464°, 113.35769°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -15.714254°", + " Longitude: 122.822051°", + "FINAL ANSWER: -15.714254, 122.822051" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 5.8245, + "lon": -73.03408, + "name": "Duitama" + }, + "point_b": { + "lat": 43.28444, + "lon": -2.16992, + "name": "Zarautz" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 29.132796, + "lon": -43.891719 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (5.8245°, -73.03408°)", + " Point B: (43.28444°, -2.16992°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 29.132796°", + " Longitude: -43.891719°", + "FINAL ANSWER: 29.132796, -43.891719" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 13.66108, + "lon": -89.18252, + "name": "San Marcos" + }, + "point_b": { + "lat": 9.26667, + "lon": -9.01667, + "name": "Kérouané" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 14.844774, + "lon": -48.724427 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (13.66108°, -89.18252°)", + " Point B: (9.26667°, -9.01667°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 14.844774°", + " Longitude: -48.724427°", + "FINAL ANSWER: 14.844774, -48.724427" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -20.66028, + "lon": -43.78611, + "name": "Conselheiro Lafaiete" + }, + "point_b": { + "lat": -33.84808, + "lon": 18.71723, + "name": "Kraaifontein" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -33.573745, + "lon": 1.790808 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-20.66028°, -43.78611°)", + " Point B: (-33.84808°, 18.71723°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -33.573745°", + " Longitude: 1.790808°", + "FINAL ANSWER: -33.573745, 1.790808" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 64.571, + "lon": 30.57667, + "name": "Kostomuksha" + }, + "point_b": { + "lat": 13.48754, + "lon": 144.78143, + "name": "Tamuning" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 52.011052, + "lon": 118.594177 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (64.571°, 30.57667°)", + " Point B: (13.48754°, 144.78143°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 52.011052°", + " Longitude: 118.594177°", + "FINAL ANSWER: 52.011052, 118.594177" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -31.09048, + "lon": 150.92905, + "name": "Tamworth" + }, + "point_b": { + "lat": 28.62989, + "lon": 79.47648, + "name": "Deoraniān" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 14.194532, + "lon": 98.266361 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-31.09048°, 150.92905°)", + " Point B: (28.62989°, 79.47648°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 14.194532°", + " Longitude: 98.266361°", + "FINAL ANSWER: 14.194532, 98.266361" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 16.74385, + "lon": 77.98597, + "name": "Mahbūbnagar" + }, + "point_b": { + "lat": 22.8275, + "lon": 86.21639, + "name": "Mango" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 18.298928, + "lon": 79.986181 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (16.74385°, 77.98597°)", + " Point B: (22.8275°, 86.21639°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 18.298928°", + " Longitude: 79.986181°", + "FINAL ANSWER: 18.298928, 79.986181" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -13.5, + "lon": 48.86667, + "name": "Ambarakaraka" + }, + "point_b": { + "lat": 13.311, + "lon": 101.11214, + "name": "Ban Bueng" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -6.981651, + "lon": 62.119837 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-13.5°, 48.86667°)", + " Point B: (13.311°, 101.11214°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -6.981651°", + " Longitude: 62.119837°", + "FINAL ANSWER: -6.981651, 62.119837" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 51.40424, + "lon": -0.41817, + "name": "Sunbury-on-Thames" + }, + "point_b": { + "lat": 50.93463, + "lon": 6.97495, + "name": "Deutz" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 51.227707, + "lon": 3.297237 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (51.40424°, -0.41817°)", + " Point B: (50.93463°, 6.97495°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 51.227707°", + " Longitude: 3.297237°", + "FINAL ANSWER: 51.227707, 3.297237" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 12.60961, + "lon": 102.10447, + "name": "Chanthaburi" + }, + "point_b": { + "lat": 41.07056, + "lon": 129.42917, + "name": "Myŏngch’ŏn" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 20.152474, + "lon": 107.758108 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (12.60961°, 102.10447°)", + " Point B: (41.07056°, 129.42917°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 20.152474°", + " Longitude: 107.758108°", + "FINAL ANSWER: 20.152474, 107.758108" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -3.61667, + "lon": 33.86667, + "name": "Kishapu" + }, + "point_b": { + "lat": 38.37881, + "lon": 128.4676, + "name": "Kosong" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 11.139886, + "lon": 52.840878 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-3.61667°, 33.86667°)", + " Point B: (38.37881°, 128.4676°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 11.139886°", + " Longitude: 52.840878°", + "FINAL ANSWER: 11.139886, 52.840878" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -33.79176, + "lon": 151.08057, + "name": "Eastwood" + }, + "point_b": { + "lat": -27.59667, + "lon": -48.54917, + "name": "Florianópolis" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -60.042462, + "lon": 169.793214 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-33.79176°, 151.08057°)", + " Point B: (-27.59667°, -48.54917°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -60.042462°", + " Longitude: 169.793214°", + "FINAL ANSWER: -60.042462, 169.793214" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -32.24295, + "lon": 148.60484, + "name": "Dubbo" + }, + "point_b": { + "lat": 7.94783, + "lon": 4.78836, + "name": "Otan Ayegbaju" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -33.973904, + "lon": 63.143716 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-32.24295°, 148.60484°)", + " Point B: (7.94783°, 4.78836°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -33.973904°", + " Longitude: 63.143716°", + "FINAL ANSWER: -33.973904, 63.143716" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 55.76232, + "lon": 52.04425, + "name": "Yelabuga" + }, + "point_b": { + "lat": 38.54491, + "lon": -121.74052, + "name": "Davis" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 76.958776, + "lon": 44.155596 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (55.76232°, 52.04425°)", + " Point B: (38.54491°, -121.74052°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 76.958776°", + " Longitude: 44.155596°", + "FINAL ANSWER: 76.958776, 44.155596" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -27.64613, + "lon": 152.85965, + "name": "Redbank Plains" + }, + "point_b": { + "lat": -9.39028, + "lon": -36.76, + "name": "Estrela de Alagoas" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -73.450405, + "lon": -89.347982 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-27.64613°, 152.85965°)", + " Point B: (-9.39028°, -36.76°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -73.450405°", + " Longitude: -89.347982°", + "FINAL ANSWER: -73.450405, -89.347982" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -25.85583, + "lon": -52.52333, + "name": "Chopinzinho" + }, + "point_b": { + "lat": 37.65639, + "lon": 126.835, + "name": "Goyang-si" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 79.499061, + "lon": 116.412654 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-25.85583°, -52.52333°)", + " Point B: (37.65639°, 126.835°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 79.499061°", + " Longitude: 116.412654°", + "FINAL ANSWER: 79.499061, 116.412654" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 25.16478, + "lon": 93.01744, + "name": "Hāflong" + }, + "point_b": { + "lat": 32.25174, + "lon": -110.73731, + "name": "Tanque Verde" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 57.568072, + "lon": -133.127527 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (25.16478°, 93.01744°)", + " Point B: (32.25174°, -110.73731°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 57.568072°", + " Longitude: -133.127527°", + "FINAL ANSWER: 57.568072, -133.127527" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 55.71667, + "lon": 37.78333, + "name": "Novokuz’minki" + }, + "point_b": { + "lat": -22.55941, + "lon": 17.08323, + "name": "Windhoek" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 16.821922, + "lon": 24.899809 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (55.71667°, 37.78333°)", + " Point B: (-22.55941°, 17.08323°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 16.821922°", + " Longitude: 24.899809°", + "FINAL ANSWER: 16.821922, 24.899809" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 11.55965, + "lon": 9.66407, + "name": "Chakwama" + }, + "point_b": { + "lat": 10.3831, + "lon": 104.48753, + "name": "Hà Tiên" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 14.99357, + "lon": 33.192987 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (11.55965°, 9.66407°)", + " Point B: (10.3831°, 104.48753°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 14.993570°", + " Longitude: 33.192987°", + "FINAL ANSWER: 14.993570, 33.192987" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 10.3401, + "lon": -68.74297, + "name": "San Felipe" + }, + "point_b": { + "lat": 22.3401, + "lon": 114.18732, + "name": "Wang Tau Hom" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 46.949497, + "lon": -73.134926 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (10.3401°, -68.74297°)", + " Point B: (22.3401°, 114.18732°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 46.949497°", + " Longitude: -73.134926°", + "FINAL ANSWER: 46.949497, -73.134926" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 59.62056, + "lon": 30.39, + "name": "Kommunar" + }, + "point_b": { + "lat": 29.08139, + "lon": 106.81639, + "name": "Longsheng" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 57.681419, + "lon": 58.453203 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (59.62056°, 30.39°)", + " Point B: (29.08139°, 106.81639°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 57.681419°", + " Longitude: 58.453203°", + "FINAL ANSWER: 57.681419, 58.453203" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 9.90028, + "lon": -84.0017, + "name": "San Diego" + }, + "point_b": { + "lat": 34.3, + "lon": 133.81667, + "name": "Utazu" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 50.993351, + "lon": 169.694788 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (9.90028°, -84.0017°)", + " Point B: (34.3°, 133.81667°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 50.993351°", + " Longitude: 169.694788°", + "FINAL ANSWER: 50.993351, 169.694788" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -30.78991, + "lon": -60.59276, + "name": "San Justo" + }, + "point_b": { + "lat": 29.56689, + "lon": -104.54487, + "name": "Ojinaga" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -16.005456, + "lon": -72.501214 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-30.78991°, -60.59276°)", + " Point B: (29.56689°, -104.54487°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -16.005456°", + " Longitude: -72.501214°", + "FINAL ANSWER: -16.005456, -72.501214" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -30.40001, + "lon": 27.70027, + "name": "Quthing" + }, + "point_b": { + "lat": 7.95642, + "lon": -72.24235, + "name": "Michelena" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -26.336137, + "lon": -1.153431 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-30.40001°, 27.70027°)", + " Point B: (7.95642°, -72.24235°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -26.336137°", + " Longitude: -1.153431°", + "FINAL ANSWER: -26.336137, -1.153431" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 22.24126, + "lon": -80.3911, + "name": "Palmira" + }, + "point_b": { + "lat": 30.61618, + "lon": 31.73514, + "name": "Al Qurayn" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 39.984351, + "lon": 4.444612 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (22.24126°, -80.3911°)", + " Point B: (30.61618°, 31.73514°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 39.984351°", + " Longitude: 4.444612°", + "FINAL ANSWER: 39.984351, 4.444612" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 30.88251, + "lon": 31.46275, + "name": "As Sinbillāwayn" + }, + "point_b": { + "lat": 34.3, + "lon": 133.81667, + "name": "Utazu" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 45.55278, + "lon": 81.281983 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (30.88251°, 31.46275°)", + " Point B: (34.3°, 133.81667°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 45.552780°", + " Longitude: 81.281983°", + "FINAL ANSWER: 45.552780, 81.281983" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 36.41528, + "lon": 128.16056, + "name": "Sangju" + }, + "point_b": { + "lat": 54.9876, + "lon": -1.74415, + "name": "Newburn" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 67.166714, + "lon": 31.47581 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (36.41528°, 128.16056°)", + " Point B: (54.9876°, -1.74415°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 67.166714°", + " Longitude: 31.475810°", + "FINAL ANSWER: 67.166714, 31.475810" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -38.26667, + "lon": 145.01667, + "name": "Mount Martha" + }, + "point_b": { + "lat": 24.7031, + "lon": 98.57007, + "name": "Puchuan" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -23.307316, + "lon": 131.032652 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-38.26667°, 145.01667°)", + " Point B: (24.7031°, 98.57007°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -23.307316°", + " Longitude: 131.032652°", + "FINAL ANSWER: -23.307316, 131.032652" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 34.90373, + "lon": -82.33317, + "name": "Wade Hampton" + }, + "point_b": { + "lat": 40.85927, + "lon": -73.89847, + "name": "Fordham" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 37.956692, + "lon": -78.286798 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (34.90373°, -82.33317°)", + " Point B: (40.85927°, -73.89847°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 37.956692°", + " Longitude: -78.286798°", + "FINAL ANSWER: 37.956692, -78.286798" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 44.22375, + "lon": 42.04624, + "name": "Cherkessk" + }, + "point_b": { + "lat": 40.35, + "lon": -3.7, + "name": "Villaverde" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 45.037862, + "lon": 30.279249 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (44.22375°, 42.04624°)", + " Point B: (40.35°, -3.7°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 45.037862°", + " Longitude: 30.279249°", + "FINAL ANSWER: 45.037862, 30.279249" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -3.35, + "lon": 37.33333, + "name": "Moshi" + }, + "point_b": { + "lat": -4.54167, + "lon": -40.71889, + "name": "Ipueiras" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -5.073954, + "lon": -1.659467 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-3.35°, 37.33333°)", + " Point B: (-4.54167°, -40.71889°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -5.073954°", + " Longitude: -1.659467°", + "FINAL ANSWER: -5.073954, -1.659467" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 14.2698, + "lon": 75.35643, + "name": "Shikaripura" + }, + "point_b": { + "lat": 21.82427, + "lon": 76.35086, + "name": "Khandwa" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 16.158873, + "lon": 75.597365 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (14.2698°, 75.35643°)", + " Point B: (21.82427°, 76.35086°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 16.158873°", + " Longitude: 75.597365°", + "FINAL ANSWER: 16.158873, 75.597365" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -21.93361, + "lon": -42.60861, + "name": "Carmo" + }, + "point_b": { + "lat": 9.25929, + "lon": 76.55642, + "name": "Māvelikara" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -12.35535, + "lon": 19.996429 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-21.93361°, -42.60861°)", + " Point B: (9.25929°, 76.55642°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -12.355350°", + " Longitude: 19.996429°", + "FINAL ANSWER: -12.355350, 19.996429" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 52.44293, + "lon": 13.43388, + "name": "Britz" + }, + "point_b": { + "lat": -10.91722, + "lon": -37.65, + "name": "Lagarto" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 5.956167, + "lon": -28.369063 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (52.44293°, 13.43388°)", + " Point B: (-10.91722°, -37.65°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 5.956167°", + " Longitude: -28.369063°", + "FINAL ANSWER: 5.956167, -28.369063" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 8.96249, + "lon": -71.60754, + "name": "Pueblo Nuevo El Chivo" + }, + "point_b": { + "lat": 54.14774, + "lon": 48.38644, + "name": "Novoul’yanovsk" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 48.317626, + "lon": -35.48278 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (8.96249°, -71.60754°)", + " Point B: (54.14774°, 48.38644°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 48.317626°", + " Longitude: -35.482780°", + "FINAL ANSWER: 48.317626, -35.482780" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 22.12745, + "lon": 75.61101, + "name": "Kasrāwad" + }, + "point_b": { + "lat": 49.49991, + "lon": -115.76879, + "name": "Cranbrook" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 75.141703, + "lon": -135.561222 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (22.12745°, 75.61101°)", + " Point B: (49.49991°, -115.76879°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 75.141703°", + " Longitude: -135.561222°", + "FINAL ANSWER: 75.141703, -135.561222" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -4.42741, + "lon": 26.66656, + "name": "Kasongo" + }, + "point_b": { + "lat": 25.15, + "lon": 76.3, + "name": "Anta" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 11.386367, + "lon": 50.204626 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-4.42741°, 26.66656°)", + " Point B: (25.15°, 76.3°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 11.386367°", + " Longitude: 50.204626°", + "FINAL ANSWER: 11.386367, 50.204626" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 19.10446, + "lon": -99.5898, + "name": "Tenango de Arista" + }, + "point_b": { + "lat": 41.45532, + "lon": -81.91792, + "name": "Westlake" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 30.574582, + "lon": -91.781147 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (19.10446°, -99.5898°)", + " Point B: (41.45532°, -81.91792°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 30.574582°", + " Longitude: -91.781147°", + "FINAL ANSWER: 30.574582, -91.781147" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 11.21266, + "lon": 79.36369, + "name": "Jayamkondacholapuram" + }, + "point_b": { + "lat": 52.33964, + "lon": 4.96256, + "name": "Diemen" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 47.347236, + "lon": 31.820963 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (11.21266°, 79.36369°)", + " Point B: (52.33964°, 4.96256°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 47.347236°", + " Longitude: 31.820963°", + "FINAL ANSWER: 47.347236, 31.820963" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -27.63917, + "lon": 153.10944, + "name": "Logan City" + }, + "point_b": { + "lat": 6.65623, + "lon": -6.16609, + "name": "Gadouan" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -44.499602, + "lon": 56.118343 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-27.63917°, 153.10944°)", + " Point B: (6.65623°, -6.16609°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -44.499602°", + " Longitude: 56.118343°", + "FINAL ANSWER: -44.499602, 56.118343" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 23.7791, + "lon": 79.14321, + "name": "Garhākota" + }, + "point_b": { + "lat": -3.22028, + "lon": -45.00361, + "name": "Viana" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 21.103571, + "lon": 12.374084 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (23.7791°, 79.14321°)", + " Point B: (-3.22028°, -45.00361°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 21.103571°", + " Longitude: 12.374084°", + "FINAL ANSWER: 21.103571, 12.374084" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -34.57365, + "lon": -58.44924, + "name": "Colegiales" + }, + "point_b": { + "lat": 13.44528, + "lon": -16.70278, + "name": "Manjai Kunda" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -23.333114, + "lon": -46.103469 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-34.57365°, -58.44924°)", + " Point B: (13.44528°, -16.70278°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -23.333114°", + " Longitude: -46.103469°", + "FINAL ANSWER: -23.333114, -46.103469" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 40.04068, + "lon": 124.33525, + "name": "Langtoucun" + }, + "point_b": { + "lat": 45.45111, + "lon": 12.22389, + "name": "Marghera" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 55.91128, + "lon": 37.162307 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (40.04068°, 124.33525°)", + " Point B: (45.45111°, 12.22389°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 55.911280°", + " Longitude: 37.162307°", + "FINAL ANSWER: 55.911280, 37.162307" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 32.54278, + "lon": 111.50861, + "name": "Danjiangkou" + }, + "point_b": { + "lat": 45.4105, + "lon": 12.36649, + "name": "Lido" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 51.128139, + "lon": 68.050478 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (32.54278°, 111.50861°)", + " Point B: (45.4105°, 12.36649°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 51.128139°", + " Longitude: 68.050478°", + "FINAL ANSWER: 51.128139, 68.050478" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -19.80083, + "lon": -41.71306, + "name": "Ipanema" + }, + "point_b": { + "lat": 39.86671, + "lon": -86.14165, + "name": "Broad Ripple" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -4.563356, + "lon": -51.849473 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-19.80083°, -41.71306°)", + " Point B: (39.86671°, -86.14165°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -4.563356°", + " Longitude: -51.849473°", + "FINAL ANSWER: -4.563356, -51.849473" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 21.47231, + "lon": 78.53415, + "name": "Narkher" + }, + "point_b": { + "lat": 36.48994, + "lon": 5.5393, + "name": "Babor" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 29.032119, + "lon": 62.877324 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (21.47231°, 78.53415°)", + " Point B: (36.48994°, 5.5393°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 29.032119°", + " Longitude: 62.877324°", + "FINAL ANSWER: 29.032119, 62.877324" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 34.03511, + "lon": 105.03286, + "name": "Zhongba" + }, + "point_b": { + "lat": 44.84247, + "lon": -0.64512, + "name": "Mérignac" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 46.203342, + "lon": 85.645944 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (34.03511°, 105.03286°)", + " Point B: (44.84247°, -0.64512°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 46.203342°", + " Longitude: 85.645944°", + "FINAL ANSWER: 46.203342, 85.645944" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 51.73262, + "lon": 6.59031, + "name": "Hamminkeln" + }, + "point_b": { + "lat": -0.68393, + "lon": 37.35701, + "name": "Wanguru" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 26.298956, + "lon": 25.673727 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (51.73262°, 6.59031°)", + " Point B: (-0.68393°, 37.35701°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 26.298956°", + " Longitude: 25.673727°", + "FINAL ANSWER: 26.298956, 25.673727" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 19.58867, + "lon": -98.56972, + "name": "Calpulalpan" + }, + "point_b": { + "lat": -7.03306, + "lon": 107.51833, + "name": "Soreang" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 11.462766, + "lon": 140.811484 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (19.58867°, -98.56972°)", + " Point B: (-7.03306°, 107.51833°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 11.462766°", + " Longitude: 140.811484°", + "FINAL ANSWER: 11.462766, 140.811484" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 31.34337, + "lon": 34.32337, + "name": "Banī Suhaylā" + }, + "point_b": { + "lat": 53.22752, + "lon": -4.12936, + "name": "Bangor" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 37.867494, + "lon": 27.133383 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (31.34337°, 34.32337°)", + " Point B: (53.22752°, -4.12936°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 37.867494°", + " Longitude: 27.133383°", + "FINAL ANSWER: 37.867494, 27.133383" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 31.17419, + "lon": 31.2218, + "name": "Biyalā" + }, + "point_b": { + "lat": 42.28819, + "lon": 24.96779, + "name": "Rakovski" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 39.54208, + "lon": 26.711613 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (31.17419°, 31.2218°)", + " Point B: (42.28819°, 24.96779°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 39.542080°", + " Longitude: 26.711613°", + "FINAL ANSWER: 39.542080, 26.711613" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 45.23992, + "lon": 4.6707, + "name": "Annonay" + }, + "point_b": { + "lat": -16.46111, + "lon": -49.96167, + "name": "Anicuns" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -0.205123, + "lon": -38.554559 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (45.23992°, 4.6707°)", + " Point B: (-16.46111°, -49.96167°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -0.205123°", + " Longitude: -38.554559°", + "FINAL ANSWER: -0.205123, -38.554559" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 54.09224, + "lon": 61.56756, + "name": "Troitsk" + }, + "point_b": { + "lat": 30.74536, + "lon": 120.4851, + "name": "Wuzhen" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 51.517708, + "lon": 80.854243 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (54.09224°, 61.56756°)", + " Point B: (30.74536°, 120.4851°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 51.517708°", + " Longitude: 80.854243°", + "FINAL ANSWER: 51.517708, 80.854243" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 13.11915, + "lon": 1.79869, + "name": "Torodi" + }, + "point_b": { + "lat": 43.92551, + "lon": 81.41212, + "name": "Hudiyuzi" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 41.929459, + "lon": 56.365726 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (13.11915°, 1.79869°)", + " Point B: (43.92551°, 81.41212°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 41.929459°", + " Longitude: 56.365726°", + "FINAL ANSWER: 41.929459, 56.365726" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 7.75, + "lon": 2.18333, + "name": "Dassa-Zoumè" + }, + "point_b": { + "lat": 53.79538, + "lon": -1.66134, + "name": "Pudsey" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 42.296757, + "lon": -0.233839 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (7.75°, 2.18333°)", + " Point B: (53.79538°, -1.66134°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 42.296757°", + " Longitude: -0.233839°", + "FINAL ANSWER: 42.296757, -0.233839" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 41.29444, + "lon": 69.67639, + "name": "Parkent" + }, + "point_b": { + "lat": 41.03578, + "lon": 14.3823, + "name": "Maddaloni" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 43.667341, + "lon": 27.767427 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (41.29444°, 69.67639°)", + " Point B: (41.03578°, 14.3823°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 43.667341°", + " Longitude: 27.767427°", + "FINAL ANSWER: 43.667341, 27.767427" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 49.83538, + "lon": 36.6865, + "name": "Chuhuiv" + }, + "point_b": { + "lat": -8.35694, + "lon": 114.61694, + "name": "Negara" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 8.928769, + "lon": 100.666179 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (49.83538°, 36.6865°)", + " Point B: (-8.35694°, 114.61694°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 8.928769°", + " Longitude: 100.666179°", + "FINAL ANSWER: 8.928769, 100.666179" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 32.47098, + "lon": -85.00077, + "name": "Phenix City" + }, + "point_b": { + "lat": -5.35218, + "lon": 21.42192, + "name": "Luebo" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 8.96037, + "lon": -1.162255 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (32.47098°, -85.00077°)", + " Point B: (-5.35218°, 21.42192°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 8.960370°", + " Longitude: -1.162255°", + "FINAL ANSWER: 8.960370, -1.162255" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 0.60732, + "lon": 9.32933, + "name": "Akanda" + }, + "point_b": { + "lat": 51.19806, + "lon": 42.24605, + "name": "Povorino" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 26.803839, + "lon": 21.90884 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (0.60732°, 9.32933°)", + " Point B: (51.19806°, 42.24605°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 26.803839°", + " Longitude: 21.908840°", + "FINAL ANSWER: 26.803839, 21.908840" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 53.42519, + "lon": -2.32443, + "name": "Sale" + }, + "point_b": { + "lat": -37.81501, + "lon": 144.96657, + "name": "Melbourne City Centre" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 50.045599, + "lon": 61.203768 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (53.42519°, -2.32443°)", + " Point B: (-37.81501°, 144.96657°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 50.045599°", + " Longitude: 61.203768°", + "FINAL ANSWER: 50.045599, 61.203768" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 43.51121, + "lon": 44.59051, + "name": "Malgobek" + }, + "point_b": { + "lat": -25.54778, + "lon": -54.58806, + "name": "Foz do Iguaçu" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -6.403589, + "lon": -32.607855 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (43.51121°, 44.59051°)", + " Point B: (-25.54778°, -54.58806°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -6.403589°", + " Longitude: -32.607855°", + "FINAL ANSWER: -6.403589, -32.607855" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 42.0, + "lon": 21.32778, + "name": "Saraj" + }, + "point_b": { + "lat": 48.89148, + "lon": 2.46451, + "name": "Noisy-le-Sec" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 44.002403, + "lon": 17.045879 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (42.0°, 21.32778°)", + " Point B: (48.89148°, 2.46451°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 44.002403°", + " Longitude: 17.045879°", + "FINAL ANSWER: 44.002403, 17.045879" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 40.59918, + "lon": 22.98613, + "name": "Pylaía" + }, + "point_b": { + "lat": 27.58031, + "lon": -80.38672, + "name": "Florida Ridge" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 47.705385, + "lon": -3.861542 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (40.59918°, 22.98613°)", + " Point B: (27.58031°, -80.38672°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 47.705385°", + " Longitude: -3.861542°", + "FINAL ANSWER: 47.705385, -3.861542" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 30.70838, + "lon": 49.16266, + "name": "Shahrak-e Shahīd Chamrān" + }, + "point_b": { + "lat": 41.8792, + "lon": -87.84312, + "name": "Maywood" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 58.835931, + "lon": -59.771094 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (30.70838°, 49.16266°)", + " Point B: (41.8792°, -87.84312°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 58.835931°", + " Longitude: -59.771094°", + "FINAL ANSWER: 58.835931, -59.771094" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -34.09345, + "lon": 21.25725, + "name": "Riversdale" + }, + "point_b": { + "lat": 43.65899, + "lon": 145.13197, + "name": "Shibetsu" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -13.494976, + "lon": 51.18094 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-34.09345°, 21.25725°)", + " Point B: (43.65899°, 145.13197°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -13.494976°", + " Longitude: 51.180940°", + "FINAL ANSWER: -13.494976, 51.180940" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 33.61601, + "lon": -7.12153, + "name": "Benslimane" + }, + "point_b": { + "lat": 32.98527, + "lon": 70.60403, + "name": "Bannu" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 38.520634, + "lon": 11.523369 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (33.61601°, -7.12153°)", + " Point B: (32.98527°, 70.60403°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 38.520634°", + " Longitude: 11.523369°", + "FINAL ANSWER: 38.520634, 11.523369" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -20.4725, + "lon": -45.12556, + "name": "Itapecerica" + }, + "point_b": { + "lat": 36.07696, + "lon": 37.37251, + "name": "As Safīrah" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -5.366302, + "lon": -25.873211 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-20.4725°, -45.12556°)", + " Point B: (36.07696°, 37.37251°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -5.366302°", + " Longitude: -25.873211°", + "FINAL ANSWER: -5.366302, -25.873211" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -12.7275, + "lon": -39.18194, + "name": "Sapeaçu" + }, + "point_b": { + "lat": 49.22594, + "lon": -123.04282, + "name": "Killarney" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 5.638746, + "lon": -54.597559 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-12.7275°, -39.18194°)", + " Point B: (49.22594°, -123.04282°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 5.638746°", + " Longitude: -54.597559°", + "FINAL ANSWER: 5.638746, -54.597559" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 40.56139, + "lon": 65.68861, + "name": "Nurota" + }, + "point_b": { + "lat": -37.95453, + "lon": -72.43438, + "name": "Collipulli" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -20.185782, + "lon": -34.916918 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (40.56139°, 65.68861°)", + " Point B: (-37.95453°, -72.43438°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -20.185782°", + " Longitude: -34.916918°", + "FINAL ANSWER: -20.185782, -34.916918" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -23.54476, + "lon": -46.64105, + "name": "Republica" + }, + "point_b": { + "lat": 6.97647, + "lon": -7.79834, + "name": "Zou" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -8.77555, + "lon": -26.417271 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-23.54476°, -46.64105°)", + " Point B: (6.97647°, -7.79834°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -8.775550°", + " Longitude: -26.417271°", + "FINAL ANSWER: -8.775550, -26.417271" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 29.36937, + "lon": 105.88323, + "name": "Zhuhai" + }, + "point_b": { + "lat": 27.81993, + "lon": -82.68944, + "name": "West and East Lealman" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 57.798309, + "lon": -91.113384 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (29.36937°, 105.88323°)", + " Point B: (27.81993°, -82.68944°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 57.798309°", + " Longitude: -91.113384°", + "FINAL ANSWER: 57.798309, -91.113384" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 25.38327, + "lon": 97.39637, + "name": "Myitkyina" + }, + "point_b": { + "lat": -25.63473, + "lon": 27.78022, + "name": "Brits" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -13.490191, + "lon": 46.135826 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (25.38327°, 97.39637°)", + " Point B: (-25.63473°, 27.78022°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -13.490191°", + " Longitude: 46.135826°", + "FINAL ANSWER: -13.490191, 46.135826" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -10.83444, + "lon": -38.53583, + "name": "Ribeira do Pombal" + }, + "point_b": { + "lat": -21.26111, + "lon": -48.49639, + "name": "Monte Alto" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -16.105403, + "lon": -43.38507 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-10.83444°, -38.53583°)", + " Point B: (-21.26111°, -48.49639°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -16.105403°", + " Longitude: -43.385070°", + "FINAL ANSWER: -16.105403, -43.385070" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 5.27247, + "lon": -3.59625, + "name": "Bonoua" + }, + "point_b": { + "lat": -5.89624, + "lon": 22.41659, + "name": "Kananga" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -0.320097, + "lon": 9.403126 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (5.27247°, -3.59625°)", + " Point B: (-5.89624°, 22.41659°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -0.320097°", + " Longitude: 9.403126°", + "FINAL ANSWER: -0.320097, 9.403126" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 8.58679, + "lon": 39.12111, + "name": "Mojo" + }, + "point_b": { + "lat": 52.15705, + "lon": 10.4154, + "name": "Salzgitter" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 19.938924, + "lon": 34.053762 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (8.58679°, 39.12111°)", + " Point B: (52.15705°, 10.4154°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 19.938924°", + " Longitude: 34.053762°", + "FINAL ANSWER: 19.938924, 34.053762" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -24.52611, + "lon": -49.94861, + "name": "Piraí do Sul" + }, + "point_b": { + "lat": -32.78588, + "lon": -71.53222, + "name": "Quintero" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -31.058195, + "lon": -65.811921 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-24.52611°, -49.94861°)", + " Point B: (-32.78588°, -71.53222°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -31.058195°", + " Longitude: -65.811921°", + "FINAL ANSWER: -31.058195, -65.811921" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 6.58412, + "lon": 3.98336, + "name": "Epe" + }, + "point_b": { + "lat": 10.82578, + "lon": 2.10479, + "name": "Kérou" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 8.706102, + "lon": 3.049401 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (6.58412°, 3.98336°)", + " Point B: (10.82578°, 2.10479°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 8.706102°", + " Longitude: 3.049401°", + "FINAL ANSWER: 8.706102, 3.049401" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 32.75, + "lon": -0.58333, + "name": "Aïn Sefra" + }, + "point_b": { + "lat": 32.77133, + "lon": -6.39231, + "name": "Bejaâd" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 32.780471, + "lon": -2.03504 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (32.75°, -0.58333°)", + " Point B: (32.77133°, -6.39231°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 32.780471°", + " Longitude: -2.035040°", + "FINAL ANSWER: 32.780471, -2.035040" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 16.394, + "lon": 120.3545, + "name": "Aringay" + }, + "point_b": { + "lat": 51.22047, + "lon": 4.40026, + "name": "Antwerpen" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 57.249703, + "lon": 43.196282 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (16.394°, 120.3545°)", + " Point B: (51.22047°, 4.40026°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 57.249703°", + " Longitude: 43.196282°", + "FINAL ANSWER: 57.249703, 43.196282" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 47.99597, + "lon": -4.09795, + "name": "Quimper" + }, + "point_b": { + "lat": 53.5, + "lon": -1.45, + "name": "Hoyland Nether" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 52.129803, + "lon": -2.17253 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (47.99597°, -4.09795°)", + " Point B: (53.5°, -1.45°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 52.129803°", + " Longitude: -2.172530°", + "FINAL ANSWER: 52.129803, -2.172530" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 16.70836, + "lon": 95.9336, + "name": "Twante" + }, + "point_b": { + "lat": 18.14968, + "lon": -65.82738, + "name": "Humacao" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 47.457082, + "lon": -41.983235 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (16.70836°, 95.9336°)", + " Point B: (18.14968°, -65.82738°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 47.457082°", + " Longitude: -41.983235°", + "FINAL ANSWER: 47.457082, -41.983235" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 10.88459, + "lon": 75.93091, + "name": "Talakkād" + }, + "point_b": { + "lat": 12.26593, + "lon": -86.56474, + "name": "Nagarote" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 38.836788, + "lon": 47.417275 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (10.88459°, 75.93091°)", + " Point B: (12.26593°, -86.56474°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 38.836788°", + " Longitude: 47.417275°", + "FINAL ANSWER: 38.836788, 47.417275" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -34.40639, + "lon": -70.85834, + "name": "Rengo" + }, + "point_b": { + "lat": -37.81667, + "lon": 144.9, + "name": "Yarraville" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -67.130404, + "lon": -139.127753 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-34.40639°, -70.85834°)", + " Point B: (-37.81667°, 144.9°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -67.130404°", + " Longitude: -139.127753°", + "FINAL ANSWER: -67.130404, -139.127753" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 50.84799, + "lon": 4.25972, + "name": "Dilbeek" + }, + "point_b": { + "lat": 21.86667, + "lon": 73.5, + "name": "Rājpīpla" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 32.439131, + "lon": 61.414905 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (50.84799°, 4.25972°)", + " Point B: (21.86667°, 73.5°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 32.439131°", + " Longitude: 61.414905°", + "FINAL ANSWER: 32.439131, 61.414905" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 30.67399, + "lon": 74.75579, + "name": "Farīdkot" + }, + "point_b": { + "lat": 26.23111, + "lon": 109.13139, + "name": "Liping" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 29.562036, + "lon": 92.316117 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (30.67399°, 74.75579°)", + " Point B: (26.23111°, 109.13139°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 29.562036°", + " Longitude: 92.316117°", + "FINAL ANSWER: 29.562036, 92.316117" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 36.1534, + "lon": 136.27029, + "name": "Maruoka" + }, + "point_b": { + "lat": 36.26468, + "lon": 68.01551, + "name": "Aībak" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 40.083652, + "lon": 119.879413 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (36.1534°, 136.27029°)", + " Point B: (36.26468°, 68.01551°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 40.083652°", + " Longitude: 119.879413°", + "FINAL ANSWER: 40.083652, 119.879413" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -7.54528, + "lon": -35.7075, + "name": "Aroeiras" + }, + "point_b": { + "lat": 31.0306, + "lon": 61.4949, + "name": "Zābol" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 17.394076, + "lon": 8.176556 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-7.54528°, -35.7075°)", + " Point B: (31.0306°, 61.4949°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 17.394076°", + " Longitude: 8.176556°", + "FINAL ANSWER: 17.394076, 8.176556" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -1.52823, + "lon": -45.07862, + "name": "Apicum-Açu" + }, + "point_b": { + "lat": 47.35818, + "lon": -122.12216, + "name": "Covington" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 28.106684, + "lon": -74.904115 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-1.52823°, -45.07862°)", + " Point B: (47.35818°, -122.12216°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 28.106684°", + " Longitude: -74.904115°", + "FINAL ANSWER: 28.106684, -74.904115" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 10.99544, + "lon": 77.09904, + "name": "Kannampālaiyam" + }, + "point_b": { + "lat": 0.87178, + "lon": 35.12213, + "name": "Moi‘s Bridge" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 6.351892, + "lon": 55.908234 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (10.99544°, 77.09904°)", + " Point B: (0.87178°, 35.12213°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 6.351892°", + " Longitude: 55.908234°", + "FINAL ANSWER: 6.351892, 55.908234" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 48.21289, + "lon": 16.52442, + "name": "Essling" + }, + "point_b": { + "lat": -14.81909, + "lon": 14.53504, + "name": "Quipungo" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 32.457369, + "lon": 15.829921 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (48.21289°, 16.52442°)", + " Point B: (-14.81909°, 14.53504°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 32.457369°", + " Longitude: 15.829921°", + "FINAL ANSWER: 32.457369, 15.829921" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 46.92436, + "lon": 7.41457, + "name": "Köniz" + }, + "point_b": { + "lat": -11.54722, + "lon": -41.9775, + "name": "Ibititá" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 33.95734, + "lon": -9.688312 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (46.92436°, 7.41457°)", + " Point B: (-11.54722°, -41.9775°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 33.957340°", + " Longitude: -9.688312°", + "FINAL ANSWER: 33.957340, -9.688312" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 16.79997, + "lon": 121.11924, + "name": "Lagawe" + }, + "point_b": { + "lat": 6.40764, + "lon": 1.88198, + "name": "Comé" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 22.324175, + "lon": 90.952725 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (16.79997°, 121.11924°)", + " Point B: (6.40764°, 1.88198°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 22.324175°", + " Longitude: 90.952725°", + "FINAL ANSWER: 22.324175, 90.952725" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 40.52828, + "lon": 72.7985, + "name": "Osh" + }, + "point_b": { + "lat": 51.59067, + "lon": -0.02077, + "name": "Walthamstow" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 52.127982, + "lon": 40.627427 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (40.52828°, 72.7985°)", + " Point B: (51.59067°, -0.02077°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 52.127982°", + " Longitude: 40.627427°", + "FINAL ANSWER: 52.127982, 40.627427" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 34.25, + "lon": 135.31667, + "name": "Iwade" + }, + "point_b": { + "lat": -6.16394, + "lon": 39.19793, + "name": "Zanzibar" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 30.097155, + "lon": 106.535943 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (34.25°, 135.31667°)", + " Point B: (-6.16394°, 39.19793°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 30.097155°", + " Longitude: 106.535943°", + "FINAL ANSWER: 30.097155, 106.535943" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 50.04523, + "lon": 18.70062, + "name": "Żory" + }, + "point_b": { + "lat": 35.86781, + "lon": 1.11143, + "name": "Ammi Moussa" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 43.29002, + "lon": 8.879753 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (50.04523°, 18.70062°)", + " Point B: (35.86781°, 1.11143°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 43.290020°", + " Longitude: 8.879753°", + "FINAL ANSWER: 43.290020, 8.879753" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 30.09299, + "lon": -93.73655, + "name": "Orange" + }, + "point_b": { + "lat": 20.14624, + "lon": 92.89835, + "name": "Sittwe" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 61.87072, + "lon": -102.895461 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (30.09299°, -93.73655°)", + " Point B: (20.14624°, 92.89835°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 61.870720°", + " Longitude: -102.895461°", + "FINAL ANSWER: 61.870720, -102.895461" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -8.81833, + "lon": -35.18639, + "name": "Barreiros" + }, + "point_b": { + "lat": 51.07592, + "lon": 17.72284, + "name": "Namysłów" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 7.312195, + "lon": -25.488876 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-8.81833°, -35.18639°)", + " Point B: (51.07592°, 17.72284°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 7.312195°", + " Longitude: -25.488876°", + "FINAL ANSWER: 7.312195, -25.488876" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -9.58833, + "lon": -67.5325, + "name": "Porto Acre" + }, + "point_b": { + "lat": -25.11364, + "lon": -64.12628, + "name": "Joaquín V. González" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -17.35818, + "lon": -65.90195 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-9.58833°, -67.5325°)", + " Point B: (-25.11364°, -64.12628°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -17.358180°", + " Longitude: -65.901950°", + "FINAL ANSWER: -17.358180, -65.901950" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 39.95559, + "lon": -86.01387, + "name": "Fishers" + }, + "point_b": { + "lat": 35.71541, + "lon": 140.55309, + "name": "Sōsa" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 53.370194, + "lon": 162.203562 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (39.95559°, -86.01387°)", + " Point B: (35.71541°, 140.55309°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 53.370194°", + " Longitude: 162.203562°", + "FINAL ANSWER: 53.370194, 162.203562" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 21.31608, + "lon": -157.80423, + "name": "Manoa" + }, + "point_b": { + "lat": 14.72051, + "lon": -17.1816, + "name": "Diamniadio" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 33.901852, + "lon": -45.264169 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (21.31608°, -157.80423°)", + " Point B: (14.72051°, -17.1816°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 33.901852°", + " Longitude: -45.264169°", + "FINAL ANSWER: 33.901852, -45.264169" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 47.20791, + "lon": 7.53714, + "name": "Solothurn" + }, + "point_b": { + "lat": 38.04668, + "lon": -97.34504, + "name": "Newton" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 56.363595, + "lon": -50.381783 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (47.20791°, 7.53714°)", + " Point B: (38.04668°, -97.34504°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 56.363595°", + " Longitude: -50.381783°", + "FINAL ANSWER: 56.363595, -50.381783" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 10.5166, + "lon": 108.93292, + "name": "Phú Quý" + }, + "point_b": { + "lat": -33.68909, + "lon": -71.21528, + "name": "Melipilla" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -28.689571, + "lon": 109.158726 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (10.5166°, 108.93292°)", + " Point B: (-33.68909°, -71.21528°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -28.689571°", + " Longitude: 109.158726°", + "FINAL ANSWER: -28.689571, 109.158726" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 17.48486, + "lon": 78.41376, + "name": "Kukatpally" + }, + "point_b": { + "lat": 44.00011, + "lon": -79.46632, + "name": "Aurora" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 44.578709, + "lon": 66.718963 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (17.48486°, 78.41376°)", + " Point B: (44.00011°, -79.46632°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 44.578709°", + " Longitude: 66.718963°", + "FINAL ANSWER: 44.578709, 66.718963" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 41.10652, + "lon": 28.86847, + "name": "Sultangazi" + }, + "point_b": { + "lat": 40.21436, + "lon": 44.57846, + "name": "Avan" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 40.92759, + "lon": 36.776326 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (41.10652°, 28.86847°)", + " Point B: (40.21436°, 44.57846°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 40.927590°", + " Longitude: 36.776326°", + "FINAL ANSWER: 40.927590, 36.776326" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 48.31661, + "lon": 31.52355, + "name": "Novoukrayinka" + }, + "point_b": { + "lat": -27.58333, + "lon": 153.1, + "name": "Eight Mile Plains" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 19.960828, + "lon": 106.625221 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (48.31661°, 31.52355°)", + " Point B: (-27.58333°, 153.1°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 19.960828°", + " Longitude: 106.625221°", + "FINAL ANSWER: 19.960828, 106.625221" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -15.32333, + "lon": -58.00361, + "name": "Lambari d'Oeste" + }, + "point_b": { + "lat": -2.21452, + "lon": -80.95151, + "name": "Salinas" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -5.606582, + "lon": -75.350062 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-15.32333°, -58.00361°)", + " Point B: (-2.21452°, -80.95151°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -5.606582°", + " Longitude: -75.350062°", + "FINAL ANSWER: -5.606582, -75.350062" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 24.00826, + "lon": 76.7325, + "name": "Rājgarh" + }, + "point_b": { + "lat": -2.94047, + "lon": -44.24898, + "name": "Rosário" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 25.949361, + "lon": 43.794049 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (24.00826°, 76.7325°)", + " Point B: (-2.94047°, -44.24898°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 25.949361°", + " Longitude: 43.794049°", + "FINAL ANSWER: 25.949361, 43.794049" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 40.01833, + "lon": 127.45472, + "name": "Yŏnggwang-ŭp" + }, + "point_b": { + "lat": 24.31365, + "lon": 79.11806, + "name": "Shāhgarh" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 38.029663, + "lon": 113.768257 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (40.01833°, 127.45472°)", + " Point B: (24.31365°, 79.11806°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 38.029663°", + " Longitude: 113.768257°", + "FINAL ANSWER: 38.029663, 113.768257" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 14.6627, + "lon": 121.0328, + "name": "Bagong Pagasa" + }, + "point_b": { + "lat": -2.21896, + "lon": 29.2343, + "name": "Gihombo" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 3.615482, + "lon": 51.570999 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (14.6627°, 121.0328°)", + " Point B: (-2.21896°, 29.2343°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 3.615482°", + " Longitude: 51.570999°", + "FINAL ANSWER: 3.615482, 51.570999" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 9.06667, + "lon": 38.5, + "name": "Genet" + }, + "point_b": { + "lat": -12.52897, + "lon": 27.88382, + "name": "Chingola" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -7.141454, + "lon": 30.584783 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (9.06667°, 38.5°)", + " Point B: (-12.52897°, 27.88382°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -7.141454°", + " Longitude: 30.584783°", + "FINAL ANSWER: -7.141454, 30.584783" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 51.13204, + "lon": 13.58312, + "name": "Coswig" + }, + "point_b": { + "lat": 53.61766, + "lon": -2.1552, + "name": "Rochdale" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 52.636437, + "lon": 5.936842 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (51.13204°, 13.58312°)", + " Point B: (53.61766°, -2.1552°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 52.636437°", + " Longitude: 5.936842°", + "FINAL ANSWER: 52.636437, 5.936842" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 24.05783, + "lon": 89.87696, + "name": "Nāgarpur" + }, + "point_b": { + "lat": 48.64682, + "lon": 2.31965, + "name": "Sainte-Geneviève-des-Bois" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 50.022601, + "lon": 29.483898 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (24.05783°, 89.87696°)", + " Point B: (48.64682°, 2.31965°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 50.022601°", + " Longitude: 29.483898°", + "FINAL ANSWER: 50.022601, 29.483898" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 32.58847, + "lon": -96.95612, + "name": "Cedar Hill" + }, + "point_b": { + "lat": 21.17429, + "lon": -86.84656, + "name": "Cancún" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 29.806409, + "lon": -94.225749 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (32.58847°, -96.95612°)", + " Point B: (21.17429°, -86.84656°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 29.806409°", + " Longitude: -94.225749°", + "FINAL ANSWER: 29.806409, -94.225749" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 8.66389, + "lon": 16.85324, + "name": "Doba" + }, + "point_b": { + "lat": -16.80993, + "lon": 29.69247, + "name": "Karoi" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -10.470859, + "lon": 26.363675 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (8.66389°, 16.85324°)", + " Point B: (-16.80993°, 29.69247°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -10.470859°", + " Longitude: 26.363675°", + "FINAL ANSWER: -10.470859, 26.363675" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 46.72594, + "lon": 131.13308, + "name": "Jixian" + }, + "point_b": { + "lat": 51.22172, + "lon": 6.77616, + "name": "Düsseldorf" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 63.566821, + "lon": 30.976993 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (46.72594°, 131.13308°)", + " Point B: (51.22172°, 6.77616°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 63.566821°", + " Longitude: 30.976993°", + "FINAL ANSWER: 63.566821, 30.976993" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 42.66085, + "lon": -8.11285, + "name": "Lalín" + }, + "point_b": { + "lat": 11.1, + "lon": -13.76667, + "name": "Sangarédi" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 26.907992, + "lon": -11.34504 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (42.66085°, -8.11285°)", + " Point B: (11.1°, -13.76667°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 26.907992°", + " Longitude: -11.345040°", + "FINAL ANSWER: 26.907992, -11.345040" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 0.33474, + "lon": 34.48796, + "name": "Mumias" + }, + "point_b": { + "lat": -21.99861, + "lon": -49.45722, + "name": "Pirajuí" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -7.492497, + "lon": 14.80864 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (0.33474°, 34.48796°)", + " Point B: (-21.99861°, -49.45722°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -7.492497°", + " Longitude: 14.808640°", + "FINAL ANSWER: -7.492497, 14.808640" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 10.05, + "lon": -5.33778, + "name": "Nambingué" + }, + "point_b": { + "lat": 41.87792, + "lon": 20.88389, + "name": "Negotino" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 34.441407, + "lon": 12.714066 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (10.05°, -5.33778°)", + " Point B: (41.87792°, 20.88389°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 34.441407°", + " Longitude: 12.714066°", + "FINAL ANSWER: 34.441407, 12.714066" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 5.78928, + "lon": -75.42725, + "name": "Abejorral" + }, + "point_b": { + "lat": 35.79167, + "lon": 127.42528, + "name": "Jinan-gun" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 59.708132, + "lon": -127.280651 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (5.78928°, -75.42725°)", + " Point B: (35.79167°, 127.42528°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 59.708132°", + " Longitude: -127.280651°", + "FINAL ANSWER: 59.708132, -127.280651" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 39.3925, + "lon": 28.13111, + "name": "Bigadiç" + }, + "point_b": { + "lat": 39.74345, + "lon": -74.28098, + "name": "Ocean Acres" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 49.207052, + "lon": -51.89145 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (39.3925°, 28.13111°)", + " Point B: (39.74345°, -74.28098°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 49.207052°", + " Longitude: -51.891450°", + "FINAL ANSWER: 49.207052, -51.891450" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -20.55722, + "lon": -48.56778, + "name": "Barretos" + }, + "point_b": { + "lat": 20.88722, + "lon": -76.26306, + "name": "Holguín" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -10.266695, + "lon": -55.712445 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-20.55722°, -48.56778°)", + " Point B: (20.88722°, -76.26306°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -10.266695°", + " Longitude: -55.712445°", + "FINAL ANSWER: -10.266695, -55.712445" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -4.37555, + "lon": -70.03179, + "name": "Benjamin Constant" + }, + "point_b": { + "lat": 45.16024, + "lon": -93.08883, + "name": "Lino Lakes" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 33.142089, + "lon": -85.369944 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-4.37555°, -70.03179°)", + " Point B: (45.16024°, -93.08883°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 33.142089°", + " Longitude: -85.369944°", + "FINAL ANSWER: 33.142089, -85.369944" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 51.3281, + "lon": 8.00369, + "name": "Sundern" + }, + "point_b": { + "lat": 43.38946, + "lon": 10.43615, + "name": "Rosignano Solvay-Castiglioncello" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 45.378696, + "lon": 9.893639 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (51.3281°, 8.00369°)", + " Point B: (43.38946°, 10.43615°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 45.378696°", + " Longitude: 9.893639°", + "FINAL ANSWER: 45.378696, 9.893639" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 21.77241, + "lon": -79.26832, + "name": "La Sierpe" + }, + "point_b": { + "lat": 9.27949, + "lon": 12.45819, + "name": "Jimeta" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 16.664845, + "lon": -8.873523 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (21.77241°, -79.26832°)", + " Point B: (9.27949°, 12.45819°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 16.664845°", + " Longitude: -8.873523°", + "FINAL ANSWER: 16.664845, -8.873523" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 19.9355, + "lon": -97.96125, + "name": "Zacatlán" + }, + "point_b": { + "lat": 33.72871, + "lon": -5.01092, + "name": "Imouzzer Kandar" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 36.241377, + "lon": -55.171839 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (19.9355°, -97.96125°)", + " Point B: (33.72871°, -5.01092°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 36.241377°", + " Longitude: -55.171839°", + "FINAL ANSWER: 36.241377, -55.171839" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 36.41528, + "lon": 128.16056, + "name": "Sangju" + }, + "point_b": { + "lat": 53.51703, + "lon": 10.2488, + "name": "Reinbek" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 61.980942, + "lon": 83.214408 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (36.41528°, 128.16056°)", + " Point B: (53.51703°, 10.2488°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 61.980942°", + " Longitude: 83.214408°", + "FINAL ANSWER: 61.980942, 83.214408" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 33.74538, + "lon": -84.13158, + "name": "Redan" + }, + "point_b": { + "lat": 40.45595, + "lon": -3.73839, + "name": "Ciudad Universitaria" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 44.572715, + "lon": -24.154763 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (33.74538°, -84.13158°)", + " Point B: (40.45595°, -3.73839°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 44.572715°", + " Longitude: -24.154763°", + "FINAL ANSWER: 44.572715, -24.154763" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 12.35, + "lon": 29.25, + "name": "Abū Zabad" + }, + "point_b": { + "lat": 45.65192, + "lon": 10.25681, + "name": "San Sebastiano" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 37.618143, + "lon": 16.411061 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (12.35°, 29.25°)", + " Point B: (45.65192°, 10.25681°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 37.618143°", + " Longitude: 16.411061°", + "FINAL ANSWER: 37.618143, 16.411061" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -41.51603, + "lon": 173.9528, + "name": "Blenheim" + }, + "point_b": { + "lat": -1.13667, + "lon": 12.46399, + "name": "Koulamoutou" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -32.530421, + "lon": 25.00824 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-41.51603°, 173.9528°)", + " Point B: (-1.13667°, 12.46399°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -32.530421°", + " Longitude: 25.008240°", + "FINAL ANSWER: -32.530421, 25.008240" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 45.05288, + "lon": 7.67979, + "name": "San Salvario" + }, + "point_b": { + "lat": 16.6614, + "lon": -9.6149, + "name": "Ayoun El Atrous" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 31.139633, + "lon": -2.284266 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (45.05288°, 7.67979°)", + " Point B: (16.6614°, -9.6149°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 31.139633°", + " Longitude: -2.284266°", + "FINAL ANSWER: 31.139633, -2.284266" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -23.35028, + "lon": -47.68861, + "name": "Iperó" + }, + "point_b": { + "lat": -23.90449, + "lon": 29.46885, + "name": "Polokwane" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -29.230791, + "lon": -9.206577 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-23.35028°, -47.68861°)", + " Point B: (-23.90449°, 29.46885°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -29.230791°", + " Longitude: -9.206577°", + "FINAL ANSWER: -29.230791, -9.206577" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 41.78232, + "lon": -72.61203, + "name": "East Hartford" + }, + "point_b": { + "lat": 12.03427, + "lon": 75.23779, + "name": "Mādāyi" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 58.937927, + "lon": 26.381224 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (41.78232°, -72.61203°)", + " Point B: (12.03427°, 75.23779°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 58.937927°", + " Longitude: 26.381224°", + "FINAL ANSWER: 58.937927, 26.381224" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 7.31667, + "lon": 38.08333, + "name": "K’olīto" + }, + "point_b": { + "lat": 51.22834, + "lon": -2.32211, + "name": "Frome" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 30.76263, + "lon": 22.634022 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (7.31667°, 38.08333°)", + " Point B: (51.22834°, -2.32211°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 30.762630°", + " Longitude: 22.634022°", + "FINAL ANSWER: 30.762630, 22.634022" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 53.61028, + "lon": 10.05917, + "name": "Steilshoop" + }, + "point_b": { + "lat": 48.86667, + "lon": 2.71667, + "name": "Lagny-sur-Marne" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 50.094228, + "lon": 4.413348 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (53.61028°, 10.05917°)", + " Point B: (48.86667°, 2.71667°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 50.094228°", + " Longitude: 4.413348°", + "FINAL ANSWER: 50.094228, 4.413348" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -19.17222, + "lon": -41.47222, + "name": "Conselheiro Pena" + }, + "point_b": { + "lat": 33.99722, + "lon": -6.74047, + "name": "Salé Al Jadida" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 7.760703, + "lon": -25.272739 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-19.17222°, -41.47222°)", + " Point B: (33.99722°, -6.74047°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 7.760703°", + " Longitude: -25.272739°", + "FINAL ANSWER: 7.760703, -25.272739" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 26.44931, + "lon": 91.61356, + "name": "Rangia" + }, + "point_b": { + "lat": 22.16667, + "lon": 111.78333, + "name": "Yangchun" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 25.63634, + "lon": 96.780772 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (26.44931°, 91.61356°)", + " Point B: (22.16667°, 111.78333°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 25.636340°", + " Longitude: 96.780772°", + "FINAL ANSWER: 25.636340, 96.780772" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 14.2897, + "lon": 120.7168, + "name": "Ternate" + }, + "point_b": { + "lat": 49.46307, + "lon": 1.09364, + "name": "Mont-Saint-Aignan" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 33.541363, + "lon": 104.405313 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (14.2897°, 120.7168°)", + " Point B: (49.46307°, 1.09364°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 33.541363°", + " Longitude: 104.405313°", + "FINAL ANSWER: 33.541363, 104.405313" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 35.47619, + "lon": 136.7721, + "name": "Yamagata" + }, + "point_b": { + "lat": -4.27333, + "lon": -41.77694, + "name": "Piripiri" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 32.886214, + "lon": -40.136452 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (35.47619°, 136.7721°)", + " Point B: (-4.27333°, -41.77694°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 32.886214°", + " Longitude: -40.136452°", + "FINAL ANSWER: 32.886214, -40.136452" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 40.4842, + "lon": -88.99369, + "name": "Bloomington" + }, + "point_b": { + "lat": -33.55384, + "lon": -71.60761, + "name": "Cartagena" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 3.505265, + "lon": -79.900648 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (40.4842°, -88.99369°)", + " Point B: (-33.55384°, -71.60761°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 3.505265°", + " Longitude: -79.900648°", + "FINAL ANSWER: 3.505265, -79.900648" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 18.04348, + "lon": 77.206, + "name": "Bhālki" + }, + "point_b": { + "lat": 56.34485, + "lon": 37.52041, + "name": "Dmitrov" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 28.595317, + "lon": 70.717272 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (18.04348°, 77.206°)", + " Point B: (56.34485°, 37.52041°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 28.595317°", + " Longitude: 70.717272°", + "FINAL ANSWER: 28.595317, 70.717272" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 52.05959, + "lon": 19.19972, + "name": "Łęczyca" + }, + "point_b": { + "lat": -37.69047, + "lon": 144.74172, + "name": "Hillside" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 39.718769, + "lon": 67.367623 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (52.05959°, 19.19972°)", + " Point B: (-37.69047°, 144.74172°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 39.718769°", + " Longitude: 67.367623°", + "FINAL ANSWER: 39.718769, 67.367623" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -2.4421, + "lon": 28.9824, + "name": "Bushenge" + }, + "point_b": { + "lat": 8.1, + "lon": 36.95, + "name": "Suntu" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 2.835791, + "lon": 32.948009 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-2.4421°, 28.9824°)", + " Point B: (8.1°, 36.95°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 2.835791°", + " Longitude: 32.948009°", + "FINAL ANSWER: 2.835791, 32.948009" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 36.76835, + "lon": 137.12572, + "name": "Imizu" + }, + "point_b": { + "lat": 37.07028, + "lon": 41.21465, + "name": "Nusaybin" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 48.28803, + "lon": 89.295962 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (36.76835°, 137.12572°)", + " Point B: (37.07028°, 41.21465°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 48.288030°", + " Longitude: 89.295962°", + "FINAL ANSWER: 48.288030, 89.295962" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 20.5087, + "lon": 72.94569, + "name": "Pārdi" + }, + "point_b": { + "lat": 36.13068, + "lon": 68.70829, + "name": "Baghlān" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 28.335966, + "lon": 70.983683 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (20.5087°, 72.94569°)", + " Point B: (36.13068°, 68.70829°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 28.335966°", + " Longitude: 70.983683°", + "FINAL ANSWER: 28.335966, 70.983683" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 19.05385, + "lon": -70.15116, + "name": "Cotuí" + }, + "point_b": { + "lat": 35.06937, + "lon": -1.13706, + "name": "Sidi Abdelli" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 26.277369, + "lon": -55.172028 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (19.05385°, -70.15116°)", + " Point B: (35.06937°, -1.13706°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 26.277369°", + " Longitude: -55.172028°", + "FINAL ANSWER: 26.277369, -55.172028" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -24.28139, + "lon": -47.45972, + "name": "Miracatu" + }, + "point_b": { + "lat": 49.17771, + "lon": 33.74415, + "name": "Revivka" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -4.281502, + "lon": -30.735127 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-24.28139°, -47.45972°)", + " Point B: (49.17771°, 33.74415°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -4.281502°", + " Longitude: -30.735127°", + "FINAL ANSWER: -4.281502, -30.735127" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 16.24004, + "lon": -92.13668, + "name": "Comitán" + }, + "point_b": { + "lat": -16.49611, + "lon": -49.42639, + "name": "Goianira" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -0.137474, + "lon": -70.796238 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (16.24004°, -92.13668°)", + " Point B: (-16.49611°, -49.42639°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -0.137474°", + " Longitude: -70.796238°", + "FINAL ANSWER: -0.137474, -70.796238" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 37.37389, + "lon": 36.09611, + "name": "Kadirli" + }, + "point_b": { + "lat": -6.35944, + "lon": -39.29861, + "name": "Iguatu" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 19.257824, + "lon": -6.519638 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (37.37389°, 36.09611°)", + " Point B: (-6.35944°, -39.29861°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 19.257824°", + " Longitude: -6.519638°", + "FINAL ANSWER: 19.257824, -6.519638" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 31.08125, + "lon": 108.41164, + "name": "Zhaojia" + }, + "point_b": { + "lat": 26.19028, + "lon": 107.5125, + "name": "Xiaoweizhai" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 28.636506, + "lon": 107.951586 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (31.08125°, 108.41164°)", + " Point B: (26.19028°, 107.5125°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 28.636506°", + " Longitude: 107.951586°", + "FINAL ANSWER: 28.636506, 107.951586" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 50.40578, + "lon": 3.89603, + "name": "Frameries" + }, + "point_b": { + "lat": 2.70167, + "lon": 33.67611, + "name": "Abim" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 27.304011, + "lon": 22.148432 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (50.40578°, 3.89603°)", + " Point B: (2.70167°, 33.67611°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 27.304011°", + " Longitude: 22.148432°", + "FINAL ANSWER: 27.304011, 22.148432" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 42.50835, + "lon": -89.03178, + "name": "Beloit" + }, + "point_b": { + "lat": -7.5325, + "lon": -46.03556, + "name": "Balsas" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 18.678277, + "lon": -64.218751 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (42.50835°, -89.03178°)", + " Point B: (-7.5325°, -46.03556°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 18.678277°", + " Longitude: -64.218751°", + "FINAL ANSWER: 18.678277, -64.218751" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 10.64061, + "lon": 36.94684, + "name": "Shendi" + }, + "point_b": { + "lat": 11.88435, + "lon": 3.44919, + "name": "Gaya" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 11.31125, + "lon": 28.607155 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (10.64061°, 36.94684°)", + " Point B: (11.88435°, 3.44919°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 11.311250°", + " Longitude: 28.607155°", + "FINAL ANSWER: 11.311250, 28.607155" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 26.18924, + "lon": -98.15529, + "name": "San Juan" + }, + "point_b": { + "lat": -4.32124, + "lon": -46.45468, + "name": "Buriticupu" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 19.664437, + "lon": -83.902124 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (26.18924°, -98.15529°)", + " Point B: (-4.32124°, -46.45468°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 19.664437°", + " Longitude: -83.902124°", + "FINAL ANSWER: 19.664437, -83.902124" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 16.90634, + "lon": -92.09349, + "name": "Ocosingo" + }, + "point_b": { + "lat": 22.74747, + "lon": 77.72736, + "name": "Narmadapuram" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 75.896895, + "lon": -18.852369 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (16.90634°, -92.09349°)", + " Point B: (22.74747°, 77.72736°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 75.896895°", + " Longitude: -18.852369°", + "FINAL ANSWER: 75.896895, -18.852369" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 13.55285, + "lon": 76.01164, + "name": "Kadūr" + }, + "point_b": { + "lat": 1.15, + "lon": 34.15, + "name": "Nakaloke" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 7.8644, + "lon": 54.773609 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (13.55285°, 76.01164°)", + " Point B: (1.15°, 34.15°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 7.864400°", + " Longitude: 54.773609°", + "FINAL ANSWER: 7.864400, 54.773609" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -25.47776, + "lon": 31.14559, + "name": "Tekwane" + }, + "point_b": { + "lat": 2.11667, + "lon": 111.51667, + "name": "Sarikei" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -21.659257, + "lon": 53.215235 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-25.47776°, 31.14559°)", + " Point B: (2.11667°, 111.51667°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -21.659257°", + " Longitude: 53.215235°", + "FINAL ANSWER: -21.659257, 53.215235" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -4.87694, + "lon": 29.62667, + "name": "Kigoma" + }, + "point_b": { + "lat": -27.94389, + "lon": -52.92306, + "name": "Sarandi" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -13.861588, + "lon": 11.170582 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-4.87694°, 29.62667°)", + " Point B: (-27.94389°, -52.92306°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -13.861588°", + " Longitude: 11.170582°", + "FINAL ANSWER: -13.861588, 11.170582" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 28.55778, + "lon": -81.4534, + "name": "Pine Hills" + }, + "point_b": { + "lat": 44.13806, + "lon": 4.81025, + "name": "Orange" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 45.110795, + "lon": -43.709298 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (28.55778°, -81.4534°)", + " Point B: (44.13806°, 4.81025°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 45.110795°", + " Longitude: -43.709298°", + "FINAL ANSWER: 45.110795, -43.709298" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 19.23502, + "lon": -101.45824, + "name": "Tacámbaro de Codallos" + }, + "point_b": { + "lat": 21.27388, + "lon": 78.5858, + "name": "Kātol" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 56.146615, + "lon": 78.651502 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (19.23502°, -101.45824°)", + " Point B: (21.27388°, 78.5858°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 56.146615°", + " Longitude: 78.651502°", + "FINAL ANSWER: 56.146615, 78.651502" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 8.58, + "lon": 125.89639, + "name": "Prosperidad" + }, + "point_b": { + "lat": 48.67211, + "lon": 2.39318, + "name": "Viry-Châtillon" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 29.460067, + "lon": 109.206803 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (8.58°, 125.89639°)", + " Point B: (48.67211°, 2.39318°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 29.460067°", + " Longitude: 109.206803°", + "FINAL ANSWER: 29.460067, 109.206803" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 38.73178, + "lon": -77.4311, + "name": "Buckhall" + }, + "point_b": { + "lat": 49.39552, + "lon": 13.29505, + "name": "Klatovy" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 53.908274, + "lon": -37.294821 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (38.73178°, -77.4311°)", + " Point B: (49.39552°, 13.29505°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 53.908274°", + " Longitude: -37.294821°", + "FINAL ANSWER: 53.908274, -37.294821" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 33.69189, + "lon": 130.76531, + "name": "Akaike" + }, + "point_b": { + "lat": 29.09926, + "lon": 104.39416, + "name": "Guanyin" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 30.74813, + "lon": 110.723406 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (33.69189°, 130.76531°)", + " Point B: (29.09926°, 104.39416°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 30.748130°", + " Longitude: 110.723406°", + "FINAL ANSWER: 30.748130, 110.723406" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 16.3982, + "lon": 78.63758, + "name": "Achampet" + }, + "point_b": { + "lat": 14.9398, + "lon": 33.234, + "name": "Al Hilāliyya" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 16.912421, + "lon": 55.850216 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (16.3982°, 78.63758°)", + " Point B: (14.9398°, 33.234°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 16.912421°", + " Longitude: 55.850216°", + "FINAL ANSWER: 16.912421, 55.850216" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 26.55951, + "lon": 76.32915, + "name": "Lālsot" + }, + "point_b": { + "lat": -17.01037, + "lon": -46.00851, + "name": "Brasilândia de Minas" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -4.109189, + "lon": -16.685777 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (26.55951°, 76.32915°)", + " Point B: (-17.01037°, -46.00851°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -4.109189°", + " Longitude: -16.685777°", + "FINAL ANSWER: -4.109189, -16.685777" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 44.09252, + "lon": 6.23199, + "name": "Digne-les-Bains" + }, + "point_b": { + "lat": 51.5175, + "lon": -0.04292, + "name": "Stepney" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 49.694678, + "lon": 1.701683 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (44.09252°, 6.23199°)", + " Point B: (51.5175°, -0.04292°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 49.694678°", + " Longitude: 1.701683°", + "FINAL ANSWER: 49.694678, 1.701683" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 45.85589, + "lon": 9.39704, + "name": "Lecco" + }, + "point_b": { + "lat": -38.19528, + "lon": 146.5415, + "name": "Traralgon" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 10.266952, + "lon": 86.709671 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (45.85589°, 9.39704°)", + " Point B: (-38.19528°, 146.5415°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 10.266952°", + " Longitude: 86.709671°", + "FINAL ANSWER: 10.266952, 86.709671" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 60.86667, + "lon": 26.7, + "name": "Kouvola" + }, + "point_b": { + "lat": -27.80138, + "lon": 28.42726, + "name": "Reitz" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 16.534271, + "lon": 27.81411 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (60.86667°, 26.7°)", + " Point B: (-27.80138°, 28.42726°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 16.534271°", + " Longitude: 27.814110°", + "FINAL ANSWER: 16.534271, 27.814110" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 51.6, + "lon": 7.76667, + "name": "Bönen" + }, + "point_b": { + "lat": 23.00959, + "lon": 74.57747, + "name": "Thandla" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 48.69974, + "lon": 29.991597 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (51.6°, 7.76667°)", + " Point B: (23.00959°, 74.57747°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 48.699740°", + " Longitude: 29.991597°", + "FINAL ANSWER: 48.699740, 29.991597" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 39.1638, + "lon": -119.7674, + "name": "Carson City" + }, + "point_b": { + "lat": 37.76922, + "lon": -3.79028, + "name": "Jaén" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 56.285111, + "lon": -60.8927 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (39.1638°, -119.7674°)", + " Point B: (37.76922°, -3.79028°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 56.285111°", + " Longitude: -60.892700°", + "FINAL ANSWER: 56.285111, -60.892700" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 14.58691, + "lon": 121.0614, + "name": "Pasig City" + }, + "point_b": { + "lat": 14.073, + "lon": 5.96, + "name": "Madaoua" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 22.278852, + "lon": 33.559014 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (14.58691°, 121.0614°)", + " Point B: (14.073°, 5.96°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 22.278852°", + " Longitude: 33.559014°", + "FINAL ANSWER: 22.278852, 33.559014" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -7.65685, + "lon": 36.98299, + "name": "Ruaha" + }, + "point_b": { + "lat": -11.66417, + "lon": -39.0075, + "name": "Serrinha" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -12.601912, + "lon": -19.895825 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-7.65685°, 36.98299°)", + " Point B: (-11.66417°, -39.0075°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -12.601912°", + " Longitude: -19.895825°", + "FINAL ANSWER: -12.601912, -19.895825" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 42.64685, + "lon": -5.55835, + "name": "Villaquilambre" + }, + "point_b": { + "lat": 43.99942, + "lon": 12.65689, + "name": "Riccione" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 43.686059, + "lon": 3.447017 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (42.64685°, -5.55835°)", + " Point B: (43.99942°, 12.65689°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 43.686059°", + " Longitude: 3.447017°", + "FINAL ANSWER: 43.686059, 3.447017" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -17.4, + "lon": -63.83333, + "name": "Villa Yapacaní" + }, + "point_b": { + "lat": 51.22097, + "lon": 18.56964, + "name": "Wieluń" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 21.681147, + "lon": -32.926673 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-17.4°, -63.83333°)", + " Point B: (51.22097°, 18.56964°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 21.681147°", + " Longitude: -32.926673°", + "FINAL ANSWER: 21.681147, -32.926673" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 50.3592, + "lon": 11.17463, + "name": "Sonneberg" + }, + "point_b": { + "lat": -27.59521, + "lon": 153.12332, + "name": "Rochedale South" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 50.854529, + "lon": 69.152826 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (50.3592°, 11.17463°)", + " Point B: (-27.59521°, 153.12332°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 50.854529°", + " Longitude: 69.152826°", + "FINAL ANSWER: 50.854529, 69.152826" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 25.55613, + "lon": 89.67097, + "name": "Chilmāri" + }, + "point_b": { + "lat": 50.71717, + "lon": 4.60138, + "name": "Wavre" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 46.451537, + "lon": 56.268541 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (25.55613°, 89.67097°)", + " Point B: (50.71717°, 4.60138°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 46.451537°", + " Longitude: 56.268541°", + "FINAL ANSWER: 46.451537, 56.268541" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 8.35122, + "lon": -62.64102, + "name": "Ciudad Guayana" + }, + "point_b": { + "lat": 34.84072, + "lon": 36.73092, + "name": "Tallbīsah" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 36.404221, + "lon": 8.143369 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (8.35122°, -62.64102°)", + " Point B: (34.84072°, 36.73092°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 36.404221°", + " Longitude: 8.143369°", + "FINAL ANSWER: 36.404221, 8.143369" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 43.64229, + "lon": 5.09478, + "name": "Salon-de-Provence" + }, + "point_b": { + "lat": -27.50578, + "lon": 153.10236, + "name": "Carindale" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -0.919103, + "lon": 125.62757 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (43.64229°, 5.09478°)", + " Point B: (-27.50578°, 153.10236°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -0.919103°", + " Longitude: 125.627570°", + "FINAL ANSWER: -0.919103, 125.627570" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 38.24719, + "lon": 125.79476, + "name": "Ayang-ni" + }, + "point_b": { + "lat": -15.11646, + "lon": 39.2666, + "name": "Nampula" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 15.627069, + "lon": 77.002133 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (38.24719°, 125.79476°)", + " Point B: (-15.11646°, 39.2666°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 15.627069°", + " Longitude: 77.002133°", + "FINAL ANSWER: 15.627069, 77.002133" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 34.2, + "lon": 118.48333, + "name": "Shiji" + }, + "point_b": { + "lat": 41.53815, + "lon": -72.80704, + "name": "Meriden" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 81.935768, + "lon": 176.069001 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (34.2°, 118.48333°)", + " Point B: (41.53815°, -72.80704°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 81.935768°", + " Longitude: 176.069001°", + "FINAL ANSWER: 81.935768, 176.069001" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 30.39603, + "lon": -86.22883, + "name": "Santa Rosa Beach" + }, + "point_b": { + "lat": 33.41477, + "lon": -111.90931, + "name": "Tempe" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 33.157681, + "lon": -105.350324 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (30.39603°, -86.22883°)", + " Point B: (33.41477°, -111.90931°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 33.157681°", + " Longitude: -105.350324°", + "FINAL ANSWER: 33.157681, -105.350324" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 30.00043, + "lon": 106.95204, + "name": "Honghu" + }, + "point_b": { + "lat": 35.34926, + "lon": 139.47666, + "name": "Fujisawa" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 32.117361, + "lon": 114.6716 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (30.00043°, 106.95204°)", + " Point B: (35.34926°, 139.47666°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 32.117361°", + " Longitude: 114.671600°", + "FINAL ANSWER: 32.117361, 114.671600" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 16.99154, + "lon": 73.31022, + "name": "Ratnagiri" + }, + "point_b": { + "lat": -37.8318, + "lon": 140.77919, + "name": "Mount Gambier" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -12.444826, + "lon": 103.400602 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (16.99154°, 73.31022°)", + " Point B: (-37.8318°, 140.77919°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -12.444826°", + " Longitude: 103.400602°", + "FINAL ANSWER: -12.444826, 103.400602" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 36.01667, + "lon": 139.98333, + "name": "Mitsukaidō" + }, + "point_b": { + "lat": -8.515, + "lon": -41.005, + "name": "Afrânio" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 74.066345, + "lon": 144.746039 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (36.01667°, 139.98333°)", + " Point B: (-8.515°, -41.005°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 74.066345°", + " Longitude: 144.746039°", + "FINAL ANSWER: 74.066345, 144.746039" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 54.99111, + "lon": -1.53397, + "name": "Wallsend" + }, + "point_b": { + "lat": 34.81667, + "lon": 135.41667, + "name": "Kawanishi" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 68.019932, + "lon": 91.147047 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (54.99111°, -1.53397°)", + " Point B: (34.81667°, 135.41667°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 68.019932°", + " Longitude: 91.147047°", + "FINAL ANSWER: 68.019932, 91.147047" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 50.44767, + "lon": 23.41616, + "name": "Tomaszów Lubelski" + }, + "point_b": { + "lat": 65.31717, + "lon": 21.47944, + "name": "Piteå" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 61.602789, + "lon": 22.134532 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (50.44767°, 23.41616°)", + " Point B: (65.31717°, 21.47944°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 61.602789°", + " Longitude: 22.134532°", + "FINAL ANSWER: 61.602789, 22.134532" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 35.73868, + "lon": 139.74065, + "name": "Komagome" + }, + "point_b": { + "lat": 14.74521, + "lon": -17.13783, + "name": "Sébikhotane" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 60.743738, + "lon": 110.276549 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (35.73868°, 139.74065°)", + " Point B: (14.74521°, -17.13783°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 60.743738°", + " Longitude: 110.276549°", + "FINAL ANSWER: 60.743738, 110.276549" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 39.15278, + "lon": 127.44361, + "name": "Wŏnsan" + }, + "point_b": { + "lat": 40.42788, + "lon": -74.41598, + "name": "East Brunswick" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 77.160888, + "lon": -156.233955 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (39.15278°, 127.44361°)", + " Point B: (40.42788°, -74.41598°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 77.160888°", + " Longitude: -156.233955°", + "FINAL ANSWER: 77.160888, -156.233955" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 50.11944, + "lon": 27.50856, + "name": "Polonne" + }, + "point_b": { + "lat": 13.49667, + "lon": 39.47528, + "name": "Mek'ele" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 31.942467, + "lon": 34.72433 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (50.11944°, 27.50856°)", + " Point B: (13.49667°, 39.47528°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 31.942467°", + " Longitude: 34.724330°", + "FINAL ANSWER: 31.942467, 34.724330" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 7.06756, + "lon": 6.2636, + "name": "Auchi" + }, + "point_b": { + "lat": 42.59671, + "lon": 23.03318, + "name": "Pernik" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 16.094467, + "lon": 9.667242 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (7.06756°, 6.2636°)", + " Point B: (42.59671°, 23.03318°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 16.094467°", + " Longitude: 9.667242°", + "FINAL ANSWER: 16.094467, 9.667242" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 50.82261, + "lon": 9.01294, + "name": "Stadtallendorf" + }, + "point_b": { + "lat": 0.91667, + "lon": 104.45833, + "name": "Tanjung Pinang" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 34.977107, + "lon": 70.673121 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (50.82261°, 9.01294°)", + " Point B: (0.91667°, 104.45833°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 34.977107°", + " Longitude: 70.673121°", + "FINAL ANSWER: 34.977107, 70.673121" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 37.69224, + "lon": -97.33754, + "name": "Wichita" + }, + "point_b": { + "lat": 9.73586, + "lon": -75.52626, + "name": "San Onofre" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 31.034961, + "lon": -90.847688 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (37.69224°, -97.33754°)", + " Point B: (9.73586°, -75.52626°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 31.034961°", + " Longitude: -90.847688°", + "FINAL ANSWER: 31.034961, -90.847688" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 56.1218, + "lon": 93.33814, + "name": "Sosnovoborsk" + }, + "point_b": { + "lat": 41.26914, + "lon": 26.68598, + "name": "Uzunköprü" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 56.420135, + "lon": 73.253423 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (56.1218°, 93.33814°)", + " Point B: (41.26914°, 26.68598°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 56.420135°", + " Longitude: 73.253423°", + "FINAL ANSWER: 56.420135, 73.253423" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -19.51861, + "lon": -42.62889, + "name": "Coronel Fabriciano" + }, + "point_b": { + "lat": -3.54964, + "lon": 143.63229, + "name": "Wewak" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -40.997112, + "lon": 155.86635 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-19.51861°, -42.62889°)", + " Point B: (-3.54964°, 143.63229°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -40.997112°", + " Longitude: 155.866350°", + "FINAL ANSWER: -40.997112, 155.866350" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 30.12996, + "lon": -81.76815, + "name": "Lakeside" + }, + "point_b": { + "lat": -12.96889, + "lon": -39.26139, + "name": "Santo Antônio de Jesus" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 20.01782, + "lon": -69.722523 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (30.12996°, -81.76815°)", + " Point B: (-12.96889°, -39.26139°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 20.017820°", + " Longitude: -69.722523°", + "FINAL ANSWER: 20.017820, -69.722523" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 22.33023, + "lon": 114.15945, + "name": "Sham Shui Po" + }, + "point_b": { + "lat": 26.23648, + "lon": 32.00387, + "name": "Al Balyanā" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 30.237918, + "lon": 52.441425 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (22.33023°, 114.15945°)", + " Point B: (26.23648°, 32.00387°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 30.237918°", + " Longitude: 52.441425°", + "FINAL ANSWER: 30.237918, 52.441425" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -0.15837, + "lon": 29.23859, + "name": "Lubero" + }, + "point_b": { + "lat": 51.5861, + "lon": -0.55543, + "name": "Gerrards Cross" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 39.3682, + "lon": 10.351675 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-0.15837°, 29.23859°)", + " Point B: (51.5861°, -0.55543°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 39.368200°", + " Longitude: 10.351675°", + "FINAL ANSWER: 39.368200, 10.351675" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 36.4701, + "lon": 2.62528, + "name": "El Affroun" + }, + "point_b": { + "lat": 0.82501, + "lon": -77.63966, + "name": "Ipiales" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 23.727761, + "lon": -42.733216 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (36.4701°, 2.62528°)", + " Point B: (0.82501°, -77.63966°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 23.727761°", + " Longitude: -42.733216°", + "FINAL ANSWER: 23.727761, -42.733216" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -13.23251, + "lon": 30.23522, + "name": "Serenje" + }, + "point_b": { + "lat": 52.7225, + "lon": 6.47639, + "name": "Hoogeveen" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 36.636546, + "lon": 15.411038 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-13.23251°, 30.23522°)", + " Point B: (52.7225°, 6.47639°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 36.636546°", + " Longitude: 15.411038°", + "FINAL ANSWER: 36.636546, 15.411038" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 9.90371, + "lon": -83.68361, + "name": "Turrialba" + }, + "point_b": { + "lat": 51.18983, + "lon": 4.56533, + "name": "Ranst" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 48.536653, + "lon": -26.906823 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (9.90371°, -83.68361°)", + " Point B: (51.18983°, 4.56533°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 48.536653°", + " Longitude: -26.906823°", + "FINAL ANSWER: 48.536653, -26.906823" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 49.93023, + "lon": 23.57357, + "name": "Novoyavorivs'k" + }, + "point_b": { + "lat": -7.2, + "lon": 35.73333, + "name": "Izazi" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 7.141128, + "lon": 33.419659 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (49.93023°, 23.57357°)", + " Point B: (-7.2°, 35.73333°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 7.141128°", + " Longitude: 33.419659°", + "FINAL ANSWER: 7.141128, 33.419659" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -3.67722, + "lon": -39.35028, + "name": "Umirim" + }, + "point_b": { + "lat": -1.71464, + "lon": -49.53152, + "name": "São Sebastião da Boa Vista" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -2.212792, + "lon": -46.989119 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-3.67722°, -39.35028°)", + " Point B: (-1.71464°, -49.53152°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -2.212792°", + " Longitude: -46.989119°", + "FINAL ANSWER: -2.212792, -46.989119" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 36.16316, + "lon": -82.83099, + "name": "Greeneville" + }, + "point_b": { + "lat": 35.67004, + "lon": 139.77544, + "name": "Chūō" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 54.243638, + "lon": 162.825366 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (36.16316°, -82.83099°)", + " Point B: (35.67004°, 139.77544°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 54.243638°", + " Longitude: 162.825366°", + "FINAL ANSWER: 54.243638, 162.825366" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -9.31833, + "lon": -35.56111, + "name": "São Luís do Quitunde" + }, + "point_b": { + "lat": -4.78333, + "lon": 38.28333, + "name": "Lushoto" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -9.544768, + "lon": -16.980554 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-9.31833°, -35.56111°)", + " Point B: (-4.78333°, 38.28333°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -9.544768°", + " Longitude: -16.980554°", + "FINAL ANSWER: -9.544768, -16.980554" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 36.91716, + "lon": 3.91311, + "name": "Dellys" + }, + "point_b": { + "lat": 46.79392, + "lon": -71.35191, + "name": "L'Ancienne-Lorette" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 43.977238, + "lon": -11.549598 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (36.91716°, 3.91311°)", + " Point B: (46.79392°, -71.35191°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 43.977238°", + " Longitude: -11.549598°", + "FINAL ANSWER: 43.977238, -11.549598" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 11.07147, + "lon": 77.01729, + "name": "Vilankurichi" + }, + "point_b": { + "lat": 24.7031, + "lon": 98.57007, + "name": "Puchuan" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 14.68656, + "lon": 82.110889 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (11.07147°, 77.01729°)", + " Point B: (24.7031°, 98.57007°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 14.686560°", + " Longitude: 82.110889°", + "FINAL ANSWER: 14.686560, 82.110889" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 40.05015, + "lon": 47.45937, + "name": "Agdzhabedy" + }, + "point_b": { + "lat": -26.06927, + "lon": 30.11489, + "name": "Carolina" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -9.522231, + "lon": 34.301146 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (40.05015°, 47.45937°)", + " Point B: (-26.06927°, 30.11489°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -9.522231°", + " Longitude: 34.301146°", + "FINAL ANSWER: -9.522231, 34.301146" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 51.46026, + "lon": 22.60952, + "name": "Lubartów" + }, + "point_b": { + "lat": 23.71177, + "lon": 76.01571, + "name": "Agar" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 47.170272, + "lon": 40.317379 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (51.46026°, 22.60952°)", + " Point B: (23.71177°, 76.01571°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 47.170272°", + " Longitude: 40.317379°", + "FINAL ANSWER: 47.170272, 40.317379" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 29.38242, + "lon": 70.91106, + "name": "Alipur" + }, + "point_b": { + "lat": 0.83611, + "lon": 33.68611, + "name": "Namutumba" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 22.950731, + "lon": 60.445709 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (29.38242°, 70.91106°)", + " Point B: (0.83611°, 33.68611°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 22.950731°", + " Longitude: 60.445709°", + "FINAL ANSWER: 22.950731, 60.445709" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 59.51833, + "lon": 34.16639, + "name": "Pikalëvo" + }, + "point_b": { + "lat": 41.99083, + "lon": 122.82528, + "name": "Xinmin" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 62.295132, + "lon": 61.657557 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (59.51833°, 34.16639°)", + " Point B: (41.99083°, 122.82528°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 62.295132°", + " Longitude: 61.657557°", + "FINAL ANSWER: 62.295132, 61.657557" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -2.99565, + "lon": -47.35488, + "name": "Paragominas" + }, + "point_b": { + "lat": -1.59106, + "lon": -78.99903, + "name": "Guaranda" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -2.006371, + "lon": -71.093888 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-2.99565°, -47.35488°)", + " Point B: (-1.59106°, -78.99903°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -2.006371°", + " Longitude: -71.093888°", + "FINAL ANSWER: -2.006371, -71.093888" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 50.07438, + "lon": 14.44367, + "name": "Královské Vinohrady" + }, + "point_b": { + "lat": 51.2, + "lon": 6.21667, + "name": "Niederkrüchten" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 50.409706, + "lon": 12.425211 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (50.07438°, 14.44367°)", + " Point B: (51.2°, 6.21667°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 50.409706°", + " Longitude: 12.425211°", + "FINAL ANSWER: 50.409706, 12.425211" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 16.514, + "lon": 80.516, + "name": "Amaravati" + }, + "point_b": { + "lat": 11.04611, + "lon": 14.14011, + "name": "Mora" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 14.24521, + "lon": 30.325296 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (16.514°, 80.516°)", + " Point B: (11.04611°, 14.14011°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 14.245210°", + " Longitude: 30.325296°", + "FINAL ANSWER: 14.245210, 30.325296" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -21.21962, + "lon": 55.31513, + "name": "Piton Saint-Leu" + }, + "point_b": { + "lat": -7.42639, + "lon": 111.02222, + "name": "Sragen" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -16.105694, + "lon": 84.10362 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-21.21962°, 55.31513°)", + " Point B: (-7.42639°, 111.02222°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -16.105694°", + " Longitude: 84.103620°", + "FINAL ANSWER: -16.105694, 84.103620" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 9.30646, + "lon": 123.30769, + "name": "Dumaguete" + }, + "point_b": { + "lat": -22.59139, + "lon": -46.52889, + "name": "Socorro" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -23.979234, + "lon": 99.009009 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (9.30646°, 123.30769°)", + " Point B: (-22.59139°, -46.52889°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -23.979234°", + " Longitude: 99.009009°", + "FINAL ANSWER: -23.979234, 99.009009" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -13.85875, + "lon": -40.08512, + "name": "Jequié" + }, + "point_b": { + "lat": 46.98956, + "lon": 3.159, + "name": "Nevers" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 17.703404, + "lon": -22.423921 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-13.85875°, -40.08512°)", + " Point B: (46.98956°, 3.159°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 17.703404°", + " Longitude: -22.423921°", + "FINAL ANSWER: 17.703404, -22.423921" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 23.72695, + "lon": 111.79723, + "name": "Nanfeng" + }, + "point_b": { + "lat": -28.51222, + "lon": -50.93389, + "name": "Vacaria" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -29.472746, + "lon": -3.802775 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (23.72695°, 111.79723°)", + " Point B: (-28.51222°, -50.93389°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -29.472746°", + " Longitude: -3.802775°", + "FINAL ANSWER: -29.472746, -3.802775" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -18.13683, + "lon": 178.42531, + "name": "Suva" + }, + "point_b": { + "lat": -16.8375, + "lon": 36.98556, + "name": "Mocuba" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -36.240073, + "lon": 148.324336 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-18.13683°, 178.42531°)", + " Point B: (-16.8375°, 36.98556°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -36.240073°", + " Longitude: 148.324336°", + "FINAL ANSWER: -36.240073, 148.324336" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 30.6109, + "lon": 108.63518, + "name": "Longju" + }, + "point_b": { + "lat": 35.54731, + "lon": 138.90959, + "name": "Tsuru" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 34.010124, + "lon": 123.337208 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (30.6109°, 108.63518°)", + " Point B: (35.54731°, 138.90959°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 34.010124°", + " Longitude: 123.337208°", + "FINAL ANSWER: 34.010124, 123.337208" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -1.1136, + "lon": 36.64205, + "name": "Limuru" + }, + "point_b": { + "lat": -3.10139, + "lon": 30.16278, + "name": "Karuzi" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -1.612876, + "lon": 35.023664 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-1.1136°, 36.64205°)", + " Point B: (-3.10139°, 30.16278°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -1.612876°", + " Longitude: 35.023664°", + "FINAL ANSWER: -1.612876, 35.023664" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 26.51839, + "lon": 92.14722, + "name": "Khārupatia" + }, + "point_b": { + "lat": 41.417, + "lon": -81.60596, + "name": "Garfield Heights" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 54.313256, + "lon": 88.09696 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (26.51839°, 92.14722°)", + " Point B: (41.417°, -81.60596°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 54.313256°", + " Longitude: 88.096960°", + "FINAL ANSWER: 54.313256, 88.096960" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 42.73012, + "lon": 133.08381, + "name": "Vrangel’" + }, + "point_b": { + "lat": 8.94333, + "lon": -6.2549, + "name": "Dianra" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 52.332556, + "lon": 41.767116 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (42.73012°, 133.08381°)", + " Point B: (8.94333°, -6.2549°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 52.332556°", + " Longitude: 41.767116°", + "FINAL ANSWER: 52.332556, 41.767116" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 39.93214, + "lon": 48.36892, + "name": "Saatlı" + }, + "point_b": { + "lat": 14.24953, + "lon": 13.10921, + "name": "Nguigmi" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 21.406354, + "lon": 20.492093 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (39.93214°, 48.36892°)", + " Point B: (14.24953°, 13.10921°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 21.406354°", + " Longitude: 20.492093°", + "FINAL ANSWER: 21.406354, 20.492093" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 40.71427, + "lon": -74.00597, + "name": "New York City" + }, + "point_b": { + "lat": 1.30306, + "lon": 103.90778, + "name": "Marine Parade" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 75.057706, + "lon": -67.154611 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (40.71427°, -74.00597°)", + " Point B: (1.30306°, 103.90778°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 75.057706°", + " Longitude: -67.154611°", + "FINAL ANSWER: 75.057706, -67.154611" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 51.38442, + "lon": 4.47556, + "name": "Kalmthout" + }, + "point_b": { + "lat": 40.389, + "lon": -3.70682, + "name": "Moscardó" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 45.959045, + "lon": -0.022467 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (51.38442°, 4.47556°)", + " Point B: (40.389°, -3.70682°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 45.959045°", + " Longitude: -0.022467°", + "FINAL ANSWER: 45.959045, -0.022467" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 53.57982, + "lon": 9.85826, + "name": "Osdorf" + }, + "point_b": { + "lat": 41.07056, + "lon": 129.42917, + "name": "Myŏngch’ŏn" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 64.660834, + "lon": 81.181079 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (53.57982°, 9.85826°)", + " Point B: (41.07056°, 129.42917°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 64.660834°", + " Longitude: 81.181079°", + "FINAL ANSWER: 64.660834, 81.181079" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 50.32607, + "lon": 19.12565, + "name": "Będzin" + }, + "point_b": { + "lat": -22.38484, + "lon": -41.78324, + "name": "Macaé" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 34.484321, + "lon": -2.992304 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (50.32607°, 19.12565°)", + " Point B: (-22.38484°, -41.78324°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 34.484321°", + " Longitude: -2.992304°", + "FINAL ANSWER: 34.484321, -2.992304" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 18.68211, + "lon": 73.73161, + "name": "Dehu Road" + }, + "point_b": { + "lat": -7.26435, + "lon": -64.79638, + "name": "Lábrea" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 5.042395, + "lon": -32.463632 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (18.68211°, 73.73161°)", + " Point B: (-7.26435°, -64.79638°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 5.042395°", + " Longitude: -32.463632°", + "FINAL ANSWER: 5.042395, -32.463632" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 51.40055, + "lon": 6.71187, + "name": "Rheinhausen" + }, + "point_b": { + "lat": 31.09407, + "lon": 105.08731, + "name": "Tongchuan" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 55.970361, + "lon": 35.925176 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (51.40055°, 6.71187°)", + " Point B: (31.09407°, 105.08731°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 55.970361°", + " Longitude: 35.925176°", + "FINAL ANSWER: 55.970361, 35.925176" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 9.24194, + "lon": -74.42667, + "name": "Mompós" + }, + "point_b": { + "lat": 44.5647, + "lon": 27.3633, + "name": "Slobozia" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 45.833469, + "lon": -5.37799 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (9.24194°, -74.42667°)", + " Point B: (44.5647°, 27.3633°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 45.833469°", + " Longitude: -5.377990°", + "FINAL ANSWER: 45.833469, -5.377990" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 21.91908, + "lon": 69.48179, + "name": "Raval" + }, + "point_b": { + "lat": -16.92366, + "lon": 145.76613, + "name": "Cairns" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -7.254702, + "lon": 126.626086 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (21.91908°, 69.48179°)", + " Point B: (-16.92366°, 145.76613°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -7.254702°", + " Longitude: 126.626086°", + "FINAL ANSWER: -7.254702, 126.626086" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -11.25583, + "lon": -39.37472, + "name": "Santaluz" + }, + "point_b": { + "lat": -26.14944, + "lon": -53.02611, + "name": "Marmeleiro" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -22.527191, + "lon": -49.366981 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-11.25583°, -39.37472°)", + " Point B: (-26.14944°, -53.02611°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -22.527191°", + " Longitude: -49.366981°", + "FINAL ANSWER: -22.527191, -49.366981" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -9.43333, + "lon": 159.95, + "name": "Honiara" + }, + "point_b": { + "lat": 56.02927, + "lon": 45.04233, + "name": "Lyskovo" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 36.292081, + "lon": 125.942575 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-9.43333°, 159.95°)", + " Point B: (56.02927°, 45.04233°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 36.292081°", + " Longitude: 125.942575°", + "FINAL ANSWER: 36.292081, 125.942575" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 41.69971, + "lon": -93.04798, + "name": "Newton" + }, + "point_b": { + "lat": -22.57306, + "lon": -47.1725, + "name": "Artur Nogueira" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 10.357151, + "lon": -67.545734 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (41.69971°, -93.04798°)", + " Point B: (-22.57306°, -47.1725°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 10.357151°", + " Longitude: -67.545734°", + "FINAL ANSWER: 10.357151, -67.545734" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 22.37286, + "lon": 114.17897, + "name": "Tai Wai" + }, + "point_b": { + "lat": 37.77493, + "lon": -122.41942, + "name": "San Francisco" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 50.399195, + "lon": 167.605177 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (22.37286°, 114.17897°)", + " Point B: (37.77493°, -122.41942°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 50.399195°", + " Longitude: 167.605177°", + "FINAL ANSWER: 50.399195, 167.605177" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 36.64262, + "lon": 2.69007, + "name": "Bou Ismaïl" + }, + "point_b": { + "lat": -23.62623, + "lon": -46.72828, + "name": "Vila Andrade" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -8.401478, + "lon": -34.782685 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (36.64262°, 2.69007°)", + " Point B: (-23.62623°, -46.72828°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -8.401478°", + " Longitude: -34.782685°", + "FINAL ANSWER: -8.401478, -34.782685" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 44.15906, + "lon": -94.00915, + "name": "Mankato" + }, + "point_b": { + "lat": 8.15, + "lon": 39.35, + "name": "Huruta" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 55.652318, + "lon": -53.111791 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (44.15906°, -94.00915°)", + " Point B: (8.15°, 39.35°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 55.652318°", + " Longitude: -53.111791°", + "FINAL ANSWER: 55.652318, -53.111791" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 6.72028, + "lon": 124.80194, + "name": "Buluan" + }, + "point_b": { + "lat": 38.23242, + "lon": -122.63665, + "name": "Petaluma" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 36.284166, + "lon": 171.161763 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (6.72028°, 124.80194°)", + " Point B: (38.23242°, -122.63665°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 36.284166°", + " Longitude: 171.161763°", + "FINAL ANSWER: 36.284166, 171.161763" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -13.53056, + "lon": -39.97083, + "name": "Jaguaquara" + }, + "point_b": { + "lat": -19.33018, + "lon": 48.97791, + "name": "Vatomandry" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -19.27897, + "lon": -18.734787 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-13.53056°, -39.97083°)", + " Point B: (-19.33018°, 48.97791°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -19.278970°", + " Longitude: -18.734787°", + "FINAL ANSWER: -19.278970, -18.734787" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 30.09299, + "lon": -93.73655, + "name": "Orange" + }, + "point_b": { + "lat": 38.5758, + "lon": 42.01558, + "name": "Güroymak" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 55.697878, + "lon": 14.684597 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (30.09299°, -93.73655°)", + " Point B: (38.5758°, 42.01558°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 55.697878°", + " Longitude: 14.684597°", + "FINAL ANSWER: 55.697878, 14.684597" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -38.08333, + "lon": 144.38333, + "name": "Corio" + }, + "point_b": { + "lat": -29.95917, + "lon": -51.72222, + "name": "São Jerônimo" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -56.379122, + "lon": -62.948116 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-38.08333°, 144.38333°)", + " Point B: (-29.95917°, -51.72222°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -56.379122°", + " Longitude: -62.948116°", + "FINAL ANSWER: -56.379122, -62.948116" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 33.63059, + "lon": -112.33322, + "name": "Surprise" + }, + "point_b": { + "lat": 43.09174, + "lon": 5.82465, + "name": "Six-Fours-les-Plages" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 48.243079, + "lon": -91.791255 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (33.63059°, -112.33322°)", + " Point B: (43.09174°, 5.82465°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 48.243079°", + " Longitude: -91.791255°", + "FINAL ANSWER: 48.243079, -91.791255" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 26.22096, + "lon": 84.35609, + "name": "Siwān" + }, + "point_b": { + "lat": -7.19806, + "lon": -37.92917, + "name": "Piancó" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 19.07122, + "lon": 17.998321 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (26.22096°, 84.35609°)", + " Point B: (-7.19806°, -37.92917°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 19.071220°", + " Longitude: 17.998321°", + "FINAL ANSWER: 19.071220, 17.998321" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 61.66393, + "lon": 50.8163, + "name": "Syktyvkar" + }, + "point_b": { + "lat": 52.89855, + "lon": -1.27136, + "name": "Long Eaton" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 61.616792, + "lon": 35.727145 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (61.66393°, 50.8163°)", + " Point B: (52.89855°, -1.27136°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 61.616792°", + " Longitude: 35.727145°", + "FINAL ANSWER: 61.616792, 35.727145" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 56.28854, + "lon": 62.58115, + "name": "Kataysk" + }, + "point_b": { + "lat": 52.25221, + "lon": 21.26902, + "name": "Sulejówek" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 54.54928, + "lon": 30.613934 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (56.28854°, 62.58115°)", + " Point B: (52.25221°, 21.26902°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 54.549280°", + " Longitude: 30.613934°", + "FINAL ANSWER: 54.549280, 30.613934" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -38.26667, + "lon": 145.01667, + "name": "Mount Martha" + }, + "point_b": { + "lat": 20.65, + "lon": 41.41667, + "name": "Al ‘Aqīq" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -13.984386, + "lon": 86.870292 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-38.26667°, 145.01667°)", + " Point B: (20.65°, 41.41667°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -13.984386°", + " Longitude: 86.870292°", + "FINAL ANSWER: -13.984386, 86.870292" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 27.11716, + "lon": 114.97927, + "name": "Ji’an" + }, + "point_b": { + "lat": 52.60831, + "lon": 1.73052, + "name": "Great Yarmouth" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 43.079554, + "lon": 99.388019 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (27.11716°, 114.97927°)", + " Point B: (52.60831°, 1.73052°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 43.079554°", + " Longitude: 99.388019°", + "FINAL ANSWER: 43.079554, 99.388019" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -45.87416, + "lon": 170.50361, + "name": "Dunedin" + }, + "point_b": { + "lat": 3.81461, + "lon": 23.68665, + "name": "Bondo" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -60.627113, + "lon": 120.659164 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-45.87416°, 170.50361°)", + " Point B: (3.81461°, 23.68665°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -60.627113°", + " Longitude: 120.659164°", + "FINAL ANSWER: -60.627113, 120.659164" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 6.95, + "lon": 1.16667, + "name": "Notsé" + }, + "point_b": { + "lat": -14.80306, + "lon": 36.53722, + "name": "Cuamba" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -9.576623, + "lon": 27.433304 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (6.95°, 1.16667°)", + " Point B: (-14.80306°, 36.53722°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -9.576623°", + " Longitude: 27.433304°", + "FINAL ANSWER: -9.576623, 27.433304" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 42.34724, + "lon": -89.039, + "name": "Machesney Park" + }, + "point_b": { + "lat": 32.13333, + "lon": 131.5, + "name": "Takanabe" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 52.07732, + "lon": 150.310216 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (42.34724°, -89.039°)", + " Point B: (32.13333°, 131.5°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 52.077320°", + " Longitude: 150.310216°", + "FINAL ANSWER: 52.077320, 150.310216" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -5.53444, + "lon": -40.77417, + "name": "Novo Oriente" + }, + "point_b": { + "lat": -33.60627, + "lon": -70.87649, + "name": "Peñaflor" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -27.143622, + "lon": -62.173562 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-5.53444°, -40.77417°)", + " Point B: (-33.60627°, -70.87649°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -27.143622°", + " Longitude: -62.173562°", + "FINAL ANSWER: -27.143622, -62.173562" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -4.16667, + "lon": -40.94278, + "name": "Carnaubal" + }, + "point_b": { + "lat": 51.59054, + "lon": -0.14212, + "name": "Muswell Hill" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 10.523198, + "lon": -33.584773 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-4.16667°, -40.94278°)", + " Point B: (51.59054°, -0.14212°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 10.523198°", + " Longitude: -33.584773°", + "FINAL ANSWER: 10.523198, -33.584773" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 41.10565, + "lon": -73.39845, + "name": "East Norwalk" + }, + "point_b": { + "lat": 40.30076, + "lon": -3.43722, + "name": "Arganda" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 45.121935, + "lon": -56.591094 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (41.10565°, -73.39845°)", + " Point B: (40.30076°, -3.43722°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 45.121935°", + " Longitude: -56.591094°", + "FINAL ANSWER: 45.121935, -56.591094" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 41.54211, + "lon": 2.4445, + "name": "Mataró" + }, + "point_b": { + "lat": 38.77261, + "lon": -77.22109, + "name": "West Springfield" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 46.466677, + "lon": -16.829892 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (41.54211°, 2.4445°)", + " Point B: (38.77261°, -77.22109°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 46.466677°", + " Longitude: -16.829892°", + "FINAL ANSWER: 46.466677, -16.829892" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -33.92893, + "lon": 151.05111, + "name": "Punchbowl" + }, + "point_b": { + "lat": 52.51108, + "lon": 4.67165, + "name": "Heemskerk" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -3.898326, + "lon": 127.044167 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-33.92893°, 151.05111°)", + " Point B: (52.51108°, 4.67165°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -3.898326°", + " Longitude: 127.044167°", + "FINAL ANSWER: -3.898326, 127.044167" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 22.19073, + "lon": 69.96351, + "name": "Lālpur" + }, + "point_b": { + "lat": 48.46147, + "lon": 37.08524, + "name": "Dobropillia" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 36.42926, + "lon": 56.318115 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (22.19073°, 69.96351°)", + " Point B: (48.46147°, 37.08524°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 36.429260°", + " Longitude: 56.318115°", + "FINAL ANSWER: 36.429260, 56.318115" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -12.08911, + "lon": -76.99876, + "name": "San Francisco De Borja" + }, + "point_b": { + "lat": 38.58283, + "lon": -90.6629, + "name": "Wildwood" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 26.00899, + "lon": -86.449558 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-12.08911°, -76.99876°)", + " Point B: (38.58283°, -90.6629°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 26.008990°", + " Longitude: -86.449558°", + "FINAL ANSWER: 26.008990, -86.449558" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 49.49991, + "lon": -115.76879, + "name": "Cranbrook" + }, + "point_b": { + "lat": 21.27914, + "lon": -157.80135, + "name": "Kaimukī" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 44.029344, + "lon": -129.527383 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (49.49991°, -115.76879°)", + " Point B: (21.27914°, -157.80135°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 44.029344°", + " Longitude: -129.527383°", + "FINAL ANSWER: 44.029344, -129.527383" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 40.6301, + "lon": -74.42737, + "name": "North Plainfield" + }, + "point_b": { + "lat": -19.58106, + "lon": -42.64953, + "name": "Timóteo" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 10.927689, + "lon": -56.78221 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (40.6301°, -74.42737°)", + " Point B: (-19.58106°, -42.64953°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 10.927689°", + " Longitude: -56.782210°", + "FINAL ANSWER: 10.927689, -56.782210" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 40.70935, + "lon": -73.81529, + "name": "Briarwood" + }, + "point_b": { + "lat": 41.34612, + "lon": 72.21707, + "name": "Tash-Kumyr" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 60.433254, + "lon": -54.325297 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (40.70935°, -73.81529°)", + " Point B: (41.34612°, 72.21707°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 60.433254°", + " Longitude: -54.325297°", + "FINAL ANSWER: 60.433254, -54.325297" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 50.48351, + "lon": 4.55006, + "name": "Fleurus" + }, + "point_b": { + "lat": -29.81292, + "lon": 30.63646, + "name": "Mpumalanga" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 30.74813, + "lon": 13.7157 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (50.48351°, 4.55006°)", + " Point B: (-29.81292°, 30.63646°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 30.748130°", + " Longitude: 13.715700°", + "FINAL ANSWER: 30.748130, 13.715700" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -24.50944, + "lon": -50.41361, + "name": "Tibagi" + }, + "point_b": { + "lat": -24.68941, + "lon": 33.25844, + "name": "Xilembene" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -29.785303, + "lon": 13.026471 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-24.50944°, -50.41361°)", + " Point B: (-24.68941°, 33.25844°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -29.785303°", + " Longitude: 13.026471°", + "FINAL ANSWER: -29.785303, 13.026471" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 20.08886, + "lon": -101.51579, + "name": "Puruándiro" + }, + "point_b": { + "lat": 44.05, + "lon": 43.05036, + "name": "Pyatigorsk" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 43.596697, + "lon": -85.543829 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (20.08886°, -101.51579°)", + " Point B: (44.05°, 43.05036°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 43.596697°", + " Longitude: -85.543829°", + "FINAL ANSWER: 43.596697, -85.543829" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 5.93876, + "lon": -6.59826, + "name": "Yabayo" + }, + "point_b": { + "lat": 6.20228, + "lon": -1.66796, + "name": "Obuase" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 6.00881, + "lon": -5.366142 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (5.93876°, -6.59826°)", + " Point B: (6.20228°, -1.66796°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 6.008810°", + " Longitude: -5.366142°", + "FINAL ANSWER: 6.008810, -5.366142" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 43.5789, + "lon": -79.6583, + "name": "Mississauga" + }, + "point_b": { + "lat": 51.3607, + "lon": 1.0257, + "name": "Whitstable" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 55.219347, + "lon": -19.969791 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (43.5789°, -79.6583°)", + " Point B: (51.3607°, 1.0257°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 55.219347°", + " Longitude: -19.969791°", + "FINAL ANSWER: 55.219347, -19.969791" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 57.10557, + "lon": 12.25078, + "name": "Varberg" + }, + "point_b": { + "lat": 31.35333, + "lon": 106.06309, + "name": "Nanlong" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 43.970033, + "lon": 92.521408 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (57.10557°, 12.25078°)", + " Point B: (31.35333°, 106.06309°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 43.970033°", + " Longitude: 92.521408°", + "FINAL ANSWER: 43.970033, 92.521408" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 50.66667, + "lon": 3.08333, + "name": "Marcq-en-Barœul" + }, + "point_b": { + "lat": -37.82289, + "lon": 147.61041, + "name": "Bairnsdale" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -10.351115, + "lon": 118.382087 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (50.66667°, 3.08333°)", + " Point B: (-37.82289°, 147.61041°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -10.351115°", + " Longitude: 118.382087°", + "FINAL ANSWER: -10.351115, 118.382087" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -33.83902, + "lon": 151.23956, + "name": "Mosman" + }, + "point_b": { + "lat": 28.51225, + "lon": 77.24083, + "name": "Tighri" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -3.332781, + "lon": 113.025211 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-33.83902°, 151.23956°)", + " Point B: (28.51225°, 77.24083°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -3.332781°", + " Longitude: 113.025211°", + "FINAL ANSWER: -3.332781, 113.025211" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -30.25833, + "lon": -54.91417, + "name": "Rosário do Sul" + }, + "point_b": { + "lat": 51.47805, + "lon": 6.8625, + "name": "Oberhausen" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 12.257767, + "lon": -29.563892 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-30.25833°, -54.91417°)", + " Point B: (51.47805°, 6.8625°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 12.257767°", + " Longitude: -29.563892°", + "FINAL ANSWER: 12.257767, -29.563892" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 33.89205, + "lon": -84.29881, + "name": "Chamblee" + }, + "point_b": { + "lat": 36.0, + "lon": 139.55722, + "name": "Okegawa" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 52.424563, + "lon": -107.23074 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (33.89205°, -84.29881°)", + " Point B: (36.0°, 139.55722°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 52.424563°", + " Longitude: -107.230740°", + "FINAL ANSWER: 52.424563, -107.230740" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -33.86482, + "lon": 151.20773, + "name": "Sydney Central Business District" + }, + "point_b": { + "lat": -31.89578, + "lon": 115.76431, + "name": "Scarborough" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -33.336947, + "lon": 124.409925 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-33.86482°, 151.20773°)", + " Point B: (-31.89578°, 115.76431°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -33.336947°", + " Longitude: 124.409925°", + "FINAL ANSWER: -33.336947, 124.409925" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 52.26667, + "lon": -2.15, + "name": "Droitwich" + }, + "point_b": { + "lat": 47.03333, + "lon": 23.91667, + "name": "Gherla" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 51.52672, + "lon": 4.865153 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (52.26667°, -2.15°)", + " Point B: (47.03333°, 23.91667°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 51.526720°", + " Longitude: 4.865153°", + "FINAL ANSWER: 51.526720, 4.865153" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 56.39733, + "lon": 38.71404, + "name": "Aleksandrov" + }, + "point_b": { + "lat": 7.38194, + "lon": -6.47778, + "name": "Vavoua" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 20.768284, + "lon": 0.750311 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (56.39733°, 38.71404°)", + " Point B: (7.38194°, -6.47778°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 20.768284°", + " Longitude: 0.750311°", + "FINAL ANSWER: 20.768284, 0.750311" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 47.73512, + "lon": -3.42952, + "name": "Ploemeur" + }, + "point_b": { + "lat": 50.78333, + "lon": 121.51667, + "name": "Genhe" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 68.25809, + "lon": 55.651675 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (47.73512°, -3.42952°)", + " Point B: (50.78333°, 121.51667°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 68.258090°", + " Longitude: 55.651675°", + "FINAL ANSWER: 68.258090, 55.651675" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 22.61243, + "lon": 72.92107, + "name": "Kanjari" + }, + "point_b": { + "lat": -34.7524, + "lon": -56.00259, + "name": "Barros Blancos" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -28.980475, + "lon": -16.867215 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (22.61243°, 72.92107°)", + " Point B: (-34.7524°, -56.00259°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -28.980475°", + " Longitude: -16.867215°", + "FINAL ANSWER: -28.980475, -16.867215" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -3.76, + "lon": -40.81639, + "name": "Frecheirinha" + }, + "point_b": { + "lat": 9.14334, + "lon": -74.22384, + "name": "Guamal" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -0.480004, + "lon": -49.12653 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-3.76°, -40.81639°)", + " Point B: (9.14334°, -74.22384°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -0.480004°", + " Longitude: -49.126530°", + "FINAL ANSWER: -0.480004, -49.126530" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 34.49621, + "lon": 116.92249, + "name": "Jing'an" + }, + "point_b": { + "lat": 11.55965, + "lon": 9.66407, + "name": "Chakwama" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 38.970544, + "lon": 86.96201 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (34.49621°, 116.92249°)", + " Point B: (11.55965°, 9.66407°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 38.970544°", + " Longitude: 86.962010°", + "FINAL ANSWER: 38.970544, 86.962010" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 38.08333, + "lon": 23.7, + "name": "Áno Liósia" + }, + "point_b": { + "lat": 38.02909, + "lon": -121.96163, + "name": "Bay Point" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 58.468415, + "lon": 2.966594 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (38.08333°, 23.7°)", + " Point B: (38.02909°, -121.96163°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 58.468415°", + " Longitude: 2.966594°", + "FINAL ANSWER: 58.468415, 2.966594" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 55.01457, + "lon": 36.47185, + "name": "Maloyaroslavets" + }, + "point_b": { + "lat": 16.48344, + "lon": 99.52153, + "name": "Kamphaeng Phet" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 39.849282, + "lon": 76.7703 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (55.01457°, 36.47185°)", + " Point B: (16.48344°, 99.52153°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 39.849282°", + " Longitude: 76.770300°", + "FINAL ANSWER: 39.849282, 76.770300" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 52.11879, + "lon": 20.67155, + "name": "Milanówek" + }, + "point_b": { + "lat": 8.30638, + "lon": 77.22398, + "name": "Nalloor" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 33.265824, + "lon": 56.12674 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (52.11879°, 20.67155°)", + " Point B: (8.30638°, 77.22398°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 33.265824°", + " Longitude: 56.126740°", + "FINAL ANSWER: 33.265824, 56.126740" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 35.31473, + "lon": -0.05037, + "name": "Bou Hanifia el Hamamat" + }, + "point_b": { + "lat": -31.94504, + "lon": -65.19025, + "name": "Villa Dolores" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 1.998867, + "lon": -33.336353 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (35.31473°, -0.05037°)", + " Point B: (-31.94504°, -65.19025°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 1.998867°", + " Longitude: -33.336353°", + "FINAL ANSWER: 1.998867, -33.336353" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -15.7907, + "lon": -47.93711, + "name": "Cruzeiro" + }, + "point_b": { + "lat": 1.35903, + "lon": 103.76368, + "name": "Bukit Batok New Town" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -27.314112, + "lon": 32.243893 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-15.7907°, -47.93711°)", + " Point B: (1.35903°, 103.76368°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -27.314112°", + " Longitude: 32.243893°", + "FINAL ANSWER: -27.314112, 32.243893" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 10.56659, + "lon": 77.21354, + "name": "Sundakkāmpālaiyam" + }, + "point_b": { + "lat": -24.09306, + "lon": -46.62083, + "name": "Mongaguá" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -22.418531, + "lon": -12.55554 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (10.56659°, 77.21354°)", + " Point B: (-24.09306°, -46.62083°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -22.418531°", + " Longitude: -12.555540°", + "FINAL ANSWER: -22.418531, -12.555540" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 38.67877, + "lon": -121.35114, + "name": "Foothill Farms" + }, + "point_b": { + "lat": 6.5808, + "lon": 1.6696, + "name": "Athiémé" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 40.476031, + "lon": -47.380736 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (38.67877°, -121.35114°)", + " Point B: (6.5808°, 1.6696°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 40.476031°", + " Longitude: -47.380736°", + "FINAL ANSWER: 40.476031, -47.380736" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 41.49142, + "lon": -87.67449, + "name": "Park Forest" + }, + "point_b": { + "lat": 16.17535, + "lon": -95.19424, + "name": "Salina Cruz" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 28.884772, + "lon": -91.899894 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (41.49142°, -87.67449°)", + " Point B: (16.17535°, -95.19424°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 28.884772°", + " Longitude: -91.899894°", + "FINAL ANSWER: 28.884772, -91.899894" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -22.23, + "lon": -45.93639, + "name": "Pouso Alegre" + }, + "point_b": { + "lat": 49.25672, + "lon": 2.48477, + "name": "Creil" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 14.719481, + "lon": -26.17292 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-22.23°, -45.93639°)", + " Point B: (49.25672°, 2.48477°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 14.719481°", + " Longitude: -26.172920°", + "FINAL ANSWER: 14.719481, -26.172920" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 25.96667, + "lon": 94.51667, + "name": "Zunheboto" + }, + "point_b": { + "lat": 16.79944, + "lon": -93.27219, + "name": "Berriozábal" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 59.082265, + "lon": 106.412742 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (25.96667°, 94.51667°)", + " Point B: (16.79944°, -93.27219°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 59.082265°", + " Longitude: 106.412742°", + "FINAL ANSWER: 59.082265, 106.412742" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 22.54925, + "lon": 71.48324, + "name": "Sāyla" + }, + "point_b": { + "lat": -33.7061, + "lon": 150.7094, + "name": "Cranebrook" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -7.219, + "lon": 108.621905 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (22.54925°, 71.48324°)", + " Point B: (-33.7061°, 150.7094°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -7.219000°", + " Longitude: 108.621905°", + "FINAL ANSWER: -7.219000, 108.621905" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 52.30083, + "lon": 4.86389, + "name": "Amstelveen" + }, + "point_b": { + "lat": 40.12617, + "lon": -82.92907, + "name": "Westerville" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 55.2144, + "lon": -45.143177 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (52.30083°, 4.86389°)", + " Point B: (40.12617°, -82.92907°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 55.214400°", + " Longitude: -45.143177°", + "FINAL ANSWER: 55.214400, -45.143177" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 24.69808, + "lon": 84.9869, + "name": "Bodh Gaya" + }, + "point_b": { + "lat": 22.41479, + "lon": -80.2931, + "name": "Lajas" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 54.900973, + "lon": 68.048577 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (24.69808°, 84.9869°)", + " Point B: (22.41479°, -80.2931°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 54.900973°", + " Longitude: 68.048577°", + "FINAL ANSWER: 54.900973, 68.048577" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -6.45, + "lon": 38.33333, + "name": "Lugoba" + }, + "point_b": { + "lat": 27.95243, + "lon": 30.78082, + "name": "Banī ‘Ubayd" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 2.16303, + "lon": 36.566513 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-6.45°, 38.33333°)", + " Point B: (27.95243°, 30.78082°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 2.163030°", + " Longitude: 36.566513°", + "FINAL ANSWER: 2.163030, 36.566513" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 33.61171, + "lon": -111.71736, + "name": "Fountain Hills" + }, + "point_b": { + "lat": 42.3751, + "lon": -70.98283, + "name": "Winthrop" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 39.793788, + "lon": -92.622975 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (33.61171°, -111.71736°)", + " Point B: (42.3751°, -70.98283°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 39.793788°", + " Longitude: -92.622975°", + "FINAL ANSWER: 39.793788, -92.622975" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -34.75155, + "lon": 149.72086, + "name": "Goulburn" + }, + "point_b": { + "lat": 14.1532, + "lon": 122.8303, + "name": "Labo" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -10.580918, + "lon": 135.143886 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-34.75155°, 149.72086°)", + " Point B: (14.1532°, 122.8303°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -10.580918°", + " Longitude: 135.143886°", + "FINAL ANSWER: -10.580918, 135.143886" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 0.43803, + "lon": 32.60246, + "name": "Kasangati" + }, + "point_b": { + "lat": 29.96974, + "lon": 40.20641, + "name": "Sakakah" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 7.840535, + "lon": 34.33553 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (0.43803°, 32.60246°)", + " Point B: (29.96974°, 40.20641°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 7.840535°", + " Longitude: 34.335530°", + "FINAL ANSWER: 7.840535, 34.335530" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 44.90924, + "lon": 8.61007, + "name": "Alessandria" + }, + "point_b": { + "lat": -23.10083, + "lon": -45.70694, + "name": "Caçapava" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -5.569422, + "lon": -33.675396 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (44.90924°, 8.61007°)", + " Point B: (-23.10083°, -45.70694°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -5.569422°", + " Longitude: -33.675396°", + "FINAL ANSWER: -5.569422, -33.675396" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 6.9625, + "lon": -8.84056, + "name": "Saclepea" + }, + "point_b": { + "lat": 43.41285, + "lon": 23.22174, + "name": "Montana" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 26.051564, + "lon": 4.642869 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (6.9625°, -8.84056°)", + " Point B: (43.41285°, 23.22174°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 26.051564°", + " Longitude: 4.642869°", + "FINAL ANSWER: 26.051564, 4.642869" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 40.61861, + "lon": 20.78083, + "name": "Korçë" + }, + "point_b": { + "lat": 26.13258, + "lon": -97.6311, + "name": "San Benito" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 51.876268, + "lon": -46.421824 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (40.61861°, 20.78083°)", + " Point B: (26.13258°, -97.6311°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 51.876268°", + " Longitude: -46.421824°", + "FINAL ANSWER: 51.876268, -46.421824" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -0.0962, + "lon": 34.27322, + "name": "Bondo" + }, + "point_b": { + "lat": 11.8277, + "lon": 39.59164, + "name": "Weldiya" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 2.888674, + "lon": 35.58509 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-0.0962°, 34.27322°)", + " Point B: (11.8277°, 39.59164°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 2.888674°", + " Longitude: 35.585090°", + "FINAL ANSWER: 2.888674, 35.585090" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 32.76704, + "lon": 22.63669, + "name": "Darnah" + }, + "point_b": { + "lat": -7.56056, + "lon": -35.0025, + "name": "Goiana" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 14.301984, + "lon": -8.769381 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (32.76704°, 22.63669°)", + " Point B: (-7.56056°, -35.0025°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 14.301984°", + " Longitude: -8.769381°", + "FINAL ANSWER: 14.301984, -8.769381" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -21.72444, + "lon": -48.10167, + "name": "Américo Brasiliense" + }, + "point_b": { + "lat": 51.5, + "lon": 7.63333, + "name": "Holzwickede" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 16.651877, + "lon": -26.196607 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-21.72444°, -48.10167°)", + " Point B: (51.5°, 7.63333°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 16.651877°", + " Longitude: -26.196607°", + "FINAL ANSWER: 16.651877, -26.196607" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -10.98303, + "lon": 26.7384, + "name": "Likasi" + }, + "point_b": { + "lat": -2.22652, + "lon": -80.85807, + "name": "Santa Elena" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -11.090921, + "lon": -27.753768 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-10.98303°, 26.7384°)", + " Point B: (-2.22652°, -80.85807°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -11.090921°", + " Longitude: -27.753768°", + "FINAL ANSWER: -11.090921, -27.753768" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 44.38358, + "lon": -89.81735, + "name": "Wisconsin Rapids" + }, + "point_b": { + "lat": -37.90232, + "lon": 145.01734, + "name": "Brighton East" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 29.970199, + "lon": -130.101872 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (44.38358°, -89.81735°)", + " Point B: (-37.90232°, 145.01734°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 29.970199°", + " Longitude: -130.101872°", + "FINAL ANSWER: 29.970199, -130.101872" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -11.08944, + "lon": -43.14167, + "name": "Barra" + }, + "point_b": { + "lat": -28.41789, + "lon": 32.18483, + "name": "Mtubatuba" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -18.549151, + "lon": -26.19756 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-11.08944°, -43.14167°)", + " Point B: (-28.41789°, 32.18483°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -18.549151°", + " Longitude: -26.197560°", + "FINAL ANSWER: -18.549151, -26.197560" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 40.55951, + "lon": -79.95867, + "name": "Allison Park" + }, + "point_b": { + "lat": -4.65, + "lon": 12.76667, + "name": "Belize" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 35.84574, + "lon": -50.153139 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (40.55951°, -79.95867°)", + " Point B: (-4.65°, 12.76667°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 35.845740°", + " Longitude: -50.153139°", + "FINAL ANSWER: 35.845740, -50.153139" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 51.89998, + "lon": -1.15357, + "name": "Bicester" + }, + "point_b": { + "lat": 25.99023, + "lon": 79.45334, + "name": "Orai" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 51.77881, + "lon": 24.959193 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (51.89998°, -1.15357°)", + " Point B: (25.99023°, 79.45334°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 51.778810°", + " Longitude: 24.959193°", + "FINAL ANSWER: 51.778810, 24.959193" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 2.15127, + "lon": 21.51672, + "name": "Lisala" + }, + "point_b": { + "lat": -33.91972, + "lon": 151.07592, + "name": "Lakemba" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -33.235363, + "lon": 75.167312 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (2.15127°, 21.51672°)", + " Point B: (-33.91972°, 151.07592°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -33.235363°", + " Longitude: 75.167312°", + "FINAL ANSWER: -33.235363, 75.167312" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 34.21052, + "lon": 133.6746, + "name": "Mitoyo" + }, + "point_b": { + "lat": 25.97349, + "lon": 84.86796, + "name": "Marhaura" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 32.465763, + "lon": 108.186741 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (34.21052°, 133.6746°)", + " Point B: (25.97349°, 84.86796°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 32.465763°", + " Longitude: 108.186741°", + "FINAL ANSWER: 32.465763, 108.186741" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 32.81034, + "lon": 35.26009, + "name": "Kafr Mandā" + }, + "point_b": { + "lat": -37.8739, + "lon": 145.02485, + "name": "Caulfield North" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -4.391009, + "lon": 87.589577 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (32.81034°, 35.26009°)", + " Point B: (-37.8739°, 145.02485°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -4.391009°", + " Longitude: 87.589577°", + "FINAL ANSWER: -4.391009, 87.589577" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 51.45278, + "lon": -2.50833, + "name": "Kingswood" + }, + "point_b": { + "lat": 32.56319, + "lon": -97.14168, + "name": "Mansfield" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 52.671118, + "lon": -59.052658 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (51.45278°, -2.50833°)", + " Point B: (32.56319°, -97.14168°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 52.671118°", + " Longitude: -59.052658°", + "FINAL ANSWER: 52.671118, -59.052658" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 30.71524, + "lon": 31.2592, + "name": "Mīt Ghamr" + }, + "point_b": { + "lat": -23.53306, + "lon": -49.24444, + "name": "Taquarituba" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 18.862322, + "lon": 8.73995 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (30.71524°, 31.2592°)", + " Point B: (-23.53306°, -49.24444°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 18.862322°", + " Longitude: 8.739950°", + "FINAL ANSWER: 18.862322, 8.739950" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 40.36412, + "lon": -111.73854, + "name": "Pleasant Grove" + }, + "point_b": { + "lat": 11.65806, + "lon": -70.215, + "name": "Punta Cardón" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 27.53199, + "lon": -88.266643 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (40.36412°, -111.73854°)", + " Point B: (11.65806°, -70.215°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 27.531990°", + " Longitude: -88.266643°", + "FINAL ANSWER: 27.531990, -88.266643" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 52.27042, + "lon": -9.70264, + "name": "Tralee" + }, + "point_b": { + "lat": -31.39195, + "lon": -58.01706, + "name": "Concordia" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 11.385697, + "lon": -38.090113 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (52.27042°, -9.70264°)", + " Point B: (-31.39195°, -58.01706°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 11.385697°", + " Longitude: -38.090113°", + "FINAL ANSWER: 11.385697, -38.090113" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 24.26778, + "lon": 87.24855, + "name": "Dumka" + }, + "point_b": { + "lat": 36.82019, + "lon": 7.71641, + "name": "Sidi Amar" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 39.13926, + "lon": 29.048169 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (24.26778°, 87.24855°)", + " Point B: (36.82019°, 7.71641°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 39.139260°", + " Longitude: 29.048169°", + "FINAL ANSWER: 39.139260, 29.048169" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 14.42139, + "lon": 78.22502, + "name": "Pulivendla" + }, + "point_b": { + "lat": 46.3, + "lon": 25.3, + "name": "Odorheiu Secuiesc" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 40.755388, + "lon": 42.448237 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (14.42139°, 78.22502°)", + " Point B: (46.3°, 25.3°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 40.755388°", + " Longitude: 42.448237°", + "FINAL ANSWER: 40.755388, 42.448237" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -22.97111, + "lon": 30.67361, + "name": "Malamulele" + }, + "point_b": { + "lat": 24.66116, + "lon": 97.85262, + "name": "Taiping" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 1.014366, + "lon": 64.015387 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-22.97111°, 30.67361°)", + " Point B: (24.66116°, 97.85262°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 1.014366°", + " Longitude: 64.015387°", + "FINAL ANSWER: 1.014366, 64.015387" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 53.54846, + "lon": -2.00455, + "name": "Saddleworth" + }, + "point_b": { + "lat": -10.8258, + "lon": -65.3581, + "name": "Guayaramerín" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 24.435716, + "lon": -42.318764 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (53.54846°, -2.00455°)", + " Point B: (-10.8258°, -65.3581°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 24.435716°", + " Longitude: -42.318764°", + "FINAL ANSWER: 24.435716, -42.318764" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -9.43215, + "lon": 160.00607, + "name": "Panatina" + }, + "point_b": { + "lat": 26.61708, + "lon": -80.07231, + "name": "Lake Worth Beach" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 16.739174, + "lon": -144.893081 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-9.43215°, 160.00607°)", + " Point B: (26.61708°, -80.07231°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 16.739174°", + " Longitude: -144.893081°", + "FINAL ANSWER: 16.739174, -144.893081" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 17.58152, + "lon": 80.67651, + "name": "Palwancha" + }, + "point_b": { + "lat": -34.53215, + "lon": 20.04031, + "name": "Bredasdorp" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -9.785094, + "lon": 52.798138 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (17.58152°, 80.67651°)", + " Point B: (-34.53215°, 20.04031°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -9.785094°", + " Longitude: 52.798138°", + "FINAL ANSWER: -9.785094, 52.798138" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -18.58111, + "lon": 36.45861, + "name": "Chinde" + }, + "point_b": { + "lat": 8.76962, + "lon": -70.11086, + "name": "Barrancas" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -14.99672, + "lon": 8.36954 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-18.58111°, 36.45861°)", + " Point B: (8.76962°, -70.11086°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -14.996720°", + " Longitude: 8.369540°", + "FINAL ANSWER: -14.996720, 8.369540" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 13.24655, + "lon": 77.71183, + "name": "Devanahalli" + }, + "point_b": { + "lat": 36.62528, + "lon": 119.71333, + "name": "Cuijiaji" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 32.066228, + "lon": 107.515817 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (13.24655°, 77.71183°)", + " Point B: (36.62528°, 119.71333°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 32.066228°", + " Longitude: 107.515817°", + "FINAL ANSWER: 32.066228, 107.515817" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 41.71087, + "lon": -87.75811, + "name": "Oak Lawn" + }, + "point_b": { + "lat": -7.125, + "lon": -34.93222, + "name": "Bayeux" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 6.11536, + "lon": -45.852836 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (41.71087°, -87.75811°)", + " Point B: (-7.125°, -34.93222°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 6.115360°", + " Longitude: -45.852836°", + "FINAL ANSWER: 6.115360, -45.852836" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 21.50279, + "lon": -158.02464, + "name": "Wahiawā" + }, + "point_b": { + "lat": 29.80123, + "lon": 72.17398, + "name": "Mailsi" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 48.467699, + "lon": 141.328183 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (21.50279°, -158.02464°)", + " Point B: (29.80123°, 72.17398°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 48.467699°", + " Longitude: 141.328183°", + "FINAL ANSWER: 48.467699, 141.328183" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -33.63638, + "lon": -70.57361, + "name": "Pirque" + }, + "point_b": { + "lat": 8.25, + "lon": 124.4, + "name": "Iligan City" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -60.528705, + "lon": -111.777854 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-33.63638°, -70.57361°)", + " Point B: (8.25°, 124.4°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -60.528705°", + " Longitude: -111.777854°", + "FINAL ANSWER: -60.528705, -111.777854" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -9.10528, + "lon": -38.14917, + "name": "Tacaratu" + }, + "point_b": { + "lat": -2.94047, + "lon": -44.24898, + "name": "Rosário" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -6.031355, + "lon": -41.21642 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-9.10528°, -38.14917°)", + " Point B: (-2.94047°, -44.24898°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -6.031355°", + " Longitude: -41.216420°", + "FINAL ANSWER: -6.031355, -41.216420" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 51.21338, + "lon": 17.38986, + "name": "Oleśnica" + }, + "point_b": { + "lat": -11.86417, + "lon": -55.5025, + "name": "Sinop" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 39.641488, + "lon": -9.950548 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (51.21338°, 17.38986°)", + " Point B: (-11.86417°, -55.5025°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 39.641488°", + " Longitude: -9.950548°", + "FINAL ANSWER: 39.641488, -9.950548" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 45.52027, + "lon": 11.33446, + "name": "Arzignano" + }, + "point_b": { + "lat": -3.28333, + "lon": 32.85, + "name": "Mhango" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 33.644116, + "lon": 18.563323 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (45.52027°, 11.33446°)", + " Point B: (-3.28333°, 32.85°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 33.644116°", + " Longitude: 18.563323°", + "FINAL ANSWER: 33.644116, 18.563323" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -23.05389, + "lon": -46.35806, + "name": "Piracaia" + }, + "point_b": { + "lat": 39.55388, + "lon": -104.96943, + "name": "Highlands Ranch" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 9.429011, + "lon": -72.830458 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-23.05389°, -46.35806°)", + " Point B: (39.55388°, -104.96943°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 9.429011°", + " Longitude: -72.830458°", + "FINAL ANSWER: 9.429011, -72.830458" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -36.8582, + "lon": 174.62019, + "name": "Lincoln" + }, + "point_b": { + "lat": 38.69101, + "lon": -121.44857, + "name": "Rio Linda" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -18.532464, + "lon": -167.825035 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-36.8582°, 174.62019°)", + " Point B: (38.69101°, -121.44857°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -18.532464°", + " Longitude: -167.825035°", + "FINAL ANSWER: -18.532464, -167.825035" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 53.56047, + "lon": -0.03225, + "name": "Cleethorpes" + }, + "point_b": { + "lat": 39.64917, + "lon": 27.88611, + "name": "Balıkesir" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 43.707682, + "lon": 22.219161 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (53.56047°, -0.03225°)", + " Point B: (39.64917°, 27.88611°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 43.707682°", + " Longitude: 22.219161°", + "FINAL ANSWER: 43.707682, 22.219161" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 26.55951, + "lon": 76.32915, + "name": "Lālsot" + }, + "point_b": { + "lat": -34.58301, + "lon": 19.35048, + "name": "Gansbaai" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -4.561141, + "lon": 49.127844 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (26.55951°, 76.32915°)", + " Point B: (-34.58301°, 19.35048°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -4.561141°", + " Longitude: 49.127844°", + "FINAL ANSWER: -4.561141, 49.127844" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 51.7002, + "lon": -0.03026, + "name": "Cheshunt" + }, + "point_b": { + "lat": -11.09639, + "lon": -77.61389, + "name": "Hualmay" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 7.187033, + "lon": -63.94168 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (51.7002°, -0.03026°)", + " Point B: (-11.09639°, -77.61389°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 7.187033°", + " Longitude: -63.941680°", + "FINAL ANSWER: 7.187033, -63.941680" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -20.93194, + "lon": -54.96139, + "name": "Sidrolândia" + }, + "point_b": { + "lat": 0.08411, + "lon": 32.46972, + "name": "Katabi" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -18.989597, + "lon": -31.724901 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-20.93194°, -54.96139°)", + " Point B: (0.08411°, 32.46972°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -18.989597°", + " Longitude: -31.724901°", + "FINAL ANSWER: -18.989597, -31.724901" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 25.6439, + "lon": 77.9129, + "name": "Narwar" + }, + "point_b": { + "lat": 50.33394, + "lon": 19.20479, + "name": "Dąbrowa Górnicza" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 41.729923, + "lon": 54.049792 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (25.6439°, 77.9129°)", + " Point B: (50.33394°, 19.20479°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 41.729923°", + " Longitude: 54.049792°", + "FINAL ANSWER: 41.729923, 54.049792" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -37.8228, + "lon": 144.96434, + "name": "Southbank" + }, + "point_b": { + "lat": 31.88542, + "lon": 35.8543, + "name": "Umm as Summāq" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -5.103592, + "lon": 87.50485 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-37.8228°, 144.96434°)", + " Point B: (31.88542°, 35.8543°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -5.103592°", + " Longitude: 87.504850°", + "FINAL ANSWER: -5.103592, 87.504850" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 6.46477, + "lon": -5.95427, + "name": "Bayota" + }, + "point_b": { + "lat": 52.19551, + "lon": 9.46421, + "name": "Bad Münder am Deister" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 40.963393, + "lon": 3.86185 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (6.46477°, -5.95427°)", + " Point B: (52.19551°, 9.46421°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 40.963393°", + " Longitude: 3.861850°", + "FINAL ANSWER: 40.963393, 3.861850" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 29.68817, + "lon": 106.58852, + "name": "Cuiyun" + }, + "point_b": { + "lat": -17.88333, + "lon": 30.7, + "name": "Norton" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -5.474694, + "lon": 49.035401 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (29.68817°, 106.58852°)", + " Point B: (-17.88333°, 30.7°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -5.474694°", + " Longitude: 49.035401°", + "FINAL ANSWER: -5.474694, 49.035401" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 31.17213, + "lon": -8.84728, + "name": "Imi-n-Tanout" + }, + "point_b": { + "lat": -8.6503, + "lon": 116.5318, + "name": "Selong" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 32.213982, + "lon": 27.91693 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (31.17213°, -8.84728°)", + " Point B: (-8.6503°, 116.5318°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 32.213982°", + " Longitude: 27.916930°", + "FINAL ANSWER: 32.213982, 27.916930" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 35.3, + "lon": 136.8, + "name": "Ichinomiya" + }, + "point_b": { + "lat": -26.08159, + "lon": 25.88124, + "name": "Itsoseng" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -9.974428, + "lon": 52.967145 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (35.3°, 136.8°)", + " Point B: (-26.08159°, 25.88124°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -9.974428°", + " Longitude: 52.967145°", + "FINAL ANSWER: -9.974428, 52.967145" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 7.15571, + "lon": 3.34509, + "name": "Abeokuta" + }, + "point_b": { + "lat": -28.11694, + "lon": 153.46584, + "name": "Palm Beach" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -16.166238, + "lon": 31.329348 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (7.15571°, 3.34509°)", + " Point B: (-28.11694°, 153.46584°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -16.166238°", + " Longitude: 31.329348°", + "FINAL ANSWER: -16.166238, 31.329348" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -4.52483, + "lon": 35.3849, + "name": "Katesh" + }, + "point_b": { + "lat": -37.87811, + "lon": 145.16476, + "name": "Glen Waverley" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -20.549294, + "lon": 55.979648 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-4.52483°, 35.3849°)", + " Point B: (-37.87811°, 145.16476°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -20.549294°", + " Longitude: 55.979648°", + "FINAL ANSWER: -20.549294, 55.979648" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 32.93257, + "lon": 130.44284, + "name": "Nagasu" + }, + "point_b": { + "lat": 43.35082, + "lon": 46.10095, + "name": "Gudermes" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 46.596019, + "lon": 91.982295 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (32.93257°, 130.44284°)", + " Point B: (43.35082°, 46.10095°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 46.596019°", + " Longitude: 91.982295°", + "FINAL ANSWER: 46.596019, 91.982295" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 40.35572, + "lon": -3.68855, + "name": "Los Rosales" + }, + "point_b": { + "lat": 9.37083, + "lon": -69.21028, + "name": "Píritu" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 19.612271, + "lon": -56.037891 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (40.35572°, -3.68855°)", + " Point B: (9.37083°, -69.21028°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 19.612271°", + " Longitude: -56.037891°", + "FINAL ANSWER: 19.612271, -56.037891" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 48.72472, + "lon": 4.58439, + "name": "Vitry-le-François" + }, + "point_b": { + "lat": 37.22349, + "lon": 39.75519, + "name": "Viranşehir" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 44.330889, + "lon": 23.873066 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (48.72472°, 4.58439°)", + " Point B: (37.22349°, 39.75519°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 44.330889°", + " Longitude: 23.873066°", + "FINAL ANSWER: 44.330889, 23.873066" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 44.11578, + "lon": 15.22514, + "name": "Zadar" + }, + "point_b": { + "lat": 51.67873, + "lon": 6.15895, + "name": "Goch" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 46.070137, + "lon": 13.19837 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (44.11578°, 15.22514°)", + " Point B: (51.67873°, 6.15895°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 46.070137°", + " Longitude: 13.198370°", + "FINAL ANSWER: 46.070137, 13.198370" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 51.61667, + "lon": 5.54861, + "name": "Veghel" + }, + "point_b": { + "lat": 37.74425, + "lon": -0.85041, + "name": "Los Alcázares" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 44.7245, + "lon": 1.963788 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (51.61667°, 5.54861°)", + " Point B: (37.74425°, -0.85041°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 44.724500°", + " Longitude: 1.963788°", + "FINAL ANSWER: 44.724500, 1.963788" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 6.69903, + "lon": -72.73233, + "name": "Málaga" + }, + "point_b": { + "lat": 11.84854, + "lon": -86.43839, + "name": "San Rafael del Sur" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 8.033152, + "lon": -76.122509 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (6.69903°, -72.73233°)", + " Point B: (11.84854°, -86.43839°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 8.033152°", + " Longitude: -76.122509°", + "FINAL ANSWER: 8.033152, -76.122509" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 10.29532, + "lon": -67.7177, + "name": "Mariara" + }, + "point_b": { + "lat": 28.02964, + "lon": 78.28571, + "name": "Atraulī" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 33.773606, + "lon": -43.386043 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (10.29532°, -67.7177°)", + " Point B: (28.02964°, 78.28571°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 33.773606°", + " Longitude: -43.386043°", + "FINAL ANSWER: 33.773606, -43.386043" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 40.03788, + "lon": -76.30551, + "name": "Lancaster" + }, + "point_b": { + "lat": -4.75639, + "lon": -42.57556, + "name": "José de Freitas" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 6.860669, + "lon": -49.691411 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (40.03788°, -76.30551°)", + " Point B: (-4.75639°, -42.57556°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 6.860669°", + " Longitude: -49.691411°", + "FINAL ANSWER: 6.860669, -49.691411" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 0.78775, + "lon": 34.71562, + "name": "Kimilili" + }, + "point_b": { + "lat": -37.83961, + "lon": 144.94228, + "name": "Port Melbourne" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -38.513565, + "lon": 110.937525 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (0.78775°, 34.71562°)", + " Point B: (-37.83961°, 144.94228°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -38.513565°", + " Longitude: 110.937525°", + "FINAL ANSWER: -38.513565, 110.937525" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 8.85488, + "lon": 0.05922, + "name": "Bimbila" + }, + "point_b": { + "lat": -14.10165, + "lon": 21.43531, + "name": "Lumbala" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -2.66963, + "lon": 10.646656 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (8.85488°, 0.05922°)", + " Point B: (-14.10165°, 21.43531°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -2.669630°", + " Longitude: 10.646656°", + "FINAL ANSWER: -2.669630, 10.646656" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 35.78111, + "lon": -0.42581, + "name": "Gdyel" + }, + "point_b": { + "lat": 40.40435, + "lon": -3.67873, + "name": "Pacífico" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 39.257149, + "lon": -2.825994 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (35.78111°, -0.42581°)", + " Point B: (40.40435°, -3.67873°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 39.257149°", + " Longitude: -2.825994°", + "FINAL ANSWER: 39.257149, -2.825994" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 50.5828, + "lon": 5.6341, + "name": "Chaudfontaine" + }, + "point_b": { + "lat": 41.81843, + "lon": -73.14372, + "name": "West Torrington" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 53.397972, + "lon": -37.508956 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (50.5828°, 5.6341°)", + " Point B: (41.81843°, -73.14372°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 53.397972°", + " Longitude: -37.508956°", + "FINAL ANSWER: 53.397972, -37.508956" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -14.24117, + "lon": 31.31975, + "name": "Petauke" + }, + "point_b": { + "lat": 10.19814, + "lon": -5.62337, + "name": "Niellé" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -2.131213, + "lon": 12.701888 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-14.24117°, 31.31975°)", + " Point B: (10.19814°, -5.62337°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -2.131213°", + " Longitude: 12.701888°", + "FINAL ANSWER: -2.131213, 12.701888" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -9.4075, + "lon": -36.07361, + "name": "Capela" + }, + "point_b": { + "lat": 50.06739, + "lon": 31.44969, + "name": "Pereiaslav" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 23.81038, + "lon": -10.364985 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-9.4075°, -36.07361°)", + " Point B: (50.06739°, 31.44969°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 23.810380°", + " Longitude: -10.364985°", + "FINAL ANSWER: 23.810380, -10.364985" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -6.77028, + "lon": -37.80167, + "name": "Pombal" + }, + "point_b": { + "lat": 5.33957, + "lon": -75.73018, + "name": "Quinchía" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 2.323202, + "lon": -66.240728 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-6.77028°, -37.80167°)", + " Point B: (5.33957°, -75.73018°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 2.323202°", + " Longitude: -66.240728°", + "FINAL ANSWER: 2.323202, -66.240728" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 28.23333, + "lon": 117.0, + "name": "Yingtan" + }, + "point_b": { + "lat": 41.70567, + "lon": -70.22863, + "name": "Yarmouth" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 68.75934, + "lon": -78.843614 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (28.23333°, 117.0°)", + " Point B: (41.70567°, -70.22863°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 68.759340°", + " Longitude: -78.843614°", + "FINAL ANSWER: 68.759340, -78.843614" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 19.14256, + "lon": 82.32536, + "name": "Kotapārh" + }, + "point_b": { + "lat": 38.92567, + "lon": -77.02942, + "name": "Columbia Heights" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 69.919203, + "lon": 30.635524 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (19.14256°, 82.32536°)", + " Point B: (38.92567°, -77.02942°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 69.919203°", + " Longitude: 30.635524°", + "FINAL ANSWER: 69.919203, 30.635524" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 6.07, + "lon": -4.31056, + "name": "Rubino" + }, + "point_b": { + "lat": -33.83902, + "lon": 151.23956, + "name": "Mosman" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -52.919392, + "lon": 107.914593 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (6.07°, -4.31056°)", + " Point B: (-33.83902°, 151.23956°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -52.919392°", + " Longitude: 107.914593°", + "FINAL ANSWER: -52.919392, 107.914593" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 52.46, + "lon": 4.65, + "name": "Velsen-Zuid" + }, + "point_b": { + "lat": 6.84684, + "lon": -1.39612, + "name": "Effiduase" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 29.685768, + "lon": 0.902604 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (52.46°, 4.65°)", + " Point B: (6.84684°, -1.39612°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 29.685768°", + " Longitude: 0.902604°", + "FINAL ANSWER: 29.685768, 0.902604" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 36.7975, + "lon": 118.29444, + "name": "Xindian" + }, + "point_b": { + "lat": -33.7457, + "lon": 151.04764, + "name": "West Pennant Hills" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 1.590368, + "lon": 134.988277 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (36.7975°, 118.29444°)", + " Point B: (-33.7457°, 151.04764°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 1.590368°", + " Longitude: 134.988277°", + "FINAL ANSWER: 1.590368, 134.988277" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -31.49285, + "lon": 25.00633, + "name": "Middelburg" + }, + "point_b": { + "lat": 1.28417, + "lon": 103.82306, + "name": "Bukit Merah Estate" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -9.411318, + "lon": 86.510805 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-31.49285°, 25.00633°)", + " Point B: (1.28417°, 103.82306°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -9.411318°", + " Longitude: 86.510805°", + "FINAL ANSWER: -9.411318, 86.510805" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 7.77917, + "lon": -68.22373, + "name": "Achaguas" + }, + "point_b": { + "lat": 47.19936, + "lon": 18.13954, + "name": "Várpalota" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 22.27904, + "lon": -53.227425 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (7.77917°, -68.22373°)", + " Point B: (47.19936°, 18.13954°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 22.279040°", + " Longitude: -53.227425°", + "FINAL ANSWER: 22.279040, -53.227425" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 34.80447, + "lon": 136.54645, + "name": "Kawage" + }, + "point_b": { + "lat": 21.06076, + "lon": 75.8098, + "name": "Kandāri" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 27.009652, + "lon": 89.267977 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (34.80447°, 136.54645°)", + " Point B: (21.06076°, 75.8098°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 27.009652°", + " Longitude: 89.267977°", + "FINAL ANSWER: 27.009652, 89.267977" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 32.7236, + "lon": -5.1025, + "name": "Boumia" + }, + "point_b": { + "lat": 32.70816, + "lon": 35.32469, + "name": "Naẕerat ‘Illit" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 33.972455, + "lon": 4.906485 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (32.7236°, -5.1025°)", + " Point B: (32.70816°, 35.32469°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 33.972455°", + " Longitude: 4.906485°", + "FINAL ANSWER: 33.972455, 4.906485" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -27.09795, + "lon": -48.91281, + "name": "Brusque" + }, + "point_b": { + "lat": -27.20338, + "lon": 152.95923, + "name": "Narangba" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -54.004013, + "lon": 172.61077 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-27.09795°, -48.91281°)", + " Point B: (-27.20338°, 152.95923°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -54.004013°", + " Longitude: 172.610770°", + "FINAL ANSWER: -54.004013, 172.610770" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -30.24162, + "lon": -68.74662, + "name": "San José de Jáchal" + }, + "point_b": { + "lat": 12.416, + "lon": 39.55971, + "name": "Alamata" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -1.38879, + "lon": 15.046476 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-30.24162°, -68.74662°)", + " Point B: (12.416°, 39.55971°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -1.388790°", + " Longitude: 15.046476°", + "FINAL ANSWER: -1.388790, 15.046476" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -7.4289, + "lon": -79.50416, + "name": "San Pedro de Lloc" + }, + "point_b": { + "lat": 14.2459, + "lon": 32.9891, + "name": "Al Manāqil" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -0.740067, + "lon": -51.828817 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-7.4289°, -79.50416°)", + " Point B: (14.2459°, 32.9891°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -0.740067°", + " Longitude: -51.828817°", + "FINAL ANSWER: -0.740067, -51.828817" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 38.97789, + "lon": -77.00748, + "name": "Takoma Park" + }, + "point_b": { + "lat": 14.10594, + "lon": -15.5508, + "name": "Kaffrine" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 22.669034, + "lon": -28.257196 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (38.97789°, -77.00748°)", + " Point B: (14.10594°, -15.5508°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 22.669034°", + " Longitude: -28.257196°", + "FINAL ANSWER: 22.669034, -28.257196" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 26.02065, + "lon": -80.18394, + "name": "West Hollywood" + }, + "point_b": { + "lat": -33.4608, + "lon": 18.72714, + "name": "Malmesbury" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 11.050027, + "lon": -55.432262 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (26.02065°, -80.18394°)", + " Point B: (-33.4608°, 18.72714°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 11.050027°", + " Longitude: -55.432262°", + "FINAL ANSWER: 11.050027, -55.432262" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 58.88, + "lon": 40.2525, + "name": "Gryazovets" + }, + "point_b": { + "lat": 3.2594, + "lon": 101.5541, + "name": "Kuang" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 48.49901, + "lon": 65.844288 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (58.88°, 40.2525°)", + " Point B: (3.2594°, 101.5541°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 48.499010°", + " Longitude: 65.844288°", + "FINAL ANSWER: 48.499010, 65.844288" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -6.35, + "lon": 36.48333, + "name": "Mpwapwa" + }, + "point_b": { + "lat": 8.4022, + "lon": 14.1698, + "name": "Tcholliré" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 1.045861, + "lon": 25.352765 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-6.35°, 36.48333°)", + " Point B: (8.4022��, 14.1698°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 1.045861°", + " Longitude: 25.352765°", + "FINAL ANSWER: 1.045861, 25.352765" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 22.64859, + "lon": 88.34115, + "name": "Bāli" + }, + "point_b": { + "lat": -31.88822, + "lon": 115.87186, + "name": "Dianella" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -18.455863, + "lon": 108.120559 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (22.64859°, 88.34115°)", + " Point B: (-31.88822°, 115.87186°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -18.455863°", + " Longitude: 108.120559°", + "FINAL ANSWER: -18.455863, 108.120559" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -37.66667, + "lon": 145.06667, + "name": "Mill Park" + }, + "point_b": { + "lat": 52.28509, + "lon": 7.44055, + "name": "Rheine" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -10.498488, + "lon": 117.383672 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-37.66667°, 145.06667°)", + " Point B: (52.28509°, 7.44055°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -10.498488°", + " Longitude: 117.383672°", + "FINAL ANSWER: -10.498488, 117.383672" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 35.37425, + "lon": 36.6033, + "name": "Kafr Zaytā" + }, + "point_b": { + "lat": -20.46444, + "lon": -45.42639, + "name": "Formiga" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -5.619034, + "lon": -26.153379 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (35.37425°, 36.6033°)", + " Point B: (-20.46444°, -45.42639°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -5.619034°", + " Longitude: -26.153379°", + "FINAL ANSWER: -5.619034, -26.153379" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 6.55591, + "lon": 2.65123, + "name": "Avrankou" + }, + "point_b": { + "lat": 35.67135, + "lon": 139.73442, + "name": "Akasaka" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 48.816639, + "lon": 102.091422 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (6.55591°, 2.65123°)", + " Point B: (35.67135°, 139.73442°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 48.816639°", + " Longitude: 102.091422°", + "FINAL ANSWER: 48.816639, 102.091422" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 33.52936, + "lon": 130.76479, + "name": "Kami" + }, + "point_b": { + "lat": 30.575, + "lon": 30.71111, + "name": "Badr" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 41.787052, + "lon": 107.275165 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (33.52936°, 130.76479°)", + " Point B: (30.575°, 30.71111°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 41.787052°", + " Longitude: 107.275165°", + "FINAL ANSWER: 41.787052, 107.275165" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 25.89086, + "lon": 93.7388, + "name": "Kuda" + }, + "point_b": { + "lat": -34.47995, + "lon": -54.33064, + "name": "Rocha" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 6.39838, + "lon": 59.765014 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (25.89086°, 93.7388°)", + " Point B: (-34.47995°, -54.33064°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 6.398380°", + " Longitude: 59.765014°", + "FINAL ANSWER: 6.398380, 59.765014" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 2.33468, + "lon": 37.99086, + "name": "Marsabit" + }, + "point_b": { + "lat": 47.02076, + "lon": 8.65414, + "name": "Schwyz" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 25.378647, + "lon": 26.152448 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (2.33468°, 37.99086°)", + " Point B: (47.02076°, 8.65414°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 25.378647°", + " Longitude: 26.152448°", + "FINAL ANSWER: 25.378647, 26.152448" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 63.56904, + "lon": 53.69141, + "name": "Ukhta" + }, + "point_b": { + "lat": 39.24611, + "lon": -94.41912, + "name": "Liberty" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 77.705298, + "lon": 14.289817 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (63.56904°, 53.69141°)", + " Point B: (39.24611°, -94.41912°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 77.705298°", + " Longitude: 14.289817°", + "FINAL ANSWER: 77.705298, 14.289817" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 41.50087, + "lon": -90.4443, + "name": "East Moline" + }, + "point_b": { + "lat": 6.37222, + "lon": -7.39891, + "name": "Nizahon II" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 38.534032, + "lon": -64.323217 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (41.50087°, -90.4443°)", + " Point B: (6.37222°, -7.39891°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 38.534032°", + " Longitude: -64.323217°", + "FINAL ANSWER: 38.534032, -64.323217" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 22.94849, + "lon": 88.01954, + "name": "Srirāmpur" + }, + "point_b": { + "lat": 32.9312, + "lon": 12.08199, + "name": "Zuwarah" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 33.913549, + "lon": 52.121028 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (22.94849°, 88.01954°)", + " Point B: (32.9312°, 12.08199°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 33.913549°", + " Longitude: 52.121028°", + "FINAL ANSWER: 33.913549, 52.121028" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 6.0059, + "lon": -6.29403, + "name": "Galébré" + }, + "point_b": { + "lat": -27.13246, + "lon": 29.97635, + "name": "Daggakraal" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -19.366544, + "lon": 19.915796 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (6.0059°, -6.29403°)", + " Point B: (-27.13246°, 29.97635°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -19.366544°", + " Longitude: 19.915796°", + "FINAL ANSWER: -19.366544, 19.915796" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -37.83634, + "lon": 144.65952, + "name": "Tarneit" + }, + "point_b": { + "lat": 42.93173, + "lon": -76.56605, + "name": "Auburn" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 30.357363, + "lon": -120.748526 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-37.83634°, 144.65952°)", + " Point B: (42.93173°, -76.56605°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 30.357363°", + " Longitude: -120.748526°", + "FINAL ANSWER: 30.357363, -120.748526" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 19.31451, + "lon": -97.9252, + "name": "Huamantla" + }, + "point_b": { + "lat": 31.40794, + "lon": 48.7946, + "name": "Sheybān" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 52.496982, + "lon": 19.344881 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (19.31451°, -97.9252°)", + " Point B: (31.40794°, 48.7946°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 52.496982°", + " Longitude: 19.344881°", + "FINAL ANSWER: 52.496982, 19.344881" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 27.6431, + "lon": 79.9402, + "name": "Shāhābād" + }, + "point_b": { + "lat": 47.86602, + "lon": -122.1551, + "name": "Silver Firs" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 51.909679, + "lon": 90.301535 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (27.6431°, 79.9402°)", + " Point B: (47.86602°, -122.1551°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 51.909679°", + " Longitude: 90.301535°", + "FINAL ANSWER: 51.909679, 90.301535" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 23.92961, + "lon": 115.76499, + "name": "Shuizhai" + }, + "point_b": { + "lat": 41.67041, + "lon": -3.6892, + "name": "Aranda de Duero" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 40.385722, + "lon": 95.856337 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (23.92961°, 115.76499°)", + " Point B: (41.67041°, -3.6892°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 40.385722°", + " Longitude: 95.856337°", + "FINAL ANSWER: 40.385722, 95.856337" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 23.09714, + "lon": 86.22292, + "name": "Balarāmpur" + }, + "point_b": { + "lat": 4.6411, + "lon": 101.1393, + "name": "Bercham" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 9.329744, + "lon": 97.608645 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (23.09714°, 86.22292°)", + " Point B: (4.6411°, 101.1393°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 9.329744°", + " Longitude: 97.608645°", + "FINAL ANSWER: 9.329744, 97.608645" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 30.08333, + "lon": 75.25, + "name": "Maur" + }, + "point_b": { + "lat": 39.11566, + "lon": -77.5636, + "name": "Leesburg" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 53.907848, + "lon": 58.957084 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (30.08333°, 75.25°)", + " Point B: (39.11566°, -77.5636°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 53.907848°", + " Longitude: 58.957084°", + "FINAL ANSWER: 53.907848, 58.957084" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 36.75587, + "lon": 5.08433, + "name": "Béjaïa" + }, + "point_b": { + "lat": 4.80293, + "lon": 8.25341, + "name": "Esuk Oron" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 20.786584, + "lon": 6.841054 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (36.75587°, 5.08433°)", + " Point B: (4.80293°, 8.25341°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 20.786584°", + " Longitude: 6.841054°", + "FINAL ANSWER: 20.786584, 6.841054" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 13.71669, + "lon": 100.57159, + "name": "Khlong Toei" + }, + "point_b": { + "lat": 8.68439, + "lon": -12.53499, + "name": "Lunsar" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 18.91686, + "lon": 72.414631 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (13.71669°, 100.57159°)", + " Point B: (8.68439°, -12.53499°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 18.916860°", + " Longitude: 72.414631°", + "FINAL ANSWER: 18.916860, 72.414631" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 31.28204, + "lon": 34.23869, + "name": "Rafaḩ" + }, + "point_b": { + "lat": 0.1324, + "lon": 117.4854, + "name": "Bontang" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 27.801259, + "lon": 58.140229 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (31.28204°, 34.23869°)", + " Point B: (0.1324°, 117.4854°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 27.801259°", + " Longitude: 58.140229°", + "FINAL ANSWER: 27.801259, 58.140229" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 36.29333, + "lon": 3.67319, + "name": "Aïn Bessem" + }, + "point_b": { + "lat": 40.55555, + "lon": -3.62733, + "name": "San Sebastián de los Reyes" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 39.533428, + "lon": -1.720176 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (36.29333°, 3.67319°)", + " Point B: (40.55555°, -3.62733°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 39.533428°", + " Longitude: -1.720176°", + "FINAL ANSWER: 39.533428, -1.720176" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 44.60789, + "lon": 40.10242, + "name": "Maykop" + }, + "point_b": { + "lat": 53.24488, + "lon": -3.13231, + "name": "Flint" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 52.69658, + "lon": 8.965088 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (44.60789°, 40.10242°)", + " Point B: (53.24488°, -3.13231°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 52.696580°", + " Longitude: 8.965088°", + "FINAL ANSWER: 52.696580, 8.965088" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 36.72615, + "lon": 3.18291, + "name": "Bab Ezzouar" + }, + "point_b": { + "lat": -26.50476, + "lon": 28.35921, + "name": "Heidelberg" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 21.108778, + "lon": 10.550958 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (36.72615°, 3.18291°)", + " Point B: (-26.50476°, 28.35921°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 21.108778°", + " Longitude: 10.550958°", + "FINAL ANSWER: 21.108778, 10.550958" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 36.64022, + "lon": 4.90131, + "name": "Amizour" + }, + "point_b": { + "lat": 59.41721, + "lon": 10.48343, + "name": "Horten" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 48.060829, + "lon": 7.066892 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (36.64022°, 4.90131°)", + " Point B: (59.41721°, 10.48343°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 48.060829°", + " Longitude: 7.066892°", + "FINAL ANSWER: 48.060829, 7.066892" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 45.30012, + "lon": -122.97316, + "name": "Newberg" + }, + "point_b": { + "lat": 20.78075, + "lon": 78.1407, + "name": "Dattāpur" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 70.530139, + "lon": 120.408541 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (45.30012°, -122.97316°)", + " Point B: (20.78075°, 78.1407°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 70.530139°", + " Longitude: 120.408541°", + "FINAL ANSWER: 70.530139, 120.408541" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 28.4326, + "lon": 69.58364, + "name": "Kashmor" + }, + "point_b": { + "lat": -15.47949, + "lon": -44.3652, + "name": "Januária" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 11.737694, + "lon": 8.582132 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (28.4326°, 69.58364°)", + " Point B: (-15.47949°, -44.3652°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 11.737694°", + " Longitude: 8.582132°", + "FINAL ANSWER: 11.737694, 8.582132" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 53.59398, + "lon": 142.95279, + "name": "Okha" + }, + "point_b": { + "lat": 28.56938, + "lon": 112.34733, + "name": "Heshan" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 42.068609, + "lon": 124.619833 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (53.59398°, 142.95279°)", + " Point B: (28.56938°, 112.34733°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 42.068609°", + " Longitude: 124.619833°", + "FINAL ANSWER: 42.068609, 124.619833" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 8.54665, + "lon": -71.24087, + "name": "Ejido" + }, + "point_b": { + "lat": -2.73353, + "lon": 107.63477, + "name": "Tanjung Pandan" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 50.924589, + "lon": -59.258503 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (8.54665°, -71.24087°)", + " Point B: (-2.73353°, 107.63477°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 50.924589°", + " Longitude: -59.258503°", + "FINAL ANSWER: 50.924589, -59.258503" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 0.07684, + "lon": 29.86832, + "name": "Kisinga" + }, + "point_b": { + "lat": -7.91446, + "lon": 39.66204, + "name": "Kilindoni" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -5.929216, + "lon": 37.192988 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (0.07684°, 29.86832°)", + " Point B: (-7.91446°, 39.66204°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -5.929216°", + " Longitude: 37.192988°", + "FINAL ANSWER: -5.929216, 37.192988" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 48.76486, + "lon": 1.92923, + "name": "Maurepas" + }, + "point_b": { + "lat": 56.15, + "lon": 37.93333, + "name": "Sofrino" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 55.381676, + "lon": 27.86484 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (48.76486°, 1.92923°)", + " Point B: (56.15°, 37.93333°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 55.381676°", + " Longitude: 27.864840°", + "FINAL ANSWER: 55.381676, 27.864840" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 18.80084, + "lon": 79.45206, + "name": "Rāmgundam" + }, + "point_b": { + "lat": 13.95, + "lon": 108.65, + "name": "An Khê" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 17.985904, + "lon": 86.884307 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (18.80084°, 79.45206°)", + " Point B: (13.95°, 108.65°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 17.985904°", + " Longitude: 86.884307°", + "FINAL ANSWER: 17.985904, 86.884307" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 9.43494, + "lon": -70.77495, + "name": "Sabana de Mendoza" + }, + "point_b": { + "lat": -23.04385, + "lon": 29.90319, + "name": "Louis Trichardt" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -18.633785, + "lon": 2.596348 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (9.43494°, -70.77495°)", + " Point B: (-23.04385°, 29.90319°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -18.633785°", + " Longitude: 2.596348°", + "FINAL ANSWER: -18.633785, 2.596348" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 29.30995, + "lon": 30.8418, + "name": "Al Fayyum" + }, + "point_b": { + "lat": 4.95, + "lon": 100.63333, + "name": "Simpang Empat" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 20.574958, + "lon": 68.394261 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (29.30995°, 30.8418°)", + " Point B: (4.95°, 100.63333°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 20.574958°", + " Longitude: 68.394261°", + "FINAL ANSWER: 20.574958, 68.394261" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -32.74976, + "lon": -70.72584, + "name": "San Felipe" + }, + "point_b": { + "lat": 51.50799, + "lon": 0.28333, + "name": "South Ockendon" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 11.406701, + "lon": -41.305014 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-32.74976°, -70.72584°)", + " Point B: (51.50799°, 0.28333°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 11.406701°", + " Longitude: -41.305014°", + "FINAL ANSWER: 11.406701, -41.305014" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 32.9312, + "lon": 12.08199, + "name": "Zuwarah" + }, + "point_b": { + "lat": 7.15181, + "lon": 0.47362, + "name": "Hohoe" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 20.135836, + "lon": 5.791624 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (32.9312°, 12.08199°)", + " Point B: (7.15181°, 0.47362°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 20.135836°", + " Longitude: 5.791624°", + "FINAL ANSWER: 20.135836, 5.791624" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -1.12889, + "lon": -47.62, + "name": "Igarapé-Açu" + }, + "point_b": { + "lat": 16.20546, + "lon": 77.35567, + "name": "Rāichūr" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 18.852276, + "lon": 44.981641 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-1.12889°, -47.62°)", + " Point B: (16.20546°, 77.35567°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 18.852276°", + " Longitude: 44.981641°", + "FINAL ANSWER: 18.852276, 44.981641" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 3.41364, + "lon": 30.95994, + "name": "Koboko" + }, + "point_b": { + "lat": -6.00306, + "lon": -40.29278, + "name": "Tauá" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -1.592696, + "lon": -4.58999 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (3.41364°, 30.95994°)", + " Point B: (-6.00306°, -40.29278°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -1.592696°", + " Longitude: -4.589990°", + "FINAL ANSWER: -1.592696, -4.589990" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 33.94121, + "lon": -84.21353, + "name": "Norcross" + }, + "point_b": { + "lat": 10.87655, + "lon": 76.30932, + "name": "Cherpulassery" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 60.918434, + "lon": -54.982171 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (33.94121°, -84.21353°)", + " Point B: (10.87655°, 76.30932°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 60.918434°", + " Longitude: -54.982171°", + "FINAL ANSWER: 60.918434, -54.982171" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -20.46528, + "lon": -45.95806, + "name": "Piumhi" + }, + "point_b": { + "lat": 49.40133, + "lon": 7.16424, + "name": "Ottweiler" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 16.029578, + "lon": -24.545109 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-20.46528°, -45.95806°)", + " Point B: (49.40133°, 7.16424°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 16.029578°", + " Longitude: -24.545109°", + "FINAL ANSWER: 16.029578, -24.545109" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -11.94306, + "lon": -76.70944, + "name": "Chosica" + }, + "point_b": { + "lat": 53.36831, + "lon": 34.10328, + "name": "Sel’tso" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 49.077382, + "lon": -10.82045 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-11.94306°, -76.70944°)", + " Point B: (53.36831°, 34.10328°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 49.077382°", + " Longitude: -10.820450°", + "FINAL ANSWER: 49.077382, -10.820450" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 23.71667, + "lon": 86.4, + "name": "Jāmadoba" + }, + "point_b": { + "lat": 40.09923, + "lon": -83.11408, + "name": "Dublin" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 78.406613, + "lon": 45.96815 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (23.71667°, 86.4°)", + " Point B: (40.09923°, -83.11408°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 78.406613°", + " Longitude: 45.968150°", + "FINAL ANSWER: 78.406613, 45.968150" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 40.46276, + "lon": -3.67813, + "name": "Nueva España" + }, + "point_b": { + "lat": 12.93333, + "lon": -0.85, + "name": "Yalgo" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 26.704944, + "lon": -2.089822 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (40.46276°, -3.67813°)", + " Point B: (12.93333°, -0.85°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 26.704944°", + " Longitude: -2.089822°", + "FINAL ANSWER: 26.704944, -2.089822" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 17.89241, + "lon": 75.02138, + "name": "Aklūj" + }, + "point_b": { + "lat": 24.51379, + "lon": 86.64576, + "name": "Jasidih" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 22.935952, + "lon": 83.638997 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (17.89241°, 75.02138°)", + " Point B: (24.51379°, 86.64576°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 22.935952°", + " Longitude: 83.638997°", + "FINAL ANSWER: 22.935952, 83.638997" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 43.53331, + "lon": 26.51849, + "name": "Razgrad" + }, + "point_b": { + "lat": 55.68062, + "lon": 12.45373, + "name": "Rødovre" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 49.817012, + "lon": 20.369919 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (43.53331°, 26.51849°)", + " Point B: (55.68062°, 12.45373°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 49.817012°", + " Longitude: 20.369919°", + "FINAL ANSWER: 49.817012, 20.369919" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 22.81567, + "lon": 70.86653, + "name": "Trajpar" + }, + "point_b": { + "lat": 32.13664, + "lon": 75.47291, + "name": "Dīnānagar" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 29.821283, + "lon": 74.244584 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (22.81567°, 70.86653°)", + " Point B: (32.13664°, 75.47291°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 29.821283°", + " Longitude: 74.244584°", + "FINAL ANSWER: 29.821283, 74.244584" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 49.49991, + "lon": -115.76879, + "name": "Cranbrook" + }, + "point_b": { + "lat": 14.57814, + "lon": -90.73804, + "name": "Jocotenango" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 23.687687, + "lon": -95.39612 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (49.49991°, -115.76879°)", + " Point B: (14.57814°, -90.73804°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 23.687687°", + " Longitude: -95.396120°", + "FINAL ANSWER: 23.687687, -95.396120" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -12.23333, + "lon": -38.75, + "name": "Coração de Maria" + }, + "point_b": { + "lat": -1.50583, + "lon": -48.62583, + "name": "Barcarena" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -6.894922, + "lon": -43.743908 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-12.23333°, -38.75°)", + " Point B: (-1.50583°, -48.62583°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -6.894922°", + " Longitude: -43.743908°", + "FINAL ANSWER: -6.894922, -43.743908" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 44.00012, + "lon": -77.24946, + "name": "Prince Edward" + }, + "point_b": { + "lat": -3.86881, + "lon": 23.88348, + "name": "Lukula" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 13.544312, + "lon": 5.56854 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (44.00012°, -77.24946°)", + " Point B: (-3.86881°, 23.88348°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 13.544312°", + " Longitude: 5.568540°", + "FINAL ANSWER: 13.544312, 5.568540" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 42.99806, + "lon": 21.94611, + "name": "Leskovac" + }, + "point_b": { + "lat": 42.09869, + "lon": -75.91797, + "name": "Binghamton" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 51.369968, + "lon": 0.237597 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (42.99806°, 21.94611°)", + " Point B: (42.09869°, -75.91797°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 51.369968°", + " Longitude: 0.237597°", + "FINAL ANSWER: 51.369968, 0.237597" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 29.94906, + "lon": 74.73832, + "name": "Dabwāli" + }, + "point_b": { + "lat": 34.80059, + "lon": 126.69669, + "name": "Yeongam" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 35.191789, + "lon": 99.967687 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (29.94906°, 74.73832°)", + " Point B: (34.80059°, 126.69669°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 35.191789°", + " Longitude: 99.967687°", + "FINAL ANSWER: 35.191789, 99.967687" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 43.70806, + "lon": 142.03917, + "name": "Fukagawa" + }, + "point_b": { + "lat": 29.373, + "lon": 78.13636, + "name": "Bijnor" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 41.085291, + "lon": 106.761358 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (43.70806°, 142.03917°)", + " Point B: (29.373°, 78.13636°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 41.085291°", + " Longitude: 106.761358°", + "FINAL ANSWER: 41.085291, 106.761358" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 6.65915, + "lon": 7.75961, + "name": "Eha Amufu" + }, + "point_b": { + "lat": 6.87341, + "lon": -6.84829, + "name": "Belleville" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 6.753714, + "lon": 4.10906 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (6.65915°, 7.75961°)", + " Point B: (6.87341°, -6.84829°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 6.753714°", + " Longitude: 4.109060°", + "FINAL ANSWER: 6.753714, 4.109060" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 18.68211, + "lon": 73.73161, + "name": "Dehu Road" + }, + "point_b": { + "lat": -5.85746, + "lon": 144.23058, + "name": "Mount Hagen" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 13.923496, + "lon": 92.270585 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (18.68211°, 73.73161°)", + " Point B: (-5.85746°, 144.23058°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 13.923496°", + " Longitude: 92.270585°", + "FINAL ANSWER: 13.923496, 92.270585" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 41.66199, + "lon": -86.15862, + "name": "Mishawaka" + }, + "point_b": { + "lat": 17.59898, + "lon": 33.97205, + "name": "Ed Damer" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 35.19834, + "lon": 14.388918 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (41.66199°, -86.15862°)", + " Point B: (17.59898°, 33.97205°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 35.198340°", + " Longitude: 14.388918°", + "FINAL ANSWER: 35.198340, 14.388918" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 6.36536, + "lon": 2.41833, + "name": "Cotonou" + }, + "point_b": { + "lat": 33.71706, + "lon": 130.64117, + "name": "Miyawaka" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 25.284965, + "lon": 25.659808 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (6.36536°, 2.41833°)", + " Point B: (33.71706°, 130.64117°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 25.284965°", + " Longitude: 25.659808°", + "FINAL ANSWER: 25.284965, 25.659808" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 40.35722, + "lon": 30.01417, + "name": "Osmaneli" + }, + "point_b": { + "lat": 25.45598, + "lon": 85.5329, + "name": "Bakhtiarpur" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 36.149127, + "lon": 60.323833 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (40.35722°, 30.01417°)", + " Point B: (25.45598°, 85.5329°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 36.149127°", + " Longitude: 60.323833°", + "FINAL ANSWER: 36.149127, 60.323833" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -37.78761, + "lon": 145.14888, + "name": "Doncaster East" + }, + "point_b": { + "lat": 12.66664, + "lon": -0.57469, + "name": "Boulsa" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -46.916815, + "lon": 98.476927 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-37.78761°, 145.14888°)", + " Point B: (12.66664°, -0.57469°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -46.916815°", + " Longitude: 98.476927°", + "FINAL ANSWER: -46.916815, 98.476927" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 33.94483, + "lon": -6.93106, + "name": "El Harhoura" + }, + "point_b": { + "lat": 51.64087, + "lon": -2.67683, + "name": "Chepstow" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 47.232897, + "lon": -3.995286 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (33.94483°, -6.93106°)", + " Point B: (51.64087°, -2.67683°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 47.232897°", + " Longitude: -3.995286°", + "FINAL ANSWER: 47.232897, -3.995286" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 20.617, + "lon": -105.23018, + "name": "Puerto Vallarta" + }, + "point_b": { + "lat": 33.80809, + "lon": 44.53343, + "name": "Khāliş" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 62.554994, + "lon": -42.759789 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (20.617°, -105.23018°)", + " Point B: (33.80809°, 44.53343°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 62.554994°", + " Longitude: -42.759789°", + "FINAL ANSWER: 62.554994, -42.759789" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -8.41554, + "lon": -78.75201, + "name": "Virú" + }, + "point_b": { + "lat": 47.65527, + "lon": 24.66328, + "name": "Borşa" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 43.198902, + "lon": -12.661125 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-8.41554°, -78.75201°)", + " Point B: (47.65527°, 24.66328°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 43.198902°", + " Longitude: -12.661125°", + "FINAL ANSWER: 43.198902, -12.661125" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -11.08944, + "lon": -43.14167, + "name": "Barra" + }, + "point_b": { + "lat": 36.07508, + "lon": 32.83691, + "name": "Anamur" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 27.45684, + "lon": 9.747452 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-11.08944°, -43.14167°)", + " Point B: (36.07508°, 32.83691°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 27.456840°", + " Longitude: 9.747452°", + "FINAL ANSWER: 27.456840, 9.747452" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 44.67244, + "lon": -63.47506, + "name": "Cole Harbour" + }, + "point_b": { + "lat": 38.52005, + "lon": -89.98399, + "name": "Belleville" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 40.613402, + "lon": -83.859733 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (44.67244°, -63.47506°)", + " Point B: (38.52005°, -89.98399°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 40.613402°", + " Longitude: -83.859733°", + "FINAL ANSWER: 40.613402, -83.859733" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 11.78778, + "lon": 42.88222, + "name": "Tadjoura" + }, + "point_b": { + "lat": 41.87871, + "lon": -71.38256, + "name": "Pawtucket" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 47.659572, + "lon": -37.026715 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (11.78778°, 42.88222°)", + " Point B: (41.87871°, -71.38256°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 47.659572°", + " Longitude: -37.026715°", + "FINAL ANSWER: 47.659572, -37.026715" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 6.92477, + "lon": 158.16109, + "name": "Palikir" + }, + "point_b": { + "lat": 41.45004, + "lon": 2.24741, + "name": "Badalona" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 35.78316, + "lon": 143.825046 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (6.92477°, 158.16109°)", + " Point B: (41.45004°, 2.24741°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 35.783160°", + " Longitude: 143.825046°", + "FINAL ANSWER: 35.783160, 143.825046" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 35.44951, + "lon": -97.3967, + "name": "Midwest City" + }, + "point_b": { + "lat": 30.40159, + "lon": -86.86357, + "name": "Navarre" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 33.036144, + "lon": -91.979379 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (35.44951°, -97.3967°)", + " Point B: (30.40159°, -86.86357°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 33.036144°", + " Longitude: -91.979379°", + "FINAL ANSWER: 33.036144, -91.979379" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -10.1497, + "lon": -67.73741, + "name": "Senador Guiomard" + }, + "point_b": { + "lat": -29.19167, + "lon": -54.86722, + "name": "Santiago" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -24.5268, + "lon": -58.40647 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-10.1497°, -67.73741°)", + " Point B: (-29.19167°, -54.86722°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -24.526800°", + " Longitude: -58.406470°", + "FINAL ANSWER: -24.526800, -58.406470" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 36.48333, + "lon": 140.38333, + "name": "Ishitsuka" + }, + "point_b": { + "lat": 21.3374, + "lon": -158.09676, + "name": "Makakilo / Kapolei / Honokai Hale" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 27.73705, + "lon": -171.493773 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (36.48333°, 140.38333°)", + " Point B: (21.3374°, -158.09676°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 27.737050°", + " Longitude: -171.493773°", + "FINAL ANSWER: 27.737050, -171.493773" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 45.49389, + "lon": -75.58833, + "name": "Templeton-Est" + }, + "point_b": { + "lat": 26.17993, + "lon": 56.24774, + "name": "Khasab" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 59.609106, + "lon": -42.858409 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (45.49389°, -75.58833°)", + " Point B: (26.17993°, 56.24774°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 59.609106°", + " Longitude: -42.858409°", + "FINAL ANSWER: 59.609106, -42.858409" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 40.84829, + "lon": -74.58148, + "name": "Randolph" + }, + "point_b": { + "lat": 42.37169, + "lon": -88.09008, + "name": "Round Lake Beach" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 42.140651, + "lon": -84.65767 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (40.84829°, -74.58148°)", + " Point B: (42.37169°, -88.09008°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 42.140651°", + " Longitude: -84.657670°", + "FINAL ANSWER: 42.140651, -84.657670" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -25.96222, + "lon": 32.45889, + "name": "Matola" + }, + "point_b": { + "lat": 34.13639, + "lon": -118.77453, + "name": "Agoura Hills" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 15.853708, + "lon": -34.00113 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-25.96222°, 32.45889°)", + " Point B: (34.13639°, -118.77453°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 15.853708°", + " Longitude: -34.001130°", + "FINAL ANSWER: 15.853708, -34.001130" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 41.53174, + "lon": -8.61843, + "name": "Barcelos" + }, + "point_b": { + "lat": 42.21197, + "lon": -88.23814, + "name": "Cary" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 47.584162, + "lon": -69.556205 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (41.53174°, -8.61843°)", + " Point B: (42.21197°, -88.23814°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 47.584162°", + " Longitude: -69.556205°", + "FINAL ANSWER: 47.584162, -69.556205" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 5.78333, + "lon": 36.56667, + "name": "Bako" + }, + "point_b": { + "lat": 55.37514, + "lon": 13.15691, + "name": "Trelleborg" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 18.472784, + "lon": 32.649729 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (5.78333°, 36.56667°)", + " Point B: (55.37514°, 13.15691°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 18.472784°", + " Longitude: 32.649729°", + "FINAL ANSWER: 18.472784, 32.649729" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 51.24623, + "lon": 4.44903, + "name": "Merksem" + }, + "point_b": { + "lat": -7.65685, + "lon": 36.98299, + "name": "Ruaha" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 22.569639, + "lon": 24.485391 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (51.24623°, 4.44903°)", + " Point B: (-7.65685°, 36.98299°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 22.569639°", + " Longitude: 24.485391°", + "FINAL ANSWER: 22.569639, 24.485391" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 38.89511, + "lon": -77.03637, + "name": "Washington" + }, + "point_b": { + "lat": 50.43302, + "lon": 2.82791, + "name": "Lens" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 52.097259, + "lon": -41.882117 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (38.89511°, -77.03637°)", + " Point B: (50.43302°, 2.82791°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 52.097259°", + " Longitude: -41.882117°", + "FINAL ANSWER: 52.097259, -41.882117" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 49.22104, + "lon": -123.09546, + "name": "Sunset" + }, + "point_b": { + "lat": 51.10754, + "lon": 114.54173, + "name": "Aginskoye" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 61.801016, + "lon": -143.867879 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (49.22104°, -123.09546°)", + " Point B: (51.10754°, 114.54173°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 61.801016°", + " Longitude: -143.867879°", + "FINAL ANSWER: 61.801016, -143.867879" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -28.11694, + "lon": 153.46584, + "name": "Palm Beach" + }, + "point_b": { + "lat": -15.79444, + "lon": -48.77583, + "name": "Cocalzinho de Goiás" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -54.511461, + "lon": -179.750843 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-28.11694°, 153.46584°)", + " Point B: (-15.79444°, -48.77583°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -54.511461°", + " Longitude: -179.750843°", + "FINAL ANSWER: -54.511461, -179.750843" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 55.58183, + "lon": 38.91994, + "name": "Kurovskoye" + }, + "point_b": { + "lat": 33.38067, + "lon": -84.79966, + "name": "Newnan" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 62.957392, + "lon": -42.751527 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (55.58183°, 38.91994°)", + " Point B: (33.38067°, -84.79966°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 62.957392°", + " Longitude: -42.751527°", + "FINAL ANSWER: 62.957392, -42.751527" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -5.19917, + "lon": -39.29278, + "name": "Quixeramobim" + }, + "point_b": { + "lat": -26.66008, + "lon": 153.09953, + "name": "Maroochydore" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -58.422581, + "lon": 178.792028 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-5.19917°, -39.29278°)", + " Point B: (-26.66008°, 153.09953°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -58.422581°", + " Longitude: 178.792028°", + "FINAL ANSWER: -58.422581, 178.792028" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 28.74705, + "lon": 77.11465, + "name": "Sāhibābād Daulotpur" + }, + "point_b": { + "lat": 50.81678, + "lon": 4.32775, + "name": "Forest" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 45.764472, + "lon": 47.546092 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (28.74705°, 77.11465°)", + " Point B: (50.81678°, 4.32775°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 45.764472°", + " Longitude: 47.546092°", + "FINAL ANSWER: 45.764472, 47.546092" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -22.23333, + "lon": -53.34306, + "name": "Nova Andradina" + }, + "point_b": { + "lat": 36.34814, + "lon": 37.5309, + "name": "Tādif" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -6.544698, + "lon": -31.97031 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-22.23333°, -53.34306°)", + " Point B: (36.34814°, 37.5309°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -6.544698°", + " Longitude: -31.970310°", + "FINAL ANSWER: -6.544698, -31.970310" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -4.13, + "lon": -44.12417, + "name": "Coroatá" + }, + "point_b": { + "lat": 34.69926, + "lon": -86.74833, + "name": "Madison" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 25.988948, + "lon": -74.098395 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-4.13°, -44.12417°)", + " Point B: (34.69926°, -86.74833°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 25.988948°", + " Longitude: -74.098395°", + "FINAL ANSWER: 25.988948, -74.098395" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -37.84205, + "lon": 145.0694, + "name": "Camberwell" + }, + "point_b": { + "lat": -7.87639, + "lon": 110.35889, + "name": "Sewon" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -31.191008, + "lon": 134.664061 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-37.84205°, 145.0694°)", + " Point B: (-7.87639°, 110.35889°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -31.191008°", + " Longitude: 134.664061°", + "FINAL ANSWER: -31.191008, 134.664061" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -29.02889, + "lon": -51.18167, + "name": "Flores da Cunha" + }, + "point_b": { + "lat": 45.61674, + "lon": 25.71101, + "name": "Săcele" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -9.661435, + "lon": -33.472365 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-29.02889°, -51.18167°)", + " Point B: (45.61674°, 25.71101°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -9.661435°", + " Longitude: -33.472365°", + "FINAL ANSWER: -9.661435, -33.472365" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 45.44207, + "lon": 9.09445, + "name": "Cesano Boscone" + }, + "point_b": { + "lat": 12.8905, + "lon": 75.03489, + "name": "Bantvāl" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 41.120878, + "lon": 30.345109 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (45.44207°, 9.09445°)", + " Point B: (12.8905°, 75.03489°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 41.120878°", + " Longitude: 30.345109°", + "FINAL ANSWER: 41.120878, 30.345109" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 51.6621, + "lon": 103.70996, + "name": "Slyudyanka" + }, + "point_b": { + "lat": -37.74981, + "lon": 144.9109, + "name": "Essendon" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 30.022464, + "lon": 118.016974 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (51.6621°, 103.70996°)", + " Point B: (-37.74981°, 144.9109°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 30.022464°", + " Longitude: 118.016974°", + "FINAL ANSWER: 30.022464, 118.016974" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 33.36667, + "lon": 130.51667, + "name": "Tosu" + }, + "point_b": { + "lat": -21.2075, + "lon": -159.77546, + "name": "Avarua" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -7.196032, + "lon": -176.625267 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (33.36667°, 130.51667°)", + " Point B: (-21.2075°, -159.77546°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -7.196032°", + " Longitude: -176.625267°", + "FINAL ANSWER: -7.196032, -176.625267" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 52.0814, + "lon": 21.02397, + "name": "Piaseczno" + }, + "point_b": { + "lat": 22.39846, + "lon": 114.19293, + "name": "Fo Tan" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 36.043487, + "lon": 99.640023 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (52.0814°, 21.02397°)", + " Point B: (22.39846°, 114.19293°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 36.043487°", + " Longitude: 99.640023°", + "FINAL ANSWER: 36.043487, 99.640023" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 57.25483, + "lon": 60.09052, + "name": "Novoural’sk" + }, + "point_b": { + "lat": 2.0441, + "lon": 102.6527, + "name": "Bakri" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 31.249883, + "lon": 87.984708 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (57.25483°, 60.09052°)", + " Point B: (2.0441°, 102.6527°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 31.249883°", + " Longitude: 87.984708°", + "FINAL ANSWER: 31.249883, 87.984708" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 30.15293, + "lon": 31.31501, + "name": "Al Khuşūş" + }, + "point_b": { + "lat": 8.48639, + "lon": 2.42872, + "name": "Ouessé" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 25.225786, + "lon": 23.273277 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (30.15293°, 31.31501°)", + " Point B: (8.48639°, 2.42872°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 25.225786°", + " Longitude: 23.273277°", + "FINAL ANSWER: 25.225786, 23.273277" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 49.25, + "lon": -123.06667, + "name": "Kensington-Cedar Cottage" + }, + "point_b": { + "lat": 28.63215, + "lon": 104.40783, + "name": "Shuifu" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 47.759755, + "lon": 120.545135 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (49.25°, -123.06667°)", + " Point B: (28.63215°, 104.40783°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 47.759755°", + " Longitude: 120.545135°", + "FINAL ANSWER: 47.759755, 120.545135" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -25.68991, + "lon": 30.03504, + "name": "Belfast" + }, + "point_b": { + "lat": 37.92259, + "lon": 139.04125, + "name": "Niigata" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 10.411893, + "lon": 79.21472 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-25.68991°, 30.03504°)", + " Point B: (37.92259°, 139.04125°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 10.411893°", + " Longitude: 79.214720°", + "FINAL ANSWER: 10.411893, 79.214720" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -0.80116, + "lon": 34.72579, + "name": "Ogembo" + }, + "point_b": { + "lat": 4.26425, + "lon": -75.93085, + "name": "Sevilla" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 3.041876, + "lon": -20.491768 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-0.80116°, 34.72579°)", + " Point B: (4.26425°, -75.93085°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 3.041876°", + " Longitude: -20.491768°", + "FINAL ANSWER: 3.041876, -20.491768" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 51.17655, + "lon": 4.83248, + "name": "Herentals" + }, + "point_b": { + "lat": -33.9681, + "lon": 151.13564, + "name": "Kogarah" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 25.382346, + "lon": 102.639078 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (51.17655°, 4.83248°)", + " Point B: (-33.9681°, 151.13564°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 25.382346°", + " Longitude: 102.639078°", + "FINAL ANSWER: 25.382346, 102.639078" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -34.75155, + "lon": 149.72086, + "name": "Goulburn" + }, + "point_b": { + "lat": 20.45781, + "lon": 75.01596, + "name": "Chalisgaon" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 6.021123, + "lon": 92.729974 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-34.75155°, 149.72086°)", + " Point B: (20.45781°, 75.01596°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 6.021123°", + " Longitude: 92.729974°", + "FINAL ANSWER: 6.021123, 92.729974" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 19.07283, + "lon": 72.88261, + "name": "Mumbai" + }, + "point_b": { + "lat": 52.30136, + "lon": 6.7482, + "name": "Borne" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 30.29312, + "lon": 61.686635 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (19.07283°, 72.88261°)", + " Point B: (52.30136°, 6.7482°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 30.293120°", + " Longitude: 61.686635°", + "FINAL ANSWER: 30.293120, 61.686635" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 23.89013, + "lon": 106.62684, + "name": "Baise" + }, + "point_b": { + "lat": 11.58528, + "lon": 122.75111, + "name": "Roxas City" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 14.776868, + "lon": 118.916562 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (23.89013°, 106.62684°)", + " Point B: (11.58528°, 122.75111°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 14.776868°", + " Longitude: 118.916562°", + "FINAL ANSWER: 14.776868, 118.916562" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -28.72472, + "lon": -52.84972, + "name": "Espumoso" + }, + "point_b": { + "lat": 35.80472, + "lon": 139.60194, + "name": "Asaka" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -0.286664, + "lon": -84.970495 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-28.72472°, -52.84972°)", + " Point B: (35.80472°, 139.60194°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -0.286664°", + " Longitude: -84.970495°", + "FINAL ANSWER: -0.286664, -84.970495" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 2.95395, + "lon": -76.69644, + "name": "Suárez" + }, + "point_b": { + "lat": 29.51827, + "lon": 70.84474, + "name": "Jatoi Shimali" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 45.400033, + "lon": -16.213593 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (2.95395°, -76.69644°)", + " Point B: (29.51827°, 70.84474°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 45.400033°", + " Longitude: -16.213593°", + "FINAL ANSWER: 45.400033, -16.213593" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -38.03333, + "lon": 145.35, + "name": "Berwick" + }, + "point_b": { + "lat": -6.83333, + "lon": 36.98333, + "name": "Kilosa" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -22.39411, + "lon": 57.276605 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-38.03333°, 145.35°)", + " Point B: (-6.83333°, 36.98333°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -22.394110°", + " Longitude: 57.276605°", + "FINAL ANSWER: -22.394110, 57.276605" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 34.55808, + "lon": 133.41796, + "name": "Kannabechō-yahiro" + }, + "point_b": { + "lat": 11.69348, + "lon": 75.56013, + "name": "Azhiyūr" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 31.242942, + "lon": 116.876364 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (34.55808°, 133.41796°)", + " Point B: (11.69348°, 75.56013°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 31.242942°", + " Longitude: 116.876364°", + "FINAL ANSWER: 31.242942, 116.876364" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 11.30088, + "lon": 79.55612, + "name": "Lālpettai" + }, + "point_b": { + "lat": 31.78447, + "lon": 71.10197, + "name": "Darya Khan" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 16.457445, + "lon": 77.645823 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (11.30088°, 79.55612°)", + " Point B: (31.78447°, 71.10197°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 16.457445°", + " Longitude: 77.645823°", + "FINAL ANSWER: 16.457445, 77.645823" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 10.45, + "lon": 38.2, + "name": "Bichena" + }, + "point_b": { + "lat": -28.29389, + "lon": -49.93167, + "name": "São Joaquim" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -12.307412, + "lon": -2.807618 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (10.45°, 38.2°)", + " Point B: (-28.29389°, -49.93167°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -12.307412°", + " Longitude: -2.807618°", + "FINAL ANSWER: -12.307412, -2.807618" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 32.81303, + "lon": 34.99928, + "name": "Haifa" + }, + "point_b": { + "lat": 58.34784, + "lon": 11.9424, + "name": "Uddevalla" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 39.55539, + "lon": 31.010493 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (32.81303°, 34.99928°)", + " Point B: (58.34784°, 11.9424°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 39.555390°", + " Longitude: 31.010493°", + "FINAL ANSWER: 39.555390, 31.010493" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -37.63333, + "lon": 144.86667, + "name": "Greenvale" + }, + "point_b": { + "lat": 41.09294, + "lon": -8.63219, + "name": "Valadares" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 7.465138, + "lon": 74.12305 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-37.63333°, 144.86667°)", + " Point B: (41.09294°, -8.63219°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 7.465138°", + " Longitude: 74.123050°", + "FINAL ANSWER: 7.465138, 74.123050" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 52.64817, + "lon": 19.0678, + "name": "Włocławek" + }, + "point_b": { + "lat": -31.8075, + "lon": 115.86599, + "name": "Landsdale" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 15.227902, + "lon": 78.113899 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (52.64817°, 19.0678°)", + " Point B: (-31.8075°, 115.86599°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 15.227902°", + " Longitude: 78.113899°", + "FINAL ANSWER: 15.227902, 78.113899" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 52.44653, + "lon": 13.5066, + "name": "Johannisthal" + }, + "point_b": { + "lat": 28.55207, + "lon": 70.46837, + "name": "Kot Samaba" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 36.840315, + "lon": 60.185547 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (52.44653°, 13.5066°)", + " Point B: (28.55207°, 70.46837°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 36.840315°", + " Longitude: 60.185547°", + "FINAL ANSWER: 36.840315, 60.185547" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -3.60833, + "lon": -45.34333, + "name": "Pindaré-Mirim" + }, + "point_b": { + "lat": 3.51667, + "lon": 15.05, + "name": "Yokadouma" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -1.896092, + "lon": -30.228833 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-3.60833°, -45.34333°)", + " Point B: (3.51667°, 15.05°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -1.896092°", + " Longitude: -30.228833°", + "FINAL ANSWER: -1.896092, -30.228833" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 16.90802, + "lon": 96.56037, + "name": "Kayan" + }, + "point_b": { + "lat": 4.60637, + "lon": 114.32476, + "name": "Seria" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 13.938209, + "lon": 101.152255 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (16.90802°, 96.56037°)", + " Point B: (4.60637°, 114.32476°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 13.938209°", + " Longitude: 101.152255°", + "FINAL ANSWER: 13.938209, 101.152255" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 19.25465, + "lon": -99.10356, + "name": "Xochimilco" + }, + "point_b": { + "lat": 34.57943, + "lon": -118.11646, + "name": "Palmdale" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 27.236631, + "lon": -107.954677 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (19.25465°, -99.10356°)", + " Point B: (34.57943°, -118.11646°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 27.236631°", + " Longitude: -107.954677°", + "FINAL ANSWER: 27.236631, -107.954677" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -24.67014, + "lon": 25.53975, + "name": "Thamaga" + }, + "point_b": { + "lat": 18.55, + "lon": 31.85, + "name": "Kuraymah" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -3.064705, + "lon": 28.761758 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-24.67014°, 25.53975°)", + " Point B: (18.55°, 31.85°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -3.064705°", + " Longitude: 28.761758°", + "FINAL ANSWER: -3.064705, 28.761758" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -37.81819, + "lon": 145.00176, + "name": "Richmond" + }, + "point_b": { + "lat": -23.165, + "lon": -47.74361, + "name": "Cerquilho" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -77.171129, + "lon": -97.237761 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-37.81819°, 145.00176°)", + " Point B: (-23.165°, -47.74361°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -77.171129°", + " Longitude: -97.237761°", + "FINAL ANSWER: -77.171129, -97.237761" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 15.72299, + "lon": 75.38666, + "name": "Nargund" + }, + "point_b": { + "lat": -20.31628, + "lon": 57.52594, + "name": "Curepipe" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 6.718772, + "lon": 70.897852 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (15.72299°, 75.38666°)", + " Point B: (-20.31628°, 57.52594°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 6.718772°", + " Longitude: 70.897852°", + "FINAL ANSWER: 6.718772, 70.897852" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 7.31667, + "lon": 38.08333, + "name": "K’olīto" + }, + "point_b": { + "lat": -5.84525, + "lon": 112.65173, + "name": "Sangkapura" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -2.595857, + "lon": 93.992912 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (7.31667°, 38.08333°)", + " Point B: (-5.84525°, 112.65173°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -2.595857°", + " Longitude: 93.992912°", + "FINAL ANSWER: -2.595857, 93.992912" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 50.23019, + "lon": 8.77155, + "name": "Karben" + }, + "point_b": { + "lat": 21.0, + "lon": 105.88333, + "name": "Vĩnh Tuy" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 46.636368, + "lon": 69.27194 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (50.23019°, 8.77155°)", + " Point B: (21.0°, 105.88333°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 46.636368°", + " Longitude: 69.271940°", + "FINAL ANSWER: 46.636368, 69.271940" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 51.36892, + "lon": 42.09804, + "name": "Borisoglebsk" + }, + "point_b": { + "lat": 33.92557, + "lon": -116.87641, + "name": "Banning" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 72.306396, + "lon": 19.390889 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (51.36892°, 42.09804°)", + " Point B: (33.92557°, -116.87641°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 72.306396°", + " Longitude: 19.390889°", + "FINAL ANSWER: 72.306396, 19.390889" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 16.06666, + "lon": 22.83536, + "name": "Amdjarass" + }, + "point_b": { + "lat": 26.44212, + "lon": 92.03047, + "name": "Mangaldai" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 27.009372, + "lon": 73.942895 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (16.06666°, 22.83536°)", + " Point B: (26.44212°, 92.03047°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 27.009372°", + " Longitude: 73.942895°", + "FINAL ANSWER: 27.009372, 73.942895" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 23.21494, + "lon": 81.53204, + "name": "Burhar" + }, + "point_b": { + "lat": 24.07327, + "lon": 120.56276, + "name": "Chang-hua" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 24.914398, + "lon": 100.980806 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (23.21494°, 81.53204°)", + " Point B: (24.07327°, 120.56276°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 24.914398°", + " Longitude: 100.980806°", + "FINAL ANSWER: 24.914398, 100.980806" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 45.58333, + "lon": 25.45, + "name": "Râşnov" + }, + "point_b": { + "lat": 6.66129, + "lon": -3.26984, + "name": "Niablé" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 16.827586, + "lon": 2.322861 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (45.58333°, 25.45°)", + " Point B: (6.66129°, -3.26984°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 16.827586°", + " Longitude: 2.322861°", + "FINAL ANSWER: 16.827586, 2.322861" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 26.86852, + "lon": 99.95628, + "name": "Shigu" + }, + "point_b": { + "lat": 28.4662, + "lon": 79.30657, + "name": "Fatehganj West" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 27.555145, + "lon": 94.859625 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (26.86852°, 99.95628°)", + " Point B: (28.4662°, 79.30657°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 27.555145°", + " Longitude: 94.859625°", + "FINAL ANSWER: 27.555145, 94.859625" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 39.65456, + "lon": 66.96445, + "name": "Samarkand" + }, + "point_b": { + "lat": 40.48979, + "lon": -81.44567, + "name": "New Philadelphia" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 72.066496, + "lon": -5.998832 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (39.65456°, 66.96445°)", + " Point B: (40.48979°, -81.44567°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 72.066496°", + " Longitude: -5.998832°", + "FINAL ANSWER: 72.066496, -5.998832" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -21.72028, + "lon": -51.01889, + "name": "Lucélia" + }, + "point_b": { + "lat": 14.96667, + "lon": 35.91667, + "name": "Khashm al Qirbah" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 5.532053, + "lon": 14.367052 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-21.72028°, -51.01889°)", + " Point B: (14.96667°, 35.91667°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 5.532053°", + " Longitude: 14.367052°", + "FINAL ANSWER: 5.532053, 14.367052" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 34.35, + "lon": 132.33333, + "name": "Hatsukaichi" + }, + "point_b": { + "lat": 8.96249, + "lon": -71.60754, + "name": "Pueblo Nuevo El Chivo" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 58.525679, + "lon": 165.809394 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (34.35°, 132.33333°)", + " Point B: (8.96249°, -71.60754°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 58.525679°", + " Longitude: 165.809394°", + "FINAL ANSWER: 58.525679, 165.809394" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -32.82262, + "lon": -60.71852, + "name": "Capitán Bermúdez" + }, + "point_b": { + "lat": 33.87309, + "lon": 7.87765, + "name": "Nefta" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 0.635774, + "lon": -26.656205 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-32.82262°, -60.71852°)", + " Point B: (33.87309°, 7.87765°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 0.635774°", + " Longitude: -26.656205°", + "FINAL ANSWER: 0.635774, -26.656205" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 11.0129, + "lon": 104.67292, + "name": "Ângk Tasaôm" + }, + "point_b": { + "lat": -14.2789, + "lon": -38.99584, + "name": "Itacaré" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -12.063271, + "lon": -1.943826 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (11.0129°, 104.67292°)", + " Point B: (-14.2789°, -38.99584°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -12.063271°", + " Longitude: -1.943826°", + "FINAL ANSWER: -12.063271, -1.943826" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 5.647, + "lon": 100.48772, + "name": "Sungai Petani" + }, + "point_b": { + "lat": 28.69736, + "lon": 77.0648, + "name": "Kirāri Sulemānnagar" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 17.513751, + "lon": 89.524635 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (5.647°, 100.48772°)", + " Point B: (28.69736°, 77.0648°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 17.513751°", + " Longitude: 89.524635°", + "FINAL ANSWER: 17.513751, 89.524635" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -16.40639, + "lon": -49.21861, + "name": "Nerópolis" + }, + "point_b": { + "lat": 40.60816, + "lon": -74.27765, + "name": "Rahway" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -2.021032, + "lon": -54.792138 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-16.40639°, -49.21861°)", + " Point B: (40.60816°, -74.27765°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -2.021032°", + " Longitude: -54.792138°", + "FINAL ANSWER: -2.021032, -54.792138" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 14.4996, + "lon": 121.0507, + "name": "Upper Bicutan" + }, + "point_b": { + "lat": 53.70117, + "lon": 91.70797, + "name": "Minusinsk" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 34.933934, + "lon": 109.991217 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (14.4996°, 121.0507°)", + " Point B: (53.70117°, 91.70797°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 34.933934°", + " Longitude: 109.991217°", + "FINAL ANSWER: 34.933934, 109.991217" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 13.54297, + "lon": 100.99333, + "name": "Bang Pakong" + }, + "point_b": { + "lat": 43.00141, + "lon": -85.76809, + "name": "Walker" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 73.075235, + "lon": -99.667967 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (13.54297°, 100.99333°)", + " Point B: (43.00141°, -85.76809°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 73.075235°", + " Longitude: -99.667967°", + "FINAL ANSWER: 73.075235, -99.667967" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 34.69379, + "lon": 135.50107, + "name": "Osaka" + }, + "point_b": { + "lat": -15.31737, + "lon": 28.26868, + "name": "Chunga" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 28.609878, + "lon": 103.040041 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (34.69379°, 135.50107°)", + " Point B: (-15.31737°, 28.26868°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 28.609878°", + " Longitude: 103.040041°", + "FINAL ANSWER: 28.609878, 103.040041" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 0.57387, + "lon": 32.51545, + "name": "Bombo" + }, + "point_b": { + "lat": 25.81954, + "lon": -80.35533, + "name": "Doral" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 22.918631, + "lon": -19.394796 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (0.57387°, 32.51545°)", + " Point B: (25.81954°, -80.35533°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 22.918631°", + " Longitude: -19.394796°", + "FINAL ANSWER: 22.918631, -19.394796" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 47.49989, + "lon": -52.99806, + "name": "Conception Bay South" + }, + "point_b": { + "lat": 55.48498, + "lon": 37.30736, + "name": "Troitsk" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 55.695457, + "lon": -36.252368 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (47.49989°, -52.99806°)", + " Point B: (55.48498°, 37.30736°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 55.695457°", + " Longitude: -36.252368°", + "FINAL ANSWER: 55.695457, -36.252368" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 26.9492, + "lon": 56.2691, + "name": "Qeshm" + }, + "point_b": { + "lat": 29.10239, + "lon": 75.96253, + "name": "Hānsi" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 28.832345, + "lon": 70.972195 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (26.9492°, 56.2691°)", + " Point B: (29.10239°, 75.96253°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 28.832345°", + " Longitude: 70.972195°", + "FINAL ANSWER: 28.832345, 70.972195" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 39.94706, + "lon": -75.29213, + "name": "Drexel Hill" + }, + "point_b": { + "lat": 10.97333, + "lon": 106.49325, + "name": "Củ Chi" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 75.404011, + "lon": 112.819326 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (39.94706°, -75.29213°)", + " Point B: (10.97333°, 106.49325°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 75.404011°", + " Longitude: 112.819326°", + "FINAL ANSWER: 75.404011, 112.819326" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 6.03131, + "lon": -75.43333, + "name": "La Ceja" + }, + "point_b": { + "lat": -0.25368, + "lon": -79.17628, + "name": "Santo Domingo de los Colorados" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 2.890354, + "lon": -77.309992 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (6.03131°, -75.43333°)", + " Point B: (-0.25368°, -79.17628°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 2.890354°", + " Longitude: -77.309992°", + "FINAL ANSWER: 2.890354, -77.309992" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 40.16557, + "lon": 44.29462, + "name": "Vagharshapat" + }, + "point_b": { + "lat": 51.75571, + "lon": 8.04075, + "name": "Beckum" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 50.013236, + "lon": 18.541418 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (40.16557°, 44.29462°)", + " Point B: (51.75571°, 8.04075°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 50.013236°", + " Longitude: 18.541418°", + "FINAL ANSWER: 50.013236, 18.541418" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -12.78636, + "lon": 45.21732, + "name": "Mtsapéré" + }, + "point_b": { + "lat": -21.53194, + "lon": -42.64306, + "name": "Leopoldina" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -24.025744, + "lon": -20.169561 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-12.78636°, 45.21732°)", + " Point B: (-21.53194°, -42.64306°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -24.025744°", + " Longitude: -20.169561°", + "FINAL ANSWER: -24.025744, -20.169561" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 39.47523, + "lon": -0.41825, + "name": "Mislata" + }, + "point_b": { + "lat": -10.95817, + "lon": -38.79084, + "name": "Tucano" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 15.047542, + "lon": -21.989107 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (39.47523°, -0.41825°)", + " Point B: (-10.95817°, -38.79084°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 15.047542°", + " Longitude: -21.989107°", + "FINAL ANSWER: 15.047542, -21.989107" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 46.92436, + "lon": 7.41457, + "name": "Köniz" + }, + "point_b": { + "lat": -25.29528, + "lon": -54.09389, + "name": "Medianeira" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -6.569213, + "lon": -40.578483 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (46.92436°, 7.41457°)", + " Point B: (-25.29528°, -54.09389°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -6.569213°", + " Longitude: -40.578483°", + "FINAL ANSWER: -6.569213, -40.578483" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -38.13333, + "lon": 145.13333, + "name": "Frankston East" + }, + "point_b": { + "lat": -25.93312, + "lon": 28.01213, + "name": "Diepsloot" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -50.015981, + "lon": 80.330763 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-38.13333°, 145.13333°)", + " Point B: (-25.93312°, 28.01213°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -50.015981°", + " Longitude: 80.330763°", + "FINAL ANSWER: -50.015981, 80.330763" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 16.79944, + "lon": -93.27219, + "name": "Berriozábal" + }, + "point_b": { + "lat": 22.37934, + "lon": 57.52718, + "name": "Adam" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 54.629397, + "lon": -21.681517 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (16.79944°, -93.27219°)", + " Point B: (22.37934°, 57.52718°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 54.629397°", + " Longitude: -21.681517°", + "FINAL ANSWER: 54.629397, -21.681517" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 53.07582, + "lon": 8.80717, + "name": "Bremen" + }, + "point_b": { + "lat": 37.23737, + "lon": 9.86313, + "name": "Menzel Abderhaman" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 45.157788, + "lon": 9.408998 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (53.07582°, 8.80717°)", + " Point B: (37.23737°, 9.86313°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 45.157788°", + " Longitude: 9.408998°", + "FINAL ANSWER: 45.157788, 9.408998" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 28.2489, + "lon": -81.28118, + "name": "Saint Cloud" + }, + "point_b": { + "lat": 41.84447, + "lon": -90.18874, + "name": "Clinton" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 31.70448, + "lon": -83.24577 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (28.2489°, -81.28118°)", + " Point B: (41.84447°, -90.18874°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 31.704480°", + " Longitude: -83.245770°", + "FINAL ANSWER: 31.704480, -83.245770" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 42.26833, + "lon": 118.96361, + "name": "Chifeng" + }, + "point_b": { + "lat": 40.58618, + "lon": 17.11635, + "name": "Massafra" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 50.259963, + "lon": 38.575273 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (42.26833°, 118.96361°)", + " Point B: (40.58618°, 17.11635°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 50.259963°", + " Longitude: 38.575273°", + "FINAL ANSWER: 50.259963, 38.575273" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 40.58106, + "lon": -111.85077, + "name": "Sandy Hills" + }, + "point_b": { + "lat": -8.88222, + "lon": -36.19111, + "name": "Canhotinho" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 5.614058, + "lon": -51.811394 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (40.58106°, -111.85077°)", + " Point B: (-8.88222°, -36.19111°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 5.614058°", + " Longitude: -51.811394°", + "FINAL ANSWER: 5.614058, -51.811394" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -3.33333, + "lon": 37.15, + "name": "Boma la Ngombe" + }, + "point_b": { + "lat": 40.0645, + "lon": -75.1875, + "name": "East Mount Airy" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 40.255917, + "lon": -39.237397 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-3.33333°, 37.15°)", + " Point B: (40.0645°, -75.1875°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 40.255917°", + " Longitude: -39.237397°", + "FINAL ANSWER: 40.255917, -39.237397" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 52.14583, + "lon": 4.40278, + "name": "Wassenaar" + }, + "point_b": { + "lat": 35.17388, + "lon": 138.90691, + "name": "Susono" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 53.226192, + "lon": 123.621905 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (52.14583°, 4.40278°)", + " Point B: (35.17388°, 138.90691°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 53.226192°", + " Longitude: 123.621905°", + "FINAL ANSWER: 53.226192, 123.621905" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 9.80168, + "lon": -74.39304, + "name": "Nueva Granada" + }, + "point_b": { + "lat": -29.46694, + "lon": -51.96139, + "name": "Lajeado" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -19.841755, + "lon": -58.28835 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (9.80168°, -74.39304°)", + " Point B: (-29.46694°, -51.96139°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -19.841755°", + " Longitude: -58.288350°", + "FINAL ANSWER: -19.841755, -58.288350" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -8.65, + "lon": 115.21667, + "name": "Denpasar" + }, + "point_b": { + "lat": -8.72028, + "lon": -39.11389, + "name": "Abaré" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -26.776837, + "lon": 80.788823 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-8.65°, 115.21667°)", + " Point B: (-8.72028°, -39.11389°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -26.776837°", + " Longitude: 80.788823°", + "FINAL ANSWER: -26.776837, 80.788823" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -36.38047, + "lon": 145.39867, + "name": "Shepparton" + }, + "point_b": { + "lat": 31.26562, + "lon": 56.80545, + "name": "Rāvar" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 14.814879, + "lon": 79.845571 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-36.38047°, 145.39867°)", + " Point B: (31.26562°, 56.80545°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 14.814879°", + " Longitude: 79.845571°", + "FINAL ANSWER: 14.814879, 79.845571" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 6.50727, + "lon": 45.83493, + "name": "Golwayn" + }, + "point_b": { + "lat": 34.5, + "lon": 135.85, + "name": "Sakurai" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 33.718289, + "lon": 109.727161 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (6.50727°, 45.83493°)", + " Point B: (34.5°, 135.85°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 33.718289°", + " Longitude: 109.727161°", + "FINAL ANSWER: 33.718289, 109.727161" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 51.43787, + "lon": 14.23549, + "name": "Hoyerswerda" + }, + "point_b": { + "lat": -35.13333, + "lon": 138.51667, + "name": "Morphett Vale" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 40.252484, + "lon": 61.943472 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (51.43787°, 14.23549°)", + " Point B: (-35.13333°, 138.51667°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 40.252484°", + " Longitude: 61.943472°", + "FINAL ANSWER: 40.252484, 61.943472" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 34.70882, + "lon": 11.2147, + "name": "Kellabine" + }, + "point_b": { + "lat": 47.43333, + "lon": 19.11667, + "name": "Pesterzsébet" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 44.306095, + "lon": 16.832588 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (34.70882°, 11.2147°)", + " Point B: (47.43333°, 19.11667°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 44.306095°", + " Longitude: 16.832588°", + "FINAL ANSWER: 44.306095, 16.832588" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 7.25256, + "lon": 5.19312, + "name": "Akure" + }, + "point_b": { + "lat": -20.34583, + "lon": -41.53583, + "name": "Iúna" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -7.125114, + "lon": -17.473729 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (7.25256°, 5.19312°)", + " Point B: (-20.34583°, -41.53583°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -7.125114°", + " Longitude: -17.473729°", + "FINAL ANSWER: -7.125114, -17.473729" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 6.65166, + "lon": -5.60501, + "name": "Konéfla" + }, + "point_b": { + "lat": -7.46856, + "lon": 17.03769, + "name": "Cambundi" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -0.416555, + "lon": 5.706212 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (6.65166°, -5.60501°)", + " Point B: (-7.46856°, 17.03769°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -0.416555°", + " Longitude: 5.706212°", + "FINAL ANSWER: -0.416555, 5.706212" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -25.40222, + "lon": 32.80722, + "name": "Manhiça" + }, + "point_b": { + "lat": -11.66278, + "lon": 39.55056, + "name": "Mueda" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -21.991619, + "lon": 34.603545 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-25.40222°, 32.80722°)", + " Point B: (-11.66278°, 39.55056°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -21.991619°", + " Longitude: 34.603545°", + "FINAL ANSWER: -21.991619, 34.603545" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 33.96772, + "lon": -118.24438, + "name": "Florence-Graham" + }, + "point_b": { + "lat": -26.64807, + "lon": 15.15383, + "name": "Lüderitz" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 25.937502, + "lon": -78.822567 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (33.96772°, -118.24438°)", + " Point B: (-26.64807°, 15.15383°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 25.937502°", + " Longitude: -78.822567°", + "FINAL ANSWER: 25.937502, -78.822567" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 41.55177, + "lon": 60.63143, + "name": "Urganch" + }, + "point_b": { + "lat": -9.92882, + "lon": -76.23989, + "name": "Huánuco" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 48.049501, + "lon": 14.771238 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (41.55177°, 60.63143°)", + " Point B: (-9.92882°, -76.23989°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 48.049501°", + " Longitude: 14.771238°", + "FINAL ANSWER: 48.049501, 14.771238" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -33.7511, + "lon": 151.28886, + "name": "Dee Why" + }, + "point_b": { + "lat": -11.3, + "lon": 35.03333, + "name": "Tingi" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -37.906168, + "lon": 85.619958 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-33.7511°, 151.28886°)", + " Point B: (-11.3°, 35.03333°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -37.906168°", + " Longitude: 85.619958°", + "FINAL ANSWER: -37.906168, 85.619958" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 14.81154, + "lon": -91.45536, + "name": "Cantel" + }, + "point_b": { + "lat": 33.6803, + "lon": -116.17389, + "name": "Coachella" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 19.871575, + "lon": -96.986115 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (14.81154°, -91.45536°)", + " Point B: (33.6803°, -116.17389°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 19.871575°", + " Longitude: -96.986115°", + "FINAL ANSWER: 19.871575, -96.986115" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 30.5309, + "lon": 75.87949, + "name": "Māler Kotla" + }, + "point_b": { + "lat": -0.4841, + "lon": 37.12662, + "name": "Karatina" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 23.550585, + "lon": 64.859334 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (30.5309°, 75.87949°)", + " Point B: (-0.4841°, 37.12662°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 23.550585°", + " Longitude: 64.859334°", + "FINAL ANSWER: 23.550585, 64.859334" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -3.8425, + "lon": -49.09694, + "name": "Goianésia do Pará" + }, + "point_b": { + "lat": 31.36059, + "lon": 119.82016, + "name": "Yixing" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 31.418858, + "lon": -35.263662 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-3.8425°, -49.09694°)", + " Point B: (31.36059°, 119.82016°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 31.418858°", + " Longitude: -35.263662°", + "FINAL ANSWER: 31.418858, -35.263662" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 24.91965, + "lon": 89.94812, + "name": "Jamālpur" + }, + "point_b": { + "lat": 43.64791, + "lon": -79.40849, + "name": "Trinity-Bellwoods" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 70.382827, + "lon": -65.057765 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (24.91965°, 89.94812°)", + " Point B: (43.64791°, -79.40849°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 70.382827°", + " Longitude: -65.057765°", + "FINAL ANSWER: 70.382827, -65.057765" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 38.14118, + "lon": -85.68774, + "name": "Okolona" + }, + "point_b": { + "lat": 31.27133, + "lon": 30.78617, + "name": "Sīdī Sālim" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 52.701189, + "lon": -23.609459 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (38.14118°, -85.68774°)", + " Point B: (31.27133°, 30.78617°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 52.701189°", + " Longitude: -23.609459°", + "FINAL ANSWER: 52.701189, -23.609459" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 19.75938, + "lon": -72.19815, + "name": "Cap-Haïtien" + }, + "point_b": { + "lat": 46.87095, + "lon": -1.0156, + "name": "Les Herbiers" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 30.060546, + "lon": -59.033669 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (19.75938°, -72.19815°)", + " Point B: (46.87095°, -1.0156°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 30.060546°", + " Longitude: -59.033669°", + "FINAL ANSWER: 30.060546, -59.033669" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 48.29045, + "lon": 25.93241, + "name": "Chernivtsi" + }, + "point_b": { + "lat": 10.3773, + "lon": 123.6386, + "name": "Toledo" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 39.825955, + "lon": 87.241919 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (48.29045°, 25.93241°)", + " Point B: (10.3773°, 123.6386°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 39.825955°", + " Longitude: 87.241919°", + "FINAL ANSWER: 39.825955, 87.241919" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 25.85587, + "lon": 88.35943, + "name": "Pīrgaaj" + }, + "point_b": { + "lat": 22.91533, + "lon": 79.06378, + "name": "Kareli" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 23.702927, + "lon": 81.347034 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (25.85587°, 88.35943°)", + " Point B: (22.91533°, 79.06378°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 23.702927°", + " Longitude: 81.347034°", + "FINAL ANSWER: 23.702927, 81.347034" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -39.09631, + "lon": -67.08374, + "name": "Villa Regina" + }, + "point_b": { + "lat": 12.92028, + "lon": 80.20806, + "name": "Jalladiampet" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -37.601146, + "lon": 27.696444 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-39.09631°, -67.08374°)", + " Point B: (12.92028°, 80.20806°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -37.601146°", + " Longitude: 27.696444°", + "FINAL ANSWER: -37.601146, 27.696444" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 49.56263, + "lon": 15.93924, + "name": "Žďár nad Sázavou" + }, + "point_b": { + "lat": 58.14671, + "lon": 7.9956, + "name": "Kristiansand" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 56.052486, + "lon": 10.305933 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (49.56263°, 15.93924°)", + " Point B: (58.14671°, 7.9956°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 56.052486°", + " Longitude: 10.305933°", + "FINAL ANSWER: 56.052486, 10.305933" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -15.55, + "lon": 47.66667, + "name": "Boriziny" + }, + "point_b": { + "lat": 33.43333, + "lon": 115.03333, + "name": "Huaidian" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -2.518436, + "lon": 63.297543 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-15.55°, 47.66667°)", + " Point B: (33.43333°, 115.03333°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -2.518436°", + " Longitude: 63.297543°", + "FINAL ANSWER: -2.518436, 63.297543" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 30.05, + "lon": 121.14944, + "name": "Yuyao" + }, + "point_b": { + "lat": 12.56596, + "lon": -70.03198, + "name": "Noord" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 45.242576, + "lon": -81.107813 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (30.05°, 121.14944°)", + " Point B: (12.56596°, -70.03198°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 45.242576°", + " Longitude: -81.107813°", + "FINAL ANSWER: 45.242576, -81.107813" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 48.77644, + "lon": 2.29026, + "name": "Sceaux" + }, + "point_b": { + "lat": 19.21667, + "lon": 73.08333, + "name": "Dombivali" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 30.043684, + "lon": 60.423067 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (48.77644°, 2.29026°)", + " Point B: (19.21667°, 73.08333°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 30.043684°", + " Longitude: 60.423067°", + "FINAL ANSWER: 30.043684, 60.423067" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 37.51803, + "lon": 15.00913, + "name": "Misterbianco" + }, + "point_b": { + "lat": 27.04422, + "lon": -82.23593, + "name": "North Port" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 43.658125, + "lon": -9.891912 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (37.51803°, 15.00913°)", + " Point B: (27.04422°, -82.23593°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 43.658125°", + " Longitude: -9.891912°", + "FINAL ANSWER: 43.658125, -9.891912" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 50.24413, + "lon": 127.49016, + "name": "Heihe" + }, + "point_b": { + "lat": 2.1381, + "lon": 45.1212, + "name": "Afgooye" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 32.693603, + "lon": 75.432332 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (50.24413°, 127.49016°)", + " Point B: (2.1381°, 45.1212°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 32.693603°", + " Longitude: 75.432332°", + "FINAL ANSWER: 32.693603, 75.432332" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -6.09528, + "lon": -39.4525, + "name": "Acopiara" + }, + "point_b": { + "lat": 32.44363, + "lon": -117.00371, + "name": "La Joya" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 16.67813, + "lon": -74.467097 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-6.09528°, -39.4525°)", + " Point B: (32.44363°, -117.00371°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 16.678130°", + " Longitude: -74.467097°", + "FINAL ANSWER: 16.678130, -74.467097" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 42.41537, + "lon": -71.15644, + "name": "Arlington" + }, + "point_b": { + "lat": 40.55555, + "lon": -3.62733, + "name": "San Sebastián de los Reyes" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 46.766305, + "lon": -36.842112 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (42.41537°, -71.15644°)", + " Point B: (40.55555°, -3.62733°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 46.766305°", + " Longitude: -36.842112°", + "FINAL ANSWER: 46.766305, -36.842112" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 6.49263, + "lon": 17.45518, + "name": "Bossangoa" + }, + "point_b": { + "lat": -37.56622, + "lon": 143.84957, + "name": "Ballarat" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -31.040066, + "lon": 68.099166 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (6.49263°, 17.45518°)", + " Point B: (-37.56622°, 143.84957°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -31.040066°", + " Longitude: 68.099166°", + "FINAL ANSWER: -31.040066, 68.099166" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 33.72255, + "lon": -116.37697, + "name": "Palm Desert" + }, + "point_b": { + "lat": -24.78864, + "lon": 31.07938, + "name": "Mafemani" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 31.202799, + "lon": -71.569147 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (33.72255°, -116.37697°)", + " Point B: (-24.78864°, 31.07938°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 31.202799°", + " Longitude: -71.569147°", + "FINAL ANSWER: 31.202799, -71.569147" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 32.85788, + "lon": 51.5529, + "name": "Shāhīn Shahr" + }, + "point_b": { + "lat": 29.19634, + "lon": 108.2705, + "name": "Xintian" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 34.352562, + "lon": 80.506284 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (32.85788°, 51.5529°)", + " Point B: (29.19634°, 108.2705°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 34.352562°", + " Longitude: 80.506284°", + "FINAL ANSWER: 34.352562, 80.506284" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 26.9423, + "lon": 68.11759, + "name": "Tharu Shah" + }, + "point_b": { + "lat": -15.83722, + "lon": -54.38917, + "name": "Poxoréu" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -2.527045, + "lon": -25.454281 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (26.9423°, 68.11759°)", + " Point B: (-15.83722°, -54.38917°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -2.527045°", + " Longitude: -25.454281°", + "FINAL ANSWER: -2.527045, -25.454281" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 13.63126, + "lon": 74.6902, + "name": "Kundapura" + }, + "point_b": { + "lat": 5.14079, + "lon": 10.52535, + "name": "Bangangté" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 8.403912, + "lon": 26.227329 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (13.63126°, 74.6902°)", + " Point B: (5.14079°, 10.52535°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 8.403912°", + " Longitude: 26.227329°", + "FINAL ANSWER: 8.403912, 26.227329" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 9.25025, + "lon": 0.78213, + "name": "Bassar" + }, + "point_b": { + "lat": -0.25368, + "lon": -79.17628, + "name": "Santo Domingo de los Colorados" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 5.861772, + "lon": -39.511254 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (9.25025°, 0.78213°)", + " Point B: (-0.25368°, -79.17628°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 5.861772°", + " Longitude: -39.511254°", + "FINAL ANSWER: 5.861772, -39.511254" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 53.84861, + "lon": -1.83857, + "name": "Bingley" + }, + "point_b": { + "lat": -33.92399, + "lon": 151.22749, + "name": "Kingsford" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 31.645026, + "lon": 109.898109 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (53.84861°, -1.83857°)", + " Point B: (-33.92399°, 151.22749°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 31.645026°", + " Longitude: 109.898109°", + "FINAL ANSWER: 31.645026, 109.898109" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -32.77477, + "lon": 26.63376, + "name": "Fort Beaufort" + }, + "point_b": { + "lat": 47.47997, + "lon": 19.25388, + "name": "Budapest XVII. kerület" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 27.438151, + "lon": 21.687512 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-32.77477°, 26.63376°)", + " Point B: (47.47997°, 19.25388°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 27.438151°", + " Longitude: 21.687512°", + "FINAL ANSWER: 27.438151, 21.687512" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -15.57079, + "lon": 28.2701, + "name": "Chilanga Township" + }, + "point_b": { + "lat": 55.80202, + "lon": 37.67159, + "name": "Sokol’niki" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 2.302504, + "lon": 29.978474 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-15.57079°, 28.2701°)", + " Point B: (55.80202°, 37.67159°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 2.302504°", + " Longitude: 29.978474°", + "FINAL ANSWER: 2.302504, 29.978474" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 36.68178, + "lon": 4.26378, + "name": "Mekla" + }, + "point_b": { + "lat": 11.52639, + "lon": 42.85194, + "name": "Arta" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 25.348876, + "lon": 25.55933 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (36.68178°, 4.26378°)", + " Point B: (11.52639°, 42.85194°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 25.348876°", + " Longitude: 25.559330°", + "FINAL ANSWER: 25.348876, 25.559330" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 25.7294, + "lon": 119.37469, + "name": "Fuqing" + }, + "point_b": { + "lat": 40.97056, + "lon": 35.66222, + "name": "Havza" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 43.57436, + "lon": 58.769658 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (25.7294°, 119.37469°)", + " Point B: (40.97056°, 35.66222°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 43.574360°", + " Longitude: 58.769658°", + "FINAL ANSWER: 43.574360, 58.769658" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 58.85244, + "lon": 5.73521, + "name": "Sandnes" + }, + "point_b": { + "lat": 20.37175, + "lon": 72.90493, + "name": "Vapi" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 44.294855, + "lon": 50.17814 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (58.85244°, 5.73521°)", + " Point B: (20.37175°, 72.90493°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 44.294855°", + " Longitude: 50.178140°", + "FINAL ANSWER: 44.294855, 50.178140" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 42.46615, + "lon": -2.45115, + "name": "Logroño" + }, + "point_b": { + "lat": 41.70149, + "lon": -71.15505, + "name": "Fall River" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 45.918839, + "lon": -54.986029 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (42.46615°, -2.45115°)", + " Point B: (41.70149°, -71.15505°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 45.918839°", + " Longitude: -54.986029°", + "FINAL ANSWER: 45.918839, -54.986029" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 26.79404, + "lon": -80.26749, + "name": "The Acreage" + }, + "point_b": { + "lat": 52.40692, + "lon": 16.92993, + "name": "Poznań" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 55.592955, + "lon": -14.004676 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (26.79404°, -80.26749°)", + " Point B: (52.40692°, 16.92993°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 55.592955°", + " Longitude: -14.004676°", + "FINAL ANSWER: 55.592955, -14.004676" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 36.11667, + "lon": 139.6, + "name": "Kazo" + }, + "point_b": { + "lat": 49.46129, + "lon": 28.51541, + "name": "Kalynivka" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 49.483933, + "lon": 121.504249 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (36.11667°, 139.6°)", + " Point B: (49.46129°, 28.51541°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 49.483933°", + " Longitude: 121.504249°", + "FINAL ANSWER: 49.483933, 121.504249" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 42.95044, + "lon": 129.85571, + "name": "Namyang" + }, + "point_b": { + "lat": 32.93457, + "lon": -97.25168, + "name": "Keller" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 62.580115, + "lon": -154.790699 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (42.95044°, 129.85571°)", + " Point B: (32.93457°, -97.25168°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 62.580115°", + " Longitude: -154.790699°", + "FINAL ANSWER: 62.580115, -154.790699" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 22.75278, + "lon": 88.34222, + "name": "Shrīrāmpur" + }, + "point_b": { + "lat": -7.15389, + "lon": 112.65611, + "name": "Gresik" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 7.975843, + "lon": 100.950681 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (22.75278°, 88.34222°)", + " Point B: (-7.15389°, 112.65611°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 7.975843°", + " Longitude: 100.950681°", + "FINAL ANSWER: 7.975843, 100.950681" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 4.29005, + "lon": -74.81612, + "name": "Flandes" + }, + "point_b": { + "lat": -25.67916, + "lon": -49.53718, + "name": "Contenda" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -18.43144, + "lon": -56.467144 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (4.29005°, -74.81612°)", + " Point B: (-25.67916°, -49.53718°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -18.431440°", + " Longitude: -56.467144°", + "FINAL ANSWER: -18.431440, -56.467144" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 32.6852, + "lon": -4.74512, + "name": "Midelt" + }, + "point_b": { + "lat": -10.95444, + "lon": -40.57583, + "name": "Mirangaba" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 0.22585, + "lon": -32.336142 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (32.6852°, -4.74512°)", + " Point B: (-10.95444°, -40.57583°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 0.225850°", + " Longitude: -32.336142°", + "FINAL ANSWER: 0.225850, -32.336142" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 58.61232, + "lon": 125.40002, + "name": "Aldan" + }, + "point_b": { + "lat": -26.66008, + "lon": 153.09953, + "name": "Maroochydore" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -5.151865, + "lon": 147.853871 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (58.61232°, 125.40002°)", + " Point B: (-26.66008°, 153.09953°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -5.151865°", + " Longitude: 147.853871°", + "FINAL ANSWER: -5.151865, 147.853871" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 43.86682, + "lon": -79.2663, + "name": "Markham" + }, + "point_b": { + "lat": 46.30444, + "lon": 16.33778, + "name": "Varaždin" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 53.835664, + "lon": -5.418931 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (43.86682°, -79.2663°)", + " Point B: (46.30444°, 16.33778°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 53.835664°", + " Longitude: -5.418931°", + "FINAL ANSWER: 53.835664, -5.418931" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 55.40276, + "lon": 11.35459, + "name": "Slagelse" + }, + "point_b": { + "lat": 26.86879, + "lon": 100.22072, + "name": "Lijiang" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 50.08149, + "lon": 68.072198 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (55.40276°, 11.35459°)", + " Point B: (26.86879°, 100.22072°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 50.081490°", + " Longitude: 68.072198°", + "FINAL ANSWER: 50.081490, 68.072198" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -7.65194, + "lon": -40.14889, + "name": "Ipubi" + }, + "point_b": { + "lat": 36.3208, + "lon": -121.24381, + "name": "Greenfield" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 5.703948, + "lon": -57.494928 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-7.65194°, -40.14889°)", + " Point B: (36.3208°, -121.24381°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 5.703948°", + " Longitude: -57.494928°", + "FINAL ANSWER: 5.703948, -57.494928" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -18.79417, + "lon": -52.62278, + "name": "Chapadão do Sul" + }, + "point_b": { + "lat": -28.65083, + "lon": -49.21, + "name": "Morro da Fumaça" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -21.264996, + "lon": -51.815697 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-18.79417°, -52.62278°)", + " Point B: (-28.65083°, -49.21°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -21.264996°", + " Longitude: -51.815697°", + "FINAL ANSWER: -21.264996, -51.815697" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 9.63497, + "lon": 106.49237, + "name": "Duyên Hải" + }, + "point_b": { + "lat": -36.9682, + "lon": 174.84019, + "name": "Papatoetoe" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -3.470908, + "lon": 121.337631 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (9.63497°, 106.49237°)", + " Point B: (-36.9682°, 174.84019°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -3.470908°", + " Longitude: 121.337631°", + "FINAL ANSWER: -3.470908, 121.337631" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 31.87808, + "lon": 34.73983, + "name": "Yavné" + }, + "point_b": { + "lat": 4.3, + "lon": 101.15, + "name": "Kampar" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 21.298108, + "lon": 70.948353 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (31.87808°, 34.73983°)", + " Point B: (4.3°, 101.15°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 21.298108°", + " Longitude: 70.948353°", + "FINAL ANSWER: 21.298108, 70.948353" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 45.69651, + "lon": 4.94385, + "name": "Saint-Priest" + }, + "point_b": { + "lat": -18.22047, + "lon": -49.72993, + "name": "Bom Jesus de Goiás" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -1.468167, + "lon": -38.227948 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (45.69651°, 4.94385°)", + " Point B: (-18.22047°, -49.72993°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -1.468167°", + " Longitude: -38.227948°", + "FINAL ANSWER: -1.468167, -38.227948" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 53.35934, + "lon": -1.48759, + "name": "Nether Edge" + }, + "point_b": { + "lat": 13.87139, + "lon": 100.73719, + "name": "Khlong Sam Wa" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 45.43833, + "lon": 66.104871 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (53.35934°, -1.48759°)", + " Point B: (13.87139°, 100.73719°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 45.438330°", + " Longitude: 66.104871°", + "FINAL ANSWER: 45.438330, 66.104871" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -27.58504, + "lon": -56.68707, + "name": "Ituzaingó" + }, + "point_b": { + "lat": 45.5, + "lon": 124.3, + "name": "Dalai" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 53.384153, + "lon": -60.410877 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-27.58504°, -56.68707°)", + " Point B: (45.5°, 124.3°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 53.384153°", + " Longitude: -60.410877°", + "FINAL ANSWER: 53.384153, -60.410877" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -3.96426, + "lon": 39.5498, + "name": "Mazeras" + }, + "point_b": { + "lat": 28.40392, + "lon": 77.85773, + "name": "Bulandshahr" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 20.959187, + "lon": 67.126564 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-3.96426°, 39.5498°)", + " Point B: (28.40392°, 77.85773°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 20.959187°", + " Longitude: 67.126564°", + "FINAL ANSWER: 20.959187, 67.126564" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -12.77698, + "lon": 45.28234, + "name": "Labattoir" + }, + "point_b": { + "lat": 22.53811, + "lon": 114.01504, + "name": "Zhuzilin" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 14.897733, + "lon": 95.621384 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-12.77698°, 45.28234°)", + " Point B: (22.53811°, 114.01504°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 14.897733°", + " Longitude: 95.621384°", + "FINAL ANSWER: 14.897733, 95.621384" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 22.58213, + "lon": 88.171, + "name": "Dhulagari" + }, + "point_b": { + "lat": -27.0675, + "lon": -53.16111, + "name": "Palmitos" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -20.768081, + "lon": -14.015257 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (22.58213°, 88.171°)", + " Point B: (-27.0675°, -53.16111°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -20.768081°", + " Longitude: -14.015257°", + "FINAL ANSWER: -20.768081, -14.015257" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 53.65385, + "lon": 10.11184, + "name": "Sasel" + }, + "point_b": { + "lat": 13.44528, + "lon": -16.70278, + "name": "Manjai Kunda" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 44.243397, + "lon": 0.364512 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (53.65385°, 10.11184°)", + " Point B: (13.44528°, -16.70278°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 44.243397°", + " Longitude: 0.364512°", + "FINAL ANSWER: 44.243397, 0.364512" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 50.89328, + "lon": 6.99481, + "name": "Rodenkirchen" + }, + "point_b": { + "lat": 35.06937, + "lon": -1.13706, + "name": "Sidi Abdelli" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 46.99555, + "lon": 4.529395 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (50.89328°, 6.99481°)", + " Point B: (35.06937°, -1.13706°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 46.995550°", + " Longitude: 4.529395°", + "FINAL ANSWER: 46.995550, 4.529395" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 50.93106, + "lon": 5.33781, + "name": "Hasselt" + }, + "point_b": { + "lat": 46.49067, + "lon": 11.33982, + "name": "Bolzano" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 47.629154, + "lon": 9.936617 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (50.93106°, 5.33781°)", + " Point B: (46.49067°, 11.33982°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 47.629154°", + " Longitude: 9.936617°", + "FINAL ANSWER: 47.629154, 9.936617" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 49.03333, + "lon": 104.08333, + "name": "Erdenet" + }, + "point_b": { + "lat": 69.20279, + "lon": 33.43697, + "name": "Polyarnyy" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 63.495635, + "lon": 80.66047 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (49.03333°, 104.08333°)", + " Point B: (69.20279°, 33.43697°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 63.495635°", + " Longitude: 80.660470°", + "FINAL ANSWER: 63.495635, 80.660470" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 52.04479, + "lon": 39.72569, + "name": "Usman’" + }, + "point_b": { + "lat": 53.11865, + "lon": 13.5022, + "name": "Templin" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 53.39867, + "lon": 20.124962 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (52.04479°, 39.72569°)", + " Point B: (53.11865°, 13.5022°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 53.398670°", + " Longitude: 20.124962°", + "FINAL ANSWER: 53.398670, 20.124962" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 9.69894, + "lon": -68.43273, + "name": "Tinaco" + }, + "point_b": { + "lat": 41.55806, + "lon": 69.77083, + "name": "G‘azalkent" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 33.017277, + "lon": -49.725164 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (9.69894°, -68.43273°)", + " Point B: (41.55806°, 69.77083°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 33.017277°", + " Longitude: -49.725164°", + "FINAL ANSWER: 33.017277, -49.725164" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 6.54368, + "lon": -7.4935, + "name": "Guiglo" + }, + "point_b": { + "lat": -13.96692, + "lon": 33.78725, + "name": "Lilongwe" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -3.96538, + "lon": 12.893572 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (6.54368°, -7.4935°)", + " Point B: (-13.96692°, 33.78725°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -3.965380°", + " Longitude: 12.893572°", + "FINAL ANSWER: -3.965380, 12.893572" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 8.39307, + "lon": 8.35544, + "name": "Doma" + }, + "point_b": { + "lat": 41.48593, + "lon": -73.05066, + "name": "Naugatuck" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 38.853551, + "lon": -47.661633 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (8.39307°, 8.35544°)", + " Point B: (41.48593°, -73.05066°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 38.853551°", + " Longitude: -47.661633°", + "FINAL ANSWER: 38.853551, -47.661633" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 19.61387, + "lon": -98.9364, + "name": "Tepexpan" + }, + "point_b": { + "lat": 29.13489, + "lon": 78.27187, + "name": "Chāndpur" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 52.331546, + "lon": -96.064861 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (19.61387°, -98.9364°)", + " Point B: (29.13489°, 78.27187°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 52.331546°", + " Longitude: -96.064861°", + "FINAL ANSWER: 52.331546, -96.064861" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 50.80904, + "lon": 8.77069, + "name": "Marburg an der Lahn" + }, + "point_b": { + "lat": 6.53891, + "lon": 3.3742, + "name": "Shomolu" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 17.621921, + "lon": 4.357749 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (50.80904°, 8.77069°)", + " Point B: (6.53891°, 3.3742°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 17.621921°", + " Longitude: 4.357749°", + "FINAL ANSWER: 17.621921, 4.357749" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 15.40341, + "lon": 74.01519, + "name": "Ponda" + }, + "point_b": { + "lat": -21.2075, + "lon": -159.77546, + "name": "Avarua" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 5.231768, + "lon": 105.1349 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (15.40341°, 74.01519°)", + " Point B: (-21.2075°, -159.77546°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 5.231768°", + " Longitude: 105.134900°", + "FINAL ANSWER: 5.231768, 105.134900" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 23.95946, + "lon": 88.04018, + "name": "Kāndi" + }, + "point_b": { + "lat": 38.13708, + "lon": 41.00817, + "name": "Silvan" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 36.378249, + "lon": 54.093005 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (23.95946°, 88.04018°)", + " Point B: (38.13708°, 41.00817°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 36.378249°", + " Longitude: 54.093005°", + "FINAL ANSWER: 36.378249, 54.093005" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 13.41609, + "lon": 76.62063, + "name": "Chiknāyakanhalli" + }, + "point_b": { + "lat": 22.79505, + "lon": -81.53617, + "name": "Unión de Reyes" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 59.670196, + "lon": 5.45531 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (13.41609°, 76.62063°)", + " Point B: (22.79505°, -81.53617°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 59.670196°", + " Longitude: 5.455310°", + "FINAL ANSWER: 59.670196, 5.455310" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 10.22776, + "lon": 78.22969, + "name": "Natham" + }, + "point_b": { + "lat": 37.96215, + "lon": -122.34553, + "name": "San Pablo" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 63.775997, + "lon": -154.184232 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (10.22776°, 78.22969°)", + " Point B: (37.96215°, -122.34553°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 63.775997°", + " Longitude: -154.184232°", + "FINAL ANSWER: 63.775997, -154.184232" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -33.9125, + "lon": 151.10279, + "name": "Campsie" + }, + "point_b": { + "lat": 32.0284, + "lon": 34.8796, + "name": "Yehud-Monosson" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -20.284453, + "lon": 118.547229 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-33.9125°, 151.10279°)", + " Point B: (32.0284°, 34.8796°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -20.284453°", + " Longitude: 118.547229°", + "FINAL ANSWER: -20.284453, 118.547229" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 15.5, + "lon": 120.843, + "name": "Aliaga" + }, + "point_b": { + "lat": 47.53333, + "lon": 25.56667, + "name": "Câmpulung Moldovenesc" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 41.782531, + "lon": 84.130303 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (15.5°, 120.843°)", + " Point B: (47.53333°, 25.56667°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 41.782531°", + " Longitude: 84.130303°", + "FINAL ANSWER: 41.782531, 84.130303" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 45.20978, + "lon": 5.77762, + "name": "Meylan" + }, + "point_b": { + "lat": 34.96667, + "lon": 139.08333, + "name": "Itō" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 52.898228, + "lon": 120.229992 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (45.20978°, 5.77762°)", + " Point B: (34.96667°, 139.08333°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 52.898228°", + " Longitude: 120.229992°", + "FINAL ANSWER: 52.898228, 120.229992" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 19.80755, + "lon": 109.34539, + "name": "Mutang" + }, + "point_b": { + "lat": 55.86216, + "lon": -4.02469, + "name": "Coatbridge" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 60.810874, + "lon": 36.527931 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (19.80755°, 109.34539°)", + " Point B: (55.86216°, -4.02469°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 60.810874°", + " Longitude: 36.527931°", + "FINAL ANSWER: 60.810874, 36.527931" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 49.48667, + "lon": 105.92278, + "name": "Darhan" + }, + "point_b": { + "lat": 38.75212, + "lon": -121.28801, + "name": "Roseville" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 63.935277, + "lon": 133.469362 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (49.48667°, 105.92278°)", + " Point B: (38.75212°, -121.28801°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 63.935277°", + " Longitude: 133.469362°", + "FINAL ANSWER: 63.935277, 133.469362" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -27.41444, + "lon": -49.6025, + "name": "Ituporanga" + }, + "point_b": { + "lat": 57.3438, + "lon": 28.35363, + "name": "Ostrov" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 18.64048, + "lon": -21.787927 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-27.41444°, -49.6025°)", + " Point B: (57.3438°, 28.35363°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 18.640480°", + " Longitude: -21.787927°", + "FINAL ANSWER: 18.640480, -21.787927" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 14.95806, + "lon": 120.91778, + "name": "Bustos" + }, + "point_b": { + "lat": 22.42114, + "lon": 87.32257, + "name": "Medinīpur" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 17.376833, + "lon": 112.810408 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (14.95806°, 120.91778°)", + " Point B: (22.42114°, 87.32257°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 17.376833°", + " Longitude: 112.810408°", + "FINAL ANSWER: 17.376833, 112.810408" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -4.20493, + "lon": 13.28608, + "name": "Kayes" + }, + "point_b": { + "lat": 34.93722, + "lon": 105.64667, + "name": "Yebao" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 30.851006, + "lon": 77.888692 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-4.20493°, 13.28608°)", + " Point B: (34.93722°, 105.64667°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 30.851006°", + " Longitude: 77.888692°", + "FINAL ANSWER: 30.851006, 77.888692" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -37.8739, + "lon": 145.02485, + "name": "Caulfield North" + }, + "point_b": { + "lat": 36.74328, + "lon": 3.7173, + "name": "Bordj Menaïel" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 20.951759, + "lon": 42.791621 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-37.8739°, 145.02485°)", + " Point B: (36.74328°, 3.7173°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 20.951759°", + " Longitude: 42.791621°", + "FINAL ANSWER: 20.951759, 42.791621" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 23.11012, + "lon": -82.42322, + "name": "Almendares" + }, + "point_b": { + "lat": 14.81361, + "lon": 74.12972, + "name": "Karwar" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 48.952083, + "lon": -54.529413 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (23.11012°, -82.42322°)", + " Point B: (14.81361°, 74.12972°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 48.952083°", + " Longitude: -54.529413°", + "FINAL ANSWER: 48.952083, -54.529413" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -18.60472, + "lon": -43.37944, + "name": "Serro" + }, + "point_b": { + "lat": 31.18517, + "lon": 108.39544, + "name": "Zhendong" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 35.784512, + "lon": 62.883115 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-18.60472°, -43.37944°)", + " Point B: (31.18517°, 108.39544°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 35.784512°", + " Longitude: 62.883115°", + "FINAL ANSWER: 35.784512, 62.883115" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -15.46694, + "lon": 36.97778, + "name": "Gurúè" + }, + "point_b": { + "lat": 43.91333, + "lon": 42.72083, + "name": "Kislovodsk" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 29.086456, + "lon": 40.835264 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-15.46694°, 36.97778°)", + " Point B: (43.91333°, 42.72083°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 29.086456°", + " Longitude: 40.835264°", + "FINAL ANSWER: 29.086456, 40.835264" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -24.96675, + "lon": 25.33273, + "name": "Kanye" + }, + "point_b": { + "lat": 56.18648, + "lon": 50.89404, + "name": "Kukmor" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -4.517328, + "lon": 30.312147 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-24.96675°, 25.33273°)", + " Point B: (56.18648°, 50.89404°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -4.517328°", + " Longitude: 30.312147°", + "FINAL ANSWER: -4.517328, 30.312147" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 38.67033, + "lon": -89.98455, + "name": "Collinsville" + }, + "point_b": { + "lat": 32.84318, + "lon": 71.36192, + "name": "Kamar Mushani" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 77.0145, + "lon": 3.267894 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (38.67033°, -89.98455°)", + " Point B: (32.84318°, 71.36192°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 77.014500°", + " Longitude: 3.267894°", + "FINAL ANSWER: 77.014500, 3.267894" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -39.93333, + "lon": 175.05, + "name": "Whanganui" + }, + "point_b": { + "lat": 32.32091, + "lon": 35.36989, + "name": "Ţūbās" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -10.833737, + "lon": 97.675024 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-39.93333°, 175.05°)", + " Point B: (32.32091°, 35.36989°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -10.833737°", + " Longitude: 97.675024°", + "FINAL ANSWER: -10.833737, 97.675024" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 46.81705, + "lon": 0.54518, + "name": "Châtellerault" + }, + "point_b": { + "lat": 40.46538, + "lon": -74.33043, + "name": "Sayreville Junction" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 50.196254, + "lon": -39.212492 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (46.81705°, 0.54518°)", + " Point B: (40.46538°, -74.33043°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 50.196254°", + " Longitude: -39.212492°", + "FINAL ANSWER: 50.196254, -39.212492" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 28.58459, + "lon": 65.41501, + "name": "Kharan" + }, + "point_b": { + "lat": -26.50476, + "lon": 28.35921, + "name": "Heidelberg" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 15.030884, + "lon": 55.448473 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (28.58459°, 65.41501°)", + " Point B: (-26.50476°, 28.35921°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 15.030884°", + " Longitude: 55.448473°", + "FINAL ANSWER: 15.030884, 55.448473" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 30.75545, + "lon": 20.22625, + "name": "Ajdabiya" + }, + "point_b": { + "lat": 12.50583, + "lon": 39.52278, + "name": "Korem" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 21.910618, + "lon": 30.494889 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (30.75545°, 20.22625°)", + " Point B: (12.50583°, 39.52278°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 21.910618°", + " Longitude: 30.494889°", + "FINAL ANSWER: 21.910618, 30.494889" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 35.3943, + "lon": 136.66898, + "name": "Mizuho" + }, + "point_b": { + "lat": -25.43998, + "lon": -54.40161, + "name": "Santa Terezinha de Itaipu" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 53.509057, + "lon": -168.995632 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (35.3943°, 136.66898°)", + " Point B: (-25.43998°, -54.40161°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 53.509057°", + " Longitude: -168.995632°", + "FINAL ANSWER: 53.509057, -168.995632" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -41.43876, + "lon": 147.13467, + "name": "Launceston" + }, + "point_b": { + "lat": -16.25667, + "lon": -56.62278, + "name": "Poconé" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -43.507756, + "lon": -70.111463 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-41.43876°, 147.13467°)", + " Point B: (-16.25667°, -56.62278°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -43.507756°", + " Longitude: -70.111463°", + "FINAL ANSWER: -43.507756, -70.111463" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 35.47619, + "lon": 136.7721, + "name": "Yamagata" + }, + "point_b": { + "lat": 48.92312, + "lon": 24.71248, + "name": "Ivano-Frankivsk" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 58.038189, + "lon": 89.757339 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (35.47619°, 136.7721°)", + " Point B: (48.92312°, 24.71248°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 58.038189°", + " Longitude: 89.757339°", + "FINAL ANSWER: 58.038189, 89.757339" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 9.74569, + "lon": -63.18323, + "name": "Maturín" + }, + "point_b": { + "lat": 12.31963, + "lon": -2.47094, + "name": "Réo" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 11.630292, + "lon": -48.158752 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (9.74569°, -63.18323°)", + " Point B: (12.31963°, -2.47094°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 11.630292°", + " Longitude: -48.158752°", + "FINAL ANSWER: 11.630292, -48.158752" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 50.64083, + "lon": 5.79353, + "name": "Herve" + }, + "point_b": { + "lat": -20.44278, + "lon": -54.64639, + "name": "Campo Grande" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -1.637407, + "lon": -42.624 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (50.64083°, 5.79353°)", + " Point B: (-20.44278°, -54.64639°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -1.637407°", + " Longitude: -42.624000°", + "FINAL ANSWER: -1.637407, -42.624000" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 29.56444, + "lon": -104.41639, + "name": "Manuel Ojinaga" + }, + "point_b": { + "lat": -23.38032, + "lon": 150.50595, + "name": "Rockhampton" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 19.32107, + "lon": -133.689607 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (29.56444°, -104.41639°)", + " Point B: (-23.38032°, 150.50595°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 19.321070°", + " Longitude: -133.689607°", + "FINAL ANSWER: 19.321070, -133.689607" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -29.79145, + "lon": -58.0499, + "name": "Curuzú Cuatiá" + }, + "point_b": { + "lat": 35.07465, + "lon": -1.22431, + "name": "Bensekrane" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 19.624866, + "lon": -17.371415 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-29.79145°, -58.0499°)", + " Point B: (35.07465°, -1.22431°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 19.624866°", + " Longitude: -17.371415°", + "FINAL ANSWER: 19.624866, -17.371415" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 36.47396, + "lon": 140.56355, + "name": "Tokai" + }, + "point_b": { + "lat": -10.06667, + "lon": 38.93333, + "name": "Ruangwa" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 5.47338, + "lon": 60.258946 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (36.47396°, 140.56355°)", + " Point B: (-10.06667°, 38.93333°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 5.473380°", + " Longitude: 60.258946°", + "FINAL ANSWER: 5.473380, 60.258946" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -30.24162, + "lon": -68.74662, + "name": "San José de Jáchal" + }, + "point_b": { + "lat": 20.59193, + "lon": 96.05202, + "name": "Pyawbwe" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -6.439352, + "lon": 64.928705 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-30.24162°, -68.74662°)", + " Point B: (20.59193°, 96.05202°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -6.439352°", + " Longitude: 64.928705°", + "FINAL ANSWER: -6.439352, 64.928705" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 24.32431, + "lon": 83.81613, + "name": "Majhiāon Kalān" + }, + "point_b": { + "lat": 13.48773, + "lon": 144.78138, + "name": "Tamuning-Tumon-Harmon Village" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 21.670504, + "lon": 115.394241 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (24.32431°, 83.81613°)", + " Point B: (13.48773°, 144.78138°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 21.670504°", + " Longitude: 115.394241°", + "FINAL ANSWER: 21.670504, 115.394241" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 35.69906, + "lon": -0.63588, + "name": "Oran" + }, + "point_b": { + "lat": 47.37328, + "lon": 8.58038, + "name": "Zürich (Kreis 7)" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 44.52789, + "lon": 5.94319 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (35.69906°, -0.63588°)", + " Point B: (47.37328°, 8.58038°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 44.527890°", + " Longitude: 5.943190°", + "FINAL ANSWER: 44.527890, 5.943190" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 52.73632, + "lon": 41.44102, + "name": "Tambov" + }, + "point_b": { + "lat": 28.92095, + "lon": 30.85367, + "name": "Sumusţā al Waqf" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 46.883223, + "lon": 37.965538 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (52.73632°, 41.44102°)", + " Point B: (28.92095°, 30.85367°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 46.883223°", + " Longitude: 37.965538°", + "FINAL ANSWER: 46.883223, 37.965538" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 33.9, + "lon": 118.13333, + "name": "Shaji" + }, + "point_b": { + "lat": 24.81878, + "lon": 103.33237, + "name": "Shilin" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 31.790509, + "lon": 114.176215 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (33.9°, 118.13333°)", + " Point B: (24.81878°, 103.33237°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 31.790509°", + " Longitude: 114.176215°", + "FINAL ANSWER: 31.790509, 114.176215" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 10.0938, + "lon": 76.4198, + "name": "Vāzhakulam" + }, + "point_b": { + "lat": 37.64563, + "lon": -84.77217, + "name": "Danville" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 40.141388, + "lon": 63.131851 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (10.0938°, 76.4198°)", + " Point B: (37.64563°, -84.77217°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 40.141388°", + " Longitude: 63.131851°", + "FINAL ANSWER: 40.141388, 63.131851" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 22.32891, + "lon": 114.15399, + "name": "Fu Cheong Estate" + }, + "point_b": { + "lat": 51.86083, + "lon": 5.76667, + "name": "Beuningen" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 38.337857, + "lon": 98.658099 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (22.32891°, 114.15399°)", + " Point B: (51.86083°, 5.76667°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 38.337857°", + " Longitude: 98.658099°", + "FINAL ANSWER: 38.337857, 98.658099" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 5.78333, + "lon": 36.56667, + "name": "Bako" + }, + "point_b": { + "lat": 31.03361, + "lon": 112.20472, + "name": "Jingmen" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 22.812272, + "lon": 71.073993 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (5.78333°, 36.56667°)", + " Point B: (31.03361°, 112.20472°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 22.812272°", + " Longitude: 71.073993°", + "FINAL ANSWER: 22.812272, 71.073993" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -10.73912, + "lon": 17.71766, + "name": "Luquembo" + }, + "point_b": { + "lat": 53.79391, + "lon": -1.75206, + "name": "Bradford" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 37.943586, + "lon": 5.697913 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-10.73912°, 17.71766°)", + " Point B: (53.79391°, -1.75206°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 37.943586°", + " Longitude: 5.697913°", + "FINAL ANSWER: 37.943586, 5.697913" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 28.86993, + "lon": 75.9165, + "name": "Toshām" + }, + "point_b": { + "lat": 39.46667, + "lon": -8.46667, + "name": "Entroncamento" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 43.259686, + "lon": 13.71988 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (28.86993°, 75.9165°)", + " Point B: (39.46667°, -8.46667°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 43.259686°", + " Longitude: 13.719880°", + "FINAL ANSWER: 43.259686, 13.719880" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -21.60333, + "lon": -48.36583, + "name": "Matão" + }, + "point_b": { + "lat": 17.65399, + "lon": 95.78813, + "name": "Tharyarwady" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -6.388012, + "lon": 25.888408 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-21.60333°, -48.36583°)", + " Point B: (17.65399°, 95.78813°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -6.388012°", + " Longitude: 25.888408°", + "FINAL ANSWER: -6.388012, 25.888408" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 50.78069, + "lon": 3.03854, + "name": "Wervik" + }, + "point_b": { + "lat": -31.33139, + "lon": -54.10694, + "name": "Bagé" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 11.006641, + "lon": -30.181681 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (50.78069°, 3.03854°)", + " Point B: (-31.33139°, -54.10694°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 11.006641°", + " Longitude: -30.181681°", + "FINAL ANSWER: 11.006641, -30.181681" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 33.94633, + "lon": -4.99509, + "name": "Oulad Tayeb" + }, + "point_b": { + "lat": -8.81833, + "lon": -35.18639, + "name": "Barreiros" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 12.994572, + "lon": -21.439107 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (33.94633°, -4.99509°)", + " Point B: (-8.81833°, -35.18639°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 12.994572°", + " Longitude: -21.439107°", + "FINAL ANSWER: 12.994572, -21.439107" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 17.32098, + "lon": 78.53046, + "name": "Mīrpeta" + }, + "point_b": { + "lat": 19.10059, + "lon": -98.8788, + "name": "Juchitepec" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 85.970336, + "lon": 2.558996 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (17.32098°, 78.53046°)", + " Point B: (19.10059°, -98.8788°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 85.970336°", + " Longitude: 2.558996°", + "FINAL ANSWER: 85.970336, 2.558996" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 2.53453, + "lon": 34.66659, + "name": "Moroto" + }, + "point_b": { + "lat": 25.43596, + "lon": 92.19132, + "name": "Jowai" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 9.454436, + "lon": 47.992954 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (2.53453°, 34.66659°)", + " Point B: (25.43596°, 92.19132°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 9.454436°", + " Longitude: 47.992954°", + "FINAL ANSWER: 9.454436, 47.992954" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 31.7965, + "lon": -106.57999, + "name": "Sunland Park" + }, + "point_b": { + "lat": 44.5647, + "lon": 27.3633, + "name": "Slobozia" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 50.512338, + "lon": -88.007774 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (31.7965°, -106.57999°)", + " Point B: (44.5647°, 27.3633°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 50.512338°", + " Longitude: -88.007774°", + "FINAL ANSWER: 50.512338, -88.007774" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 13.65805, + "lon": 102.56365, + "name": "Paoy Paet" + }, + "point_b": { + "lat": 10.34954, + "lon": -67.04266, + "name": "Los Teques" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 47.569986, + "lon": 80.751238 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (13.65805°, 102.56365°)", + " Point B: (10.34954°, -67.04266°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 47.569986°", + " Longitude: 80.751238°", + "FINAL ANSWER: 47.569986, 80.751238" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -33.78333, + "lon": 150.93333, + "name": "Seven Hills" + }, + "point_b": { + "lat": 14.77099, + "lon": -17.06107, + "name": "Pout" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -52.442814, + "lon": 31.247931 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-33.78333°, 150.93333°)", + " Point B: (14.77099°, -17.06107°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -52.442814°", + " Longitude: 31.247931°", + "FINAL ANSWER: -52.442814, 31.247931" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 57.67603, + "lon": 46.61171, + "name": "Shakhun’ya" + }, + "point_b": { + "lat": 28.50167, + "lon": -81.54091, + "name": "Lake Butler" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 62.404428, + "lon": -44.066632 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (57.67603°, 46.61171°)", + " Point B: (28.50167°, -81.54091°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 62.404428°", + " Longitude: -44.066632°", + "FINAL ANSWER: 62.404428, -44.066632" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 47.85775, + "lon": 11.48054, + "name": "Geretsried" + }, + "point_b": { + "lat": -38.17058, + "lon": 144.3114, + "name": "Highton" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -14.861638, + "lon": 112.901738 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (47.85775°, 11.48054°)", + " Point B: (-38.17058°, 144.3114°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -14.861638°", + " Longitude: 112.901738°", + "FINAL ANSWER: -14.861638, 112.901738" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -27.54333, + "lon": 153.20287, + "name": "Capalaba" + }, + "point_b": { + "lat": 36.74773, + "lon": -119.77237, + "name": "Fresno" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 23.205206, + "lon": -145.527769 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-27.54333°, 153.20287°)", + " Point B: (36.74773°, -119.77237°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 23.205206°", + " Longitude: -145.527769°", + "FINAL ANSWER: 23.205206, -145.527769" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 7.59383, + "lon": 6.21798, + "name": "Ogaminana" + }, + "point_b": { + "lat": -33.89101, + "lon": -60.57462, + "name": "Pergamino" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -15.60646, + "lon": -23.840273 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (7.59383°, 6.21798°)", + " Point B: (-33.89101°, -60.57462°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -15.606460°", + " Longitude: -23.840273°", + "FINAL ANSWER: -15.606460, -23.840273" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -33.76667, + "lon": 150.81667, + "name": "Mount Druitt" + }, + "point_b": { + "lat": 37.96727, + "lon": 23.99684, + "name": "Artémida" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 24.949489, + "lon": 61.588285 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-33.76667°, 150.81667°)", + " Point B: (37.96727°, 23.99684°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 24.949489°", + " Longitude: 61.588285°", + "FINAL ANSWER: 24.949489, 61.588285" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 38.5244, + "lon": -8.8882, + "name": "Setúbal" + }, + "point_b": { + "lat": 11.13764, + "lon": 77.31064, + "name": "Velampālaiyam" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 22.740868, + "lon": 60.19314 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (38.5244°, -8.8882°)", + " Point B: (11.13764°, 77.31064°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 22.740868°", + " Longitude: 60.193140°", + "FINAL ANSWER: 22.740868, 60.193140" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -12.41713, + "lon": -41.77049, + "name": "Seabra" + }, + "point_b": { + "lat": 47.16878, + "lon": -1.4729, + "name": "Vertou" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 3.020731, + "lon": -33.695333 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-12.41713°, -41.77049°)", + " Point B: (47.16878°, -1.4729°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 3.020731°", + " Longitude: -33.695333°", + "FINAL ANSWER: 3.020731, -33.695333" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 45.36452, + "lon": 40.19679, + "name": "Tbilisskaya" + }, + "point_b": { + "lat": 48.52496, + "lon": 25.03712, + "name": "Kolomyia" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 47.926276, + "lon": 28.989722 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (45.36452°, 40.19679°)", + " Point B: (48.52496°, 25.03712°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 47.926276°", + " Longitude: 28.989722°", + "FINAL ANSWER: 47.926276, 28.989722" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 11.00089, + "lon": 76.00618, + "name": "Kōttakkal" + }, + "point_b": { + "lat": 31.72888, + "lon": 34.74632, + "name": "Qiryat Mal’akhi" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 17.061497, + "lon": 66.760724 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (11.00089°, 76.00618°)", + " Point B: (31.72888°, 34.74632°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 17.061497°", + " Longitude: 66.760724°", + "FINAL ANSWER: 17.061497, 66.760724" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -23.00583, + "lon": -46.83889, + "name": "Itatiba" + }, + "point_b": { + "lat": 41.66616, + "lon": -81.33955, + "name": "Mentor" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 26.019118, + "lon": -70.462746 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-23.00583°, -46.83889°)", + " Point B: (41.66616°, -81.33955°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 26.019118°", + " Longitude: -70.462746°", + "FINAL ANSWER: 26.019118, -70.462746" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 31.6008, + "lon": -7.98653, + "name": "Méchouar-Kasba" + }, + "point_b": { + "lat": -19.30861, + "lon": -47.52528, + "name": "Santa Juliana" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -6.476352, + "lon": -37.925776 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (31.6008°, -7.98653°)", + " Point B: (-19.30861°, -47.52528°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -6.476352°", + " Longitude: -37.925776°", + "FINAL ANSWER: -6.476352, -37.925776" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -9.23333, + "lon": 33.61667, + "name": "Katumba" + }, + "point_b": { + "lat": -33.04459, + "lon": -61.16423, + "name": "Casilda" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -29.635249, + "lon": -8.709338 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-9.23333°, 33.61667°)", + " Point B: (-33.04459°, -61.16423°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -29.635249°", + " Longitude: -8.709338°", + "FINAL ANSWER: -29.635249, -8.709338" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 48.62893, + "lon": 35.2589, + "name": "Samar" + }, + "point_b": { + "lat": 29.93245, + "lon": -95.38021, + "name": "Aldine" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 48.394321, + "lon": -78.59391 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (48.62893°, 35.2589°)", + " Point B: (29.93245°, -95.38021°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 48.394321°", + " Longitude: -78.593910°", + "FINAL ANSWER: 48.394321, -78.593910" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -0.55085, + "lon": 166.9252, + "name": "Yaren" + }, + "point_b": { + "lat": -7.09484, + "lon": 109.025, + "name": "Margasari" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -2.538625, + "lon": 152.531753 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-0.55085°, 166.9252°)", + " Point B: (-7.09484°, 109.025°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -2.538625°", + " Longitude: 152.531753°", + "FINAL ANSWER: -2.538625, 152.531753" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 1.3803, + "lon": 103.75197, + "name": "Teck Whye" + }, + "point_b": { + "lat": 55.55487, + "lon": 37.92566, + "name": "Andreyevskoye" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 45.987909, + "lon": 63.927324 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (1.3803°, 103.75197°)", + " Point B: (55.55487°, 37.92566°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 45.987909°", + " Longitude: 63.927324°", + "FINAL ANSWER: 45.987909, 63.927324" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 28.26356, + "lon": 109.02685, + "name": "Meijiang" + }, + "point_b": { + "lat": -23.8275, + "lon": -46.72694, + "name": "Parelheiros" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 10.409817, + "lon": 26.114017 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (28.26356°, 109.02685°)", + " Point B: (-23.8275°, -46.72694°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 10.409817°", + " Longitude: 26.114017°", + "FINAL ANSWER: 10.409817, 26.114017" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 6.30054, + "lon": -10.7969, + "name": "Monrovia" + }, + "point_b": { + "lat": 30.39467, + "lon": -9.20897, + "name": "Oulad Teïma" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 24.372547, + "lon": -9.65437 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (6.30054°, -10.7969°)", + " Point B: (30.39467°, -9.20897°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 24.372547°", + " Longitude: -9.654370°", + "FINAL ANSWER: 24.372547, -9.654370" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 40.61106, + "lon": -111.89994, + "name": "Midvale" + }, + "point_b": { + "lat": 34.80243, + "lon": -86.97219, + "name": "Athens" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 38.368855, + "lon": -98.939376 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (40.61106°, -111.89994°)", + " Point B: (34.80243°, -86.97219°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 38.368855°", + " Longitude: -98.939376°", + "FINAL ANSWER: 38.368855, -98.939376" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 22.78498, + "lon": 88.32586, + "name": "Baidyabāti" + }, + "point_b": { + "lat": 28.83826, + "lon": -105.91214, + "name": "Aldama" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 75.342821, + "lon": 159.634769 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (22.78498°, 88.32586°)", + " Point B: (28.83826°, -105.91214°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 75.342821°", + " Longitude: 159.634769°", + "FINAL ANSWER: 75.342821, 159.634769" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 61.66393, + "lon": 50.8163, + "name": "Syktyvkar" + }, + "point_b": { + "lat": 60.30504, + "lon": 5.28236, + "name": "Ytrebygda" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 62.774907, + "lon": 39.42045 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (61.66393°, 50.8163°)", + " Point B: (60.30504°, 5.28236°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 62.774907°", + " Longitude: 39.420450°", + "FINAL ANSWER: 62.774907, 39.420450" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 50.81678, + "lon": 4.32775, + "name": "Forest" + }, + "point_b": { + "lat": -12.40829, + "lon": -39.50094, + "name": "Rafael Jambeiro" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 20.508818, + "lon": -22.516029 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (50.81678°, 4.32775°)", + " Point B: (-12.40829°, -39.50094°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 20.508818°", + " Longitude: -22.516029°", + "FINAL ANSWER: 20.508818, -22.516029" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 18.75031, + "lon": -69.63525, + "name": "Bayaguana" + }, + "point_b": { + "lat": 29.87405, + "lon": 106.49816, + "name": "Tianfu" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 83.006412, + "lon": -34.0702 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (18.75031°, -69.63525°)", + " Point B: (29.87405°, 106.49816°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 83.006412°", + " Longitude: -34.070200°", + "FINAL ANSWER: 83.006412, -34.070200" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 13.87583, + "lon": -88.62727, + "name": "Sensuntepeque" + }, + "point_b": { + "lat": 41.71894, + "lon": -83.71299, + "name": "Sylvania" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 34.776684, + "lon": -85.219784 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (13.87583°, -88.62727°)", + " Point B: (41.71894°, -83.71299°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 34.776684°", + " Longitude: -85.219784°", + "FINAL ANSWER: 34.776684, -85.219784" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 47.78198, + "lon": 9.61062, + "name": "Ravensburg" + }, + "point_b": { + "lat": 48.33751, + "lon": 39.95416, + "name": "Donetsk" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 48.95516, + "lon": 32.382055 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (47.78198°, 9.61062°)", + " Point B: (48.33751°, 39.95416°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 48.955160°", + " Longitude: 32.382055°", + "FINAL ANSWER: 48.955160, 32.382055" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 30.04743, + "lon": -99.14032, + "name": "Kerrville" + }, + "point_b": { + "lat": 35.91402, + "lon": -81.53898, + "name": "Lenoir" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 31.739818, + "lon": -94.961877 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (30.04743°, -99.14032°)", + " Point B: (35.91402°, -81.53898°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 31.739818°", + " Longitude: -94.961877°", + "FINAL ANSWER: 31.739818, -94.961877" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 31.49936, + "lon": 73.26763, + "name": "Khurarianwala" + }, + "point_b": { + "lat": -21.26111, + "lon": -48.49639, + "name": "Monte Alto" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 24.445753, + "lon": 37.923165 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (31.49936°, 73.26763°)", + " Point B: (-21.26111°, -48.49639°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 24.445753°", + " Longitude: 37.923165°", + "FINAL ANSWER: 24.445753, 37.923165" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 51.65877, + "lon": 6.45297, + "name": "Xanten" + }, + "point_b": { + "lat": -6.22977, + "lon": 155.56598, + "name": "Arawa" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 66.331031, + "lon": 65.007928 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (51.65877°, 6.45297°)", + " Point B: (-6.22977°, 155.56598°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 66.331031°", + " Longitude: 65.007928°", + "FINAL ANSWER: 66.331031, 65.007928" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 36.60466, + "lon": 3.98437, + "name": "Maâtkas" + }, + "point_b": { + "lat": -10.21167, + "lon": -63.82861, + "name": "Buritis" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 2.862384, + "lon": -48.997819 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (36.60466°, 3.98437°)", + " Point B: (-10.21167°, -63.82861°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 2.862384°", + " Longitude: -48.997819°", + "FINAL ANSWER: 2.862384, -48.997819" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 30.55083, + "lon": 73.39083, + "name": "Bahawalnagar" + }, + "point_b": { + "lat": 27.50641, + "lon": -99.50754, + "name": "Laredo" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 57.516442, + "lon": -92.749921 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (30.55083°, 73.39083°)", + " Point B: (27.50641°, -99.50754°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 57.516442°", + " Longitude: -92.749921°", + "FINAL ANSWER: 57.516442, -92.749921" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 26.43903, + "lon": 99.44061, + "name": "Jinding" + }, + "point_b": { + "lat": 6.62944, + "lon": 124.605, + "name": "Isulan" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 11.835391, + "lon": 118.757561 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (26.43903°, 99.44061°)", + " Point B: (6.62944°, 124.605°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 11.835391°", + " Longitude: 118.757561°", + "FINAL ANSWER: 11.835391, 118.757561" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 18.26321, + "lon": 75.46316, + "name": "Paranda" + }, + "point_b": { + "lat": 8.4902, + "lon": 77.0374, + "name": "Malayinkeezhu" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 15.820935, + "lon": 75.869576 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (18.26321°, 75.46316°)", + " Point B: (8.4902°, 77.0374°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 15.820935°", + " Longitude: 75.869576°", + "FINAL ANSWER: 15.820935, 75.869576" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 0.28422, + "lon": 34.75229, + "name": "Kakamega" + }, + "point_b": { + "lat": 10.38697, + "lon": 123.2227, + "name": "Canlaon" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 9.616954, + "lon": 100.779446 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (0.28422°, 34.75229°)", + " Point B: (10.38697°, 123.2227°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 9.616954°", + " Longitude: 100.779446°", + "FINAL ANSWER: 9.616954, 100.779446" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 14.79032, + "lon": -15.90803, + "name": "Mbaké" + }, + "point_b": { + "lat": 32.0643, + "lon": 45.24743, + "name": "‘Afak" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 26.698393, + "lon": 12.442604 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (14.79032°, -15.90803°)", + " Point B: (32.0643°, 45.24743°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 26.698393°", + " Longitude: 12.442604°", + "FINAL ANSWER: 26.698393, 12.442604" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 45.37139, + "lon": 141.82111, + "name": "Makubetsu" + }, + "point_b": { + "lat": 24.26667, + "lon": 98.28333, + "name": "Zhefang" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 36.793466, + "lon": 117.090386 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (45.37139°, 141.82111°)", + " Point B: (24.26667°, 98.28333°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 36.793466°", + " Longitude: 117.090386°", + "FINAL ANSWER: 36.793466, 117.090386" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 9.54633, + "lon": 78.5907, + "name": "Paramagudi" + }, + "point_b": { + "lat": -5.16667, + "lon": 38.78333, + "name": "Muheza" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 6.028541, + "lon": 68.521363 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (9.54633°, 78.5907°)", + " Point B: (-5.16667°, 38.78333°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 6.028541°", + " Longitude: 68.521363°", + "FINAL ANSWER: 6.028541, 68.521363" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 10.21313, + "lon": -68.32669, + "name": "Montalbán" + }, + "point_b": { + "lat": -20.25806, + "lon": -42.03361, + "name": "Manhuaçu" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -5.156839, + "lon": -55.500465 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (10.21313°, -68.32669°)", + " Point B: (-20.25806°, -42.03361°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -5.156839°", + " Longitude: -55.500465°", + "FINAL ANSWER: -5.156839, -55.500465" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -8.6199, + "lon": 122.2111, + "name": "Maumere" + }, + "point_b": { + "lat": -6.02583, + "lon": -44.24917, + "name": "Colinas" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -47.461085, + "lon": 37.576904 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-8.6199°, 122.2111°)", + " Point B: (-6.02583°, -44.24917°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -47.461085°", + " Longitude: 37.576904°", + "FINAL ANSWER: -47.461085, 37.576904" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 40.83242, + "lon": -115.76312, + "name": "Elko" + }, + "point_b": { + "lat": -33.92598, + "lon": 151.19347, + "name": "Mascot" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -15.519077, + "lon": 175.157764 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (40.83242°, -115.76312°)", + " Point B: (-33.92598°, 151.19347°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -15.519077°", + " Longitude: 175.157764°", + "FINAL ANSWER: -15.519077, 175.157764" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -37.78247, + "lon": 145.31682, + "name": "Mooroolbark" + }, + "point_b": { + "lat": 26.50823, + "lon": 87.01194, + "name": "Bīrpur" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 10.313715, + "lon": 101.321792 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-37.78247°, 145.31682°)", + " Point B: (26.50823°, 87.01194°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 10.313715°", + " Longitude: 101.321792°", + "FINAL ANSWER: 10.313715, 101.321792" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -6.22149, + "lon": 23.39254, + "name": "Miabi" + }, + "point_b": { + "lat": 7.95, + "lon": 39.13333, + "name": "Āsela" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -2.680796, + "lon": 27.331702 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-6.22149°, 23.39254°)", + " Point B: (7.95°, 39.13333°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -2.680796°", + " Longitude: 27.331702°", + "FINAL ANSWER: -2.680796, 27.331702" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 21.73748, + "lon": -78.79336, + "name": "Venezuela" + }, + "point_b": { + "lat": 21.56128, + "lon": 74.21238, + "name": "Taloda" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 46.822093, + "lon": -53.548713 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (21.73748°, -78.79336°)", + " Point B: (21.56128°, 74.21238°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 46.822093°", + " Longitude: -53.548713°", + "FINAL ANSWER: 46.822093, -53.548713" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 31.33786, + "lon": 104.22057, + "name": "Mianzhu, Deyang, Sichuan" + }, + "point_b": { + "lat": -5.79333, + "lon": -35.32944, + "name": "São Gonçalo do Amarante" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 32.706382, + "lon": 22.769474 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (31.33786°, 104.22057°)", + " Point B: (-5.79333°, -35.32944°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 32.706382°", + " Longitude: 22.769474°", + "FINAL ANSWER: 32.706382, 22.769474" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 52.5, + "lon": -1.88333, + "name": "Aston" + }, + "point_b": { + "lat": 33.6, + "lon": 130.41667, + "name": "Fukuoka" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 65.820988, + "lon": 31.073038 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (52.5°, -1.88333°)", + " Point B: (33.6°, 130.41667°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 65.820988°", + " Longitude: 31.073038°", + "FINAL ANSWER: 65.820988, 31.073038" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 29.65628, + "lon": 121.4064, + "name": "Fenghua" + }, + "point_b": { + "lat": 30.47028, + "lon": -8.87695, + "name": "Taroudant" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 46.434798, + "lon": 96.055958 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (29.65628°, 121.4064°)", + " Point B: (30.47028°, -8.87695°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 46.434798°", + " Longitude: 96.055958°", + "FINAL ANSWER: 46.434798, 96.055958" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 13.64172, + "lon": 100.83272, + "name": "Ban Khlong Bang Sao Thong" + }, + "point_b": { + "lat": -4.52483, + "lon": 35.3849, + "name": "Katesh" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 0.462558, + "lon": 51.501044 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (13.64172°, 100.83272°)", + " Point B: (-4.52483°, 35.3849°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 0.462558°", + " Longitude: 51.501044°", + "FINAL ANSWER: 0.462558, 51.501044" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 50.93409, + "lon": 4.37213, + "name": "Grimbergen" + }, + "point_b": { + "lat": 39.69333, + "lon": 125.21028, + "name": "Chŏngju" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 63.631484, + "lon": 74.732805 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (50.93409°, 4.37213°)", + " Point B: (39.69333°, 125.21028°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 63.631484°", + " Longitude: 74.732805°", + "FINAL ANSWER: 63.631484, 74.732805" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 28.2403, + "lon": 68.7755, + "name": "Thul" + }, + "point_b": { + "lat": 39.3995, + "lon": -84.56134, + "name": "Hamilton" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 62.196198, + "lon": -60.718064 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (28.2403°, 68.7755°)", + " Point B: (39.3995°, -84.56134°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 62.196198°", + " Longitude: -60.718064°", + "FINAL ANSWER: 62.196198, -60.718064" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 12.87405, + "lon": 6.48754, + "name": "Moriki" + }, + "point_b": { + "lat": 39.03361, + "lon": 66.57222, + "name": "Chiroqchi" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 21.599311, + "lon": 18.893062 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (12.87405°, 6.48754°)", + " Point B: (39.03361°, 66.57222°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 21.599311°", + " Longitude: 18.893062°", + "FINAL ANSWER: 21.599311, 18.893062" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 56.85853, + "lon": 40.54028, + "name": "Teykovo" + }, + "point_b": { + "lat": -37.78333, + "lon": 175.28333, + "name": "Hamilton" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -8.594468, + "lon": 151.555046 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (56.85853°, 40.54028°)", + " Point B: (-37.78333°, 175.28333°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -8.594468°", + " Longitude: 151.555046°", + "FINAL ANSWER: -8.594468, 151.555046" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 33.66761, + "lon": -84.01769, + "name": "Conyers" + }, + "point_b": { + "lat": 42.97839, + "lon": -78.79976, + "name": "Amherst" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 36.015877, + "lon": -82.833512 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (33.66761°, -84.01769°)", + " Point B: (42.97839°, -78.79976°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 36.015877°", + " Longitude: -82.833512°", + "FINAL ANSWER: 36.015877, -82.833512" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -11.45528, + "lon": -41.43611, + "name": "América Dourada" + }, + "point_b": { + "lat": 42.28343, + "lon": -71.06894, + "name": "Ashmont" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 2.239819, + "lon": -47.725906 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-11.45528°, -41.43611°)", + " Point B: (42.28343°, -71.06894°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 2.239819°", + " Longitude: -47.725906°", + "FINAL ANSWER: 2.239819, -47.725906" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 25.59761, + "lon": -80.38061, + "name": "South Miami Heights" + }, + "point_b": { + "lat": 22.19534, + "lon": 92.21946, + "name": "Bāndarban" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 57.832489, + "lon": -71.002074 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (25.59761°, -80.38061°)", + " Point B: (22.19534°, 92.21946°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 57.832489°", + " Longitude: -71.002074°", + "FINAL ANSWER: 57.832489, -71.002074" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 19.375, + "lon": -99.29444, + "name": "Jesús del Monte" + }, + "point_b": { + "lat": -22.42556, + "lon": -45.45278, + "name": "Itajubá" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -12.405434, + "lon": -59.603076 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (19.375°, -99.29444°)", + " Point B: (-22.42556°, -45.45278°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -12.405434°", + " Longitude: -59.603076°", + "FINAL ANSWER: -12.405434, -59.603076" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 26.72028, + "lon": 108.12972, + "name": "Kaitang" + }, + "point_b": { + "lat": 3.10278, + "lon": 18.51111, + "name": "Mindouli" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 12.623441, + "lon": 38.633306 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (26.72028°, 108.12972°)", + " Point B: (3.10278°, 18.51111°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 12.623441°", + " Longitude: 38.633306°", + "FINAL ANSWER: 12.623441, 38.633306" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 54.42903, + "lon": 50.80598, + "name": "Nurlat" + }, + "point_b": { + "lat": -8.02167, + "lon": -34.98111, + "name": "Camaragibe" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 29.630595, + "lon": -5.661082 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (54.42903°, 50.80598°)", + " Point B: (-8.02167°, -34.98111°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 29.630595°", + " Longitude: -5.661082°", + "FINAL ANSWER: 29.630595, -5.661082" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 41.05343, + "lon": -73.53873, + "name": "Stamford" + }, + "point_b": { + "lat": 11.16669, + "lon": 77.33502, + "name": "Chettipālaiyam" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 37.910248, + "lon": 61.387663 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (41.05343°, -73.53873°)", + " Point B: (11.16669°, 77.33502°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 37.910248°", + " Longitude: 61.387663°", + "FINAL ANSWER: 37.910248, 61.387663" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 20.45798, + "lon": -100.62081, + "name": "Apaseo el Alto" + }, + "point_b": { + "lat": -11.20605, + "lon": 13.84371, + "name": "Sumbe" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 8.497387, + "lon": -41.346927 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (20.45798°, -100.62081°)", + " Point B: (-11.20605°, 13.84371°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 8.497387°", + " Longitude: -41.346927°", + "FINAL ANSWER: 8.497387, -41.346927" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 11.01213, + "lon": 75.99471, + "name": "Parappur" + }, + "point_b": { + "lat": -22.66167, + "lon": -50.41222, + "name": "Assis" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -12.727281, + "lon": 16.289036 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (11.01213°, 75.99471°)", + " Point B: (-22.66167°, -50.41222°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -12.727281°", + " Longitude: 16.289036°", + "FINAL ANSWER: -12.727281, 16.289036" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 37.49583, + "lon": 121.25806, + "name": "Qingyang" + }, + "point_b": { + "lat": 40.37704, + "lon": 125.87867, + "name": "Songwŏn" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 39.674078, + "lon": 124.687938 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (37.49583°, 121.25806°)", + " Point B: (40.37704°, 125.87867°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 39.674078°", + " Longitude: 124.687938°", + "FINAL ANSWER: 39.674078, 124.687938" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 30.39213, + "lon": 47.70175, + "name": "Az Zubayr" + }, + "point_b": { + "lat": 22.31935, + "lon": 114.17136, + "name": "Mong Kok" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 31.68183, + "lon": 64.953249 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (30.39213°, 47.70175°)", + " Point B: (22.31935°, 114.17136°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 31.681830°", + " Longitude: 64.953249°", + "FINAL ANSWER: 31.681830, 64.953249" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 19.1409, + "lon": -72.01194, + "name": "Hinche" + }, + "point_b": { + "lat": -23.49696, + "lon": -46.52045, + "name": "Cangaiba" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 8.504156, + "lon": -65.558488 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (19.1409°, -72.01194°)", + " Point B: (-23.49696°, -46.52045°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 8.504156°", + " Longitude: -65.558488°", + "FINAL ANSWER: 8.504156, -65.558488" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -17.37389, + "lon": -40.22056, + "name": "Medeiros Neto" + }, + "point_b": { + "lat": 17.69737, + "lon": 77.21525, + "name": "Chitaguppa" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 10.307898, + "lon": 47.032055 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-17.37389°, -40.22056°)", + " Point B: (17.69737°, 77.21525°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 10.307898°", + " Longitude: 47.032055°", + "FINAL ANSWER: 10.307898, 47.032055" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -23.54382, + "lon": -46.74871, + "name": "Jaguare" + }, + "point_b": { + "lat": 36.01562, + "lon": -86.58194, + "name": "La Vergne" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 6.627488, + "lon": -65.367503 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-23.54382°, -46.74871°)", + " Point B: (36.01562°, -86.58194°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 6.627488°", + " Longitude: -65.367503°", + "FINAL ANSWER: 6.627488, -65.367503" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 45.2333, + "lon": -93.29134, + "name": "Andover" + }, + "point_b": { + "lat": 38.55185, + "lon": -121.36467, + "name": "Rosemont" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 40.84399, + "lon": -114.931608 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (45.2333°, -93.29134°)", + " Point B: (38.55185°, -121.36467°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 40.843990°", + " Longitude: -114.931608°", + "FINAL ANSWER: 40.843990, -114.931608" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -4.57667, + "lon": 30.1025, + "name": "Kasulu" + }, + "point_b": { + "lat": -19.69194, + "lon": -43.92333, + "name": "Vespasiano" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -15.066971, + "lon": -5.678388 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-4.57667°, 30.1025°)", + " Point B: (-19.69194°, -43.92333°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -15.066971°", + " Longitude: -5.678388°", + "FINAL ANSWER: -15.066971, -5.678388" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 31.94856, + "lon": 108.66073, + "name": "Gecheng" + }, + "point_b": { + "lat": 7.40353, + "lon": -2.46635, + "name": "Nsoatre" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 36.144545, + "lon": 77.679033 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (31.94856°, 108.66073°)", + " Point B: (7.40353°, -2.46635°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 36.144545°", + " Longitude: 77.679033°", + "FINAL ANSWER: 36.144545, 77.679033" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 43.1836, + "lon": -89.21373, + "name": "Sun Prairie" + }, + "point_b": { + "lat": -33.89743, + "lon": 150.93446, + "name": "Cabramatta" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -13.793309, + "lon": -179.790035 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (43.1836°, -89.21373°)", + " Point B: (-33.89743°, 150.93446°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -13.793309°", + " Longitude: -179.790035°", + "FINAL ANSWER: -13.793309, -179.790035" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -23.15306, + "lon": -47.05778, + "name": "Itupeva" + }, + "point_b": { + "lat": 51.55657, + "lon": 7.31155, + "name": "Castrop-Rauxel" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 34.738443, + "lon": -12.739238 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-23.15306°, -47.05778°)", + " Point B: (51.55657°, 7.31155°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 34.738443°", + " Longitude: -12.739238°", + "FINAL ANSWER: 34.738443, -12.739238" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -22.41972, + "lon": -44.29028, + "name": "Porto Real" + }, + "point_b": { + "lat": 30.93055, + "lon": 31.69864, + "name": "Awlād Şaqr" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 19.217991, + "lon": 10.329126 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-22.41972°, -44.29028°)", + " Point B: (30.93055°, 31.69864°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 19.217991°", + " Longitude: 10.329126°", + "FINAL ANSWER: 19.217991, 10.329126" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 45.13325, + "lon": 10.02129, + "name": "Cremona" + }, + "point_b": { + "lat": 30.28011, + "lon": 31.20531, + "name": "Qahā" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 41.803687, + "lon": 16.173597 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (45.13325°, 10.02129°)", + " Point B: (30.28011°, 31.20531°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 41.803687°", + " Longitude: 16.173597°", + "FINAL ANSWER: 41.803687, 16.173597" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 34.2706, + "lon": 134.13074, + "name": "Hiragi" + }, + "point_b": { + "lat": 10.45015, + "lon": 77.53035, + "name": "Sivagirippatti" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 25.018205, + "lon": 103.155743 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (34.2706°, 134.13074°)", + " Point B: (10.45015°, 77.53035°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 25.018205°", + " Longitude: 103.155743°", + "FINAL ANSWER: 25.018205, 103.155743" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -33.79798, + "lon": 151.28826, + "name": "Manly" + }, + "point_b": { + "lat": 50.42064, + "lon": 80.25025, + "name": "Semey" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 31.84388, + "lon": 105.267985 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-33.79798°, 151.28826°)", + " Point B: (50.42064°, 80.25025°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 31.843880°", + " Longitude: 105.267985°", + "FINAL ANSWER: 31.843880, 105.267985" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 47.90248, + "lon": 1.90407, + "name": "Orléans" + }, + "point_b": { + "lat": -33.9677, + "lon": 151.10149, + "name": "Hurstville" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 23.241706, + "lon": 97.547527 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (47.90248°, 1.90407°)", + " Point B: (-33.9677°, 151.10149°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 23.241706°", + " Longitude: 97.547527°", + "FINAL ANSWER: 23.241706, 97.547527" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 51.05011, + "lon": -114.08529, + "name": "Calgary" + }, + "point_b": { + "lat": 53.03333, + "lon": -1.2, + "name": "Hucknall" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 61.59465, + "lon": -93.489627 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (51.05011°, -114.08529°)", + " Point B: (53.03333°, -1.2°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 61.594650°", + " Longitude: -93.489627°", + "FINAL ANSWER: 61.594650, -93.489627" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 35.74582, + "lon": 139.82737, + "name": "Horikiri" + }, + "point_b": { + "lat": 22.11321, + "lon": 107.23592, + "name": "Baihecun" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 29.930242, + "lon": 122.425202 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (35.74582°, 139.82737°)", + " Point B: (22.11321°, 107.23592°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 29.930242°", + " Longitude: 122.425202°", + "FINAL ANSWER: 29.930242, 122.425202" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 43.77925, + "lon": 11.24626, + "name": "Florence" + }, + "point_b": { + "lat": 3.19916, + "lon": 101.64983, + "name": "Taman Petaling" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 18.094342, + "lon": 85.094847 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (43.77925°, 11.24626°)", + " Point B: (3.19916°, 101.64983°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 18.094342°", + " Longitude: 85.094847°", + "FINAL ANSWER: 18.094342, 85.094847" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 51.31306, + "lon": 3.13227, + "name": "Blankenberge" + }, + "point_b": { + "lat": 55.86661, + "lon": 48.35931, + "name": "Volzhsk" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 56.386883, + "lon": 36.390435 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (51.31306°, 3.13227°)", + " Point B: (55.86661°, 48.35931°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 56.386883°", + " Longitude: 36.390435°", + "FINAL ANSWER: 56.386883, 36.390435" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 33.99783, + "lon": 72.93493, + "name": "Haripur" + }, + "point_b": { + "lat": 11.65104, + "lon": 78.50872, + "name": "Peddanāyakkanpālaiyam" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 17.25381, + "lon": 77.270093 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (33.99783°, 72.93493°)", + " Point B: (11.65104°, 78.50872°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 17.253810°", + " Longitude: 77.270093°", + "FINAL ANSWER: 17.253810, 77.270093" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 33.88474, + "lon": -118.41091, + "name": "Manhattan Beach" + }, + "point_b": { + "lat": 47.52909, + "lon": -52.88136, + "name": "Paradise" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 45.592192, + "lon": -89.436035 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (33.88474°, -118.41091°)", + " Point B: (47.52909°, -52.88136°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 45.592192°", + " Longitude: -89.436035°", + "FINAL ANSWER: 45.592192, -89.436035" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -1.8, + "lon": -53.48, + "name": "Prainha" + }, + "point_b": { + "lat": 2.5703, + "lon": 101.833, + "name": "Lukut" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 0.000717, + "lon": -14.685343 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-1.8°, -53.48°)", + " Point B: (2.5703°, 101.833°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 0.000717°", + " Longitude: -14.685343°", + "FINAL ANSWER: 0.000717, -14.685343" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 24.0299, + "lon": 73.04632, + "name": "Khedbrahma" + }, + "point_b": { + "lat": -19.30323, + "lon": 146.72531, + "name": "Kirwan" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -8.593216, + "lon": 128.129257 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (24.0299°, 73.04632°)", + " Point B: (-19.30323°, 146.72531°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -8.593216°", + " Longitude: 128.129257°", + "FINAL ANSWER: -8.593216, 128.129257" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 36.63888, + "lon": 2.76845, + "name": "Kolea" + }, + "point_b": { + "lat": 6.25, + "lon": 37.56667, + "name": "Ch’ench’a" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 29.850381, + "lon": 13.116101 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (36.63888°, 2.76845°)", + " Point B: (6.25°, 37.56667°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 29.850381°", + " Longitude: 13.116101°", + "FINAL ANSWER: 29.850381, 13.116101" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 14.23333, + "lon": 37.0, + "name": "Abala" + }, + "point_b": { + "lat": -1.05361, + "lon": -46.76556, + "name": "Bragança" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 12.349465, + "lon": 15.444538 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (14.23333°, 37.0°)", + " Point B: (-1.05361°, -46.76556°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 12.349465°", + " Longitude: 15.444538°", + "FINAL ANSWER: 12.349465, 15.444538" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 23.49668, + "lon": 86.68363, + "name": "Adra" + }, + "point_b": { + "lat": 42.72825, + "lon": -111.53245, + "name": "Conda" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 50.208568, + "lon": 97.099249 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (23.49668°, 86.68363°)", + " Point B: (42.72825°, -111.53245°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 50.208568°", + " Longitude: 97.099249°", + "FINAL ANSWER: 50.208568, 97.099249" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -21.97895, + "lon": 27.84296, + "name": "Selebi-Phikwe" + }, + "point_b": { + "lat": 30.33355, + "lon": 107.34545, + "name": "Guixi" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -8.747545, + "lon": 47.564715 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-21.97895°, 27.84296°)", + " Point B: (30.33355°, 107.34545°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -8.747545°", + " Longitude: 47.564715°", + "FINAL ANSWER: -8.747545, 47.564715" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -43.89834, + "lon": 171.73011, + "name": "Ashburton" + }, + "point_b": { + "lat": 40.96899, + "lon": -73.71263, + "name": "Harrison" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -26.274037, + "lon": -153.317995 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-43.89834°, 171.73011°)", + " Point B: (40.96899°, -73.71263°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -26.274037°", + " Longitude: -153.317995°", + "FINAL ANSWER: -26.274037, -153.317995" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -34.06251, + "lon": 151.14961, + "name": "Cronulla" + }, + "point_b": { + "lat": 38.79911, + "lon": 42.73159, + "name": "Adilcevaz" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -16.581733, + "lon": 122.68362 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-34.06251°, 151.14961°)", + " Point B: (38.79911°, 42.73159°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -16.581733°", + " Longitude: 122.683620°", + "FINAL ANSWER: -16.581733, 122.683620" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 54.09224, + "lon": 61.56756, + "name": "Troitsk" + }, + "point_b": { + "lat": 34.27834, + "lon": -119.29317, + "name": "Ventura" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 80.083823, + "lon": -121.396407 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (54.09224°, 61.56756°)", + " Point B: (34.27834°, -119.29317°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 80.083823°", + " Longitude: -121.396407°", + "FINAL ANSWER: 80.083823, -121.396407" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -4.33111, + "lon": 20.58638, + "name": "Ilebo" + }, + "point_b": { + "lat": 13.75, + "lon": -15.8, + "name": "Nioro du Rip" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 9.473201, + "lon": -6.462208 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-4.33111°, 20.58638°)", + " Point B: (13.75°, -15.8°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 9.473201°", + " Longitude: -6.462208°", + "FINAL ANSWER: 9.473201, -6.462208" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 12.37136, + "lon": -1.41468, + "name": "Saaba" + }, + "point_b": { + "lat": 8.4855, + "lon": 76.94924, + "name": "Thiruvananthapuram" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 13.356604, + "lon": 38.058846 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (12.37136°, -1.41468°)", + " Point B: (8.4855°, 76.94924°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 13.356604°", + " Longitude: 38.058846°", + "FINAL ANSWER: 13.356604, 38.058846" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 51.49007, + "lon": 40.42236, + "name": "Anna" + }, + "point_b": { + "lat": 51.525, + "lon": 5.975, + "name": "Venray" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 52.781136, + "lon": 23.205488 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (51.49007°, 40.42236°)", + " Point B: (51.525°, 5.975°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 52.781136°", + " Longitude: 23.205488°", + "FINAL ANSWER: 52.781136, 23.205488" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 60.39299, + "lon": 5.32415, + "name": "Bergen" + }, + "point_b": { + "lat": 22.58882, + "lon": -83.24671, + "name": "Los Palacios" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 49.836428, + "lon": -55.417731 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (60.39299°, 5.32415°)", + " Point B: (22.58882°, -83.24671°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 49.836428°", + " Longitude: -55.417731°", + "FINAL ANSWER: 49.836428, -55.417731" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 48.85442, + "lon": 2.48268, + "name": "Fontenay-sous-Bois" + }, + "point_b": { + "lat": -4.87778, + "lon": -80.70528, + "name": "Marcavelica" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 11.980984, + "lon": -66.021134 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (48.85442°, 2.48268°)", + " Point B: (-4.87778°, -80.70528°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 11.980984°", + " Longitude: -66.021134°", + "FINAL ANSWER: 11.980984, -66.021134" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -28.6775, + "lon": -49.36972, + "name": "Criciúma" + }, + "point_b": { + "lat": -6.08125, + "lon": 36.64657, + "name": "Kibaigwa" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -15.485632, + "lon": 17.619202 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-28.6775°, -49.36972°)", + " Point B: (-6.08125°, 36.64657°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -15.485632°", + " Longitude: 17.619202°", + "FINAL ANSWER: -15.485632, 17.619202" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 20.93385, + "lon": 85.54489, + "name": "Kāmākhyānagar" + }, + "point_b": { + "lat": 34.20011, + "lon": -90.57093, + "name": "Clarksdale" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 82.417174, + "lon": 58.301798 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (20.93385°, 85.54489°)", + " Point B: (34.20011°, -90.57093°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 82.417174°", + " Longitude: 58.301798°", + "FINAL ANSWER: 82.417174, 58.301798" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -33.9049, + "lon": 151.01996, + "name": "Yagoona" + }, + "point_b": { + "lat": 42.4801, + "lon": -71.0995, + "name": "Stoneham" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -12.794426, + "lon": -176.121673 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-33.9049°, 151.01996°)", + " Point B: (42.4801°, -71.0995°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -12.794426°", + " Longitude: -176.121673°", + "FINAL ANSWER: -12.794426, -176.121673" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 11.1683, + "lon": 123.7223, + "name": "Bantayan" + }, + "point_b": { + "lat": 25.92058, + "lon": 81.99629, + "name": "Bela" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 23.20863, + "lon": 93.152606 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (11.1683°, 123.7223°)", + " Point B: (25.92058°, 81.99629°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 23.208630°", + " Longitude: 93.152606°", + "FINAL ANSWER: 23.208630, 93.152606" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 7.7102, + "lon": 81.6924, + "name": "Batticaloa" + }, + "point_b": { + "lat": 18.55, + "lon": 31.85, + "name": "Kuraymah" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 11.314679, + "lon": 69.668083 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (7.7102°, 81.6924°)", + " Point B: (18.55°, 31.85°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 11.314679°", + " Longitude: 69.668083°", + "FINAL ANSWER: 11.314679, 69.668083" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 55.78187, + "lon": 38.65025, + "name": "Pavlovskiy Posad" + }, + "point_b": { + "lat": 22.37115, + "lon": 77.2274, + "name": "Timurni" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 40.602402, + "lon": 62.813544 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (55.78187°, 38.65025°)", + " Point B: (22.37115°, 77.2274°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 40.602402°", + " Longitude: 62.813544°", + "FINAL ANSWER: 40.602402, 62.813544" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 15.30174, + "lon": -61.38808, + "name": "Roseau" + }, + "point_b": { + "lat": 52.08829, + "lon": 16.64866, + "name": "Kościan" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 48.817971, + "lon": -10.79611 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (15.30174°, -61.38808°)", + " Point B: (52.08829°, 16.64866°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 48.817971°", + " Longitude: -10.796110°", + "FINAL ANSWER: 48.817971, -10.796110" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 32.28034, + "lon": 119.16999, + "name": "Zhenzhou" + }, + "point_b": { + "lat": 31.16844, + "lon": 31.7655, + "name": "Kafr al Kurdī" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 37.861824, + "lon": 52.104 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (32.28034°, 119.16999°)", + " Point B: (31.16844°, 31.7655°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 37.861824°", + " Longitude: 52.104000°", + "FINAL ANSWER: 37.861824, 52.104000" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 38.62533, + "lon": -0.57225, + "name": "Ibi" + }, + "point_b": { + "lat": 50.34802, + "lon": 18.93282, + "name": "Bytom" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 47.748935, + "lon": 13.279065 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (38.62533°, -0.57225°)", + " Point B: (50.34802°, 18.93282°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 47.748935°", + " Longitude: 13.279065°", + "FINAL ANSWER: 47.748935, 13.279065" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 51.46369, + "lon": -0.03652, + "name": "Brockley" + }, + "point_b": { + "lat": -23.52927, + "lon": -46.73437, + "name": "Vila Leopoldina" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 34.048548, + "lon": -17.148742 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (51.46369°, -0.03652°)", + " Point B: (-23.52927°, -46.73437°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 34.048548°", + " Longitude: -17.148742°", + "FINAL ANSWER: 34.048548, -17.148742" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 32.94712, + "lon": 104.68139, + "name": "Wenxian Chengguanzhen" + }, + "point_b": { + "lat": 18.88139, + "lon": -99.17778, + "name": "Jiutepec" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 58.140418, + "lon": 131.116553 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (32.94712°, 104.68139°)", + " Point B: (18.88139°, -99.17778°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 58.140418°", + " Longitude: 131.116553°", + "FINAL ANSWER: 58.140418, 131.116553" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -20.23389, + "lon": -41.51056, + "name": "Ibatiba" + }, + "point_b": { + "lat": -23.065, + "lon": -54.19056, + "name": "Naviraí" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -21.030856, + "lon": -44.633167 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-20.23389°, -41.51056°)", + " Point B: (-23.065°, -54.19056°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -21.030856°", + " Longitude: -44.633167°", + "FINAL ANSWER: -21.030856, -44.633167" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 27.56246, + "lon": 76.625, + "name": "Alwar" + }, + "point_b": { + "lat": -34.40639, + "lon": -70.85834, + "name": "Rengo" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -29.285472, + "lon": -26.345054 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (27.56246°, 76.625°)", + " Point B: (-34.40639°, -70.85834°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -29.285472°", + " Longitude: -26.345054°", + "FINAL ANSWER: -29.285472, -26.345054" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -11.95972, + "lon": -40.16806, + "name": "Baixa Grande" + }, + "point_b": { + "lat": 29.12368, + "lon": 76.40516, + "name": "Shādīpur Julāna" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 26.006808, + "lon": 42.948957 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-11.95972°, -40.16806°)", + " Point B: (29.12368°, 76.40516°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 26.006808°", + " Longitude: 42.948957°", + "FINAL ANSWER: 26.006808, 42.948957" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -12.69056, + "lon": -43.18417, + "name": "Paratinga" + }, + "point_b": { + "lat": 40.56217, + "lon": -111.92966, + "name": "South Jordan" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 16.675686, + "lon": -72.693195 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-12.69056°, -43.18417°)", + " Point B: (40.56217°, -111.92966°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 16.675686°", + " Longitude: -72.693195°", + "FINAL ANSWER: 16.675686, -72.693195" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 59.62157, + "lon": 17.85476, + "name": "Märsta" + }, + "point_b": { + "lat": 45.43399, + "lon": 8.7364, + "name": "Trecate" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 56.145477, + "lon": 14.962465 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (59.62157°, 17.85476°)", + " Point B: (45.43399°, 8.7364°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 56.145477°", + " Longitude: 14.962465°", + "FINAL ANSWER: 56.145477, 14.962465" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 31.09956, + "lon": 108.21964, + "name": "Linjiang" + }, + "point_b": { + "lat": 35.20453, + "lon": -89.87398, + "name": "Bartlett" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 61.137049, + "lon": -105.957564 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (31.09956°, 108.21964°)", + " Point B: (35.20453°, -89.87398°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 61.137049°", + " Longitude: -105.957564°", + "FINAL ANSWER: 61.137049, -105.957564" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 44.38333, + "lon": 26.16667, + "name": "Popeşti-Leordeni" + }, + "point_b": { + "lat": 38.92583, + "lon": 76.17139, + "name": "Yengisar" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 44.460208, + "lon": 52.301753 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (44.38333°, 26.16667°)", + " Point B: (38.92583°, 76.17139°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 44.460208°", + " Longitude: 52.301753°", + "FINAL ANSWER: 44.460208, 52.301753" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 41.15367, + "lon": -81.35789, + "name": "Kent" + }, + "point_b": { + "lat": 14.95186, + "lon": -16.8152, + "name": "Tivaouane" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 24.173772, + "lon": -29.778277 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (41.15367°, -81.35789°)", + " Point B: (14.95186°, -16.8152°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 24.173772°", + " Longitude: -29.778277°", + "FINAL ANSWER: 24.173772, -29.778277" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 36.26791, + "lon": 36.56747, + "name": "Reyhanlı" + }, + "point_b": { + "lat": 36.9838, + "lon": -5.93933, + "name": "Las Cabezas de San Juan" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 38.576328, + "lon": 15.417564 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (36.26791°, 36.56747°)", + " Point B: (36.9838°, -5.93933°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 38.576328°", + " Longitude: 15.417564°", + "FINAL ANSWER: 38.576328, 15.417564" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 38.19394, + "lon": 15.55256, + "name": "Messina" + }, + "point_b": { + "lat": 29.83, + "lon": 80.55, + "name": "Dārchulā" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 38.649727, + "lon": 49.851639 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (38.19394°, 15.55256°)", + " Point B: (29.83°, 80.55°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 38.649727°", + " Longitude: 49.851639°", + "FINAL ANSWER: 38.649727, 49.851639" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -10.16062, + "lon": 32.63353, + "name": "Isoka" + }, + "point_b": { + "lat": 27.91161, + "lon": -15.40558, + "name": "Carrizal" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 9.698856, + "lon": 9.989425 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-10.16062°, 32.63353°)", + " Point B: (27.91161°, -15.40558°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 9.698856°", + " Longitude: 9.989425°", + "FINAL ANSWER: 9.698856, 9.989425" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 29.56884, + "lon": -97.96473, + "name": "Seguin" + }, + "point_b": { + "lat": 40.96417, + "lon": 129.32778, + "name": "Kilju" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 56.61886, + "lon": 158.059206 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (29.56884°, -97.96473°)", + " Point B: (40.96417°, 129.32778°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 56.618860°", + " Longitude: 158.059206°", + "FINAL ANSWER: 56.618860, 158.059206" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -3.36667, + "lon": 36.68333, + "name": "Arusha" + }, + "point_b": { + "lat": 32.91262, + "lon": -96.63888, + "name": "Garland" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 16.686308, + "lon": 11.644817 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-3.36667°, 36.68333°)", + " Point B: (32.91262°, -96.63888°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 16.686308°", + " Longitude: 11.644817°", + "FINAL ANSWER: 16.686308, 11.644817" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -0.1181, + "lon": -67.08527, + "name": "São Gabriel da Cachoeira" + }, + "point_b": { + "lat": -14.54329, + "lon": 48.74981, + "name": "Bealanana" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -16.102892, + "lon": 18.980503 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-0.1181°, -67.08527°)", + " Point B: (-14.54329°, 48.74981°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -16.102892°", + " Longitude: 18.980503°", + "FINAL ANSWER: -16.102892, 18.980503" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -8.18812, + "lon": 15.37495, + "name": "Camabatela" + }, + "point_b": { + "lat": 35.83479, + "lon": 140.16361, + "name": "Inzai" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 37.540688, + "lon": 101.680149 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-8.18812°, 15.37495°)", + " Point B: (35.83479°, 140.16361°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 37.540688°", + " Longitude: 101.680149°", + "FINAL ANSWER: 37.540688, 101.680149" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 34.10668, + "lon": -117.80673, + "name": "San Dimas" + }, + "point_b": { + "lat": -7.81667, + "lon": 112.01667, + "name": "Kediri" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 11.61425, + "lon": 137.346378 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (34.10668°, -117.80673°)", + " Point B: (-7.81667°, 112.01667°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 11.614250°", + " Longitude: 137.346378°", + "FINAL ANSWER: 11.614250, 137.346378" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -15.19611, + "lon": 12.15222, + "name": "Mossamedes" + }, + "point_b": { + "lat": 18.41025, + "lon": 83.90295, + "name": "Amudālavalasa" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 1.983009, + "lon": 47.676516 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-15.19611°, 12.15222°)", + " Point B: (18.41025°, 83.90295°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 1.983009°", + " Longitude: 47.676516°", + "FINAL ANSWER: 1.983009, 47.676516" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 47.44843, + "lon": -122.15734, + "name": "Fairwood" + }, + "point_b": { + "lat": 13.68835, + "lon": 75.24548, + "name": "Tīrthahalli" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 68.474332, + "lon": 107.038543 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (47.44843°, -122.15734°)", + " Point B: (13.68835°, 75.24548°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 68.474332°", + " Longitude: 107.038543°", + "FINAL ANSWER: 68.474332, 107.038543" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 30.45113, + "lon": 115.25593, + "name": "Qingquan" + }, + "point_b": { + "lat": 4.17521, + "lon": 73.50916, + "name": "Male" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 18.442724, + "lon": 92.793318 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (30.45113°, 115.25593°)", + " Point B: (4.17521°, 73.50916°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 18.442724°", + " Longitude: 92.793318°", + "FINAL ANSWER: 18.442724, 92.793318" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 33.22901, + "lon": -87.57723, + "name": "Northport" + }, + "point_b": { + "lat": 9.80168, + "lon": -74.39304, + "name": "Nueva Granada" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 21.644459, + "lon": -80.443942 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (33.22901°, -87.57723°)", + " Point B: (9.80168°, -74.39304°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 21.644459°", + " Longitude: -80.443942°", + "FINAL ANSWER: 21.644459, -80.443942" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 29.53086, + "lon": 108.21126, + "name": "Longshe" + }, + "point_b": { + "lat": 30.17746, + "lon": -81.38758, + "name": "Palm Valley" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 81.700189, + "lon": -168.797152 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (29.53086°, 108.21126°)", + " Point B: (30.17746°, -81.38758°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 81.700189°", + " Longitude: -168.797152°", + "FINAL ANSWER: 81.700189, -168.797152" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -5.16667, + "lon": 38.78333, + "name": "Muheza" + }, + "point_b": { + "lat": 4.603, + "lon": 9.0404, + "name": "Ekondo Titi" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -0.291602, + "lon": 23.905469 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-5.16667°, 38.78333°)", + " Point B: (4.603°, 9.0404°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -0.291602°", + " Longitude: 23.905469°", + "FINAL ANSWER: -0.291602, 23.905469" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -22.61222, + "lon": -46.0575, + "name": "Cambuí" + }, + "point_b": { + "lat": 4.2168, + "lon": 100.6996, + "name": "Sitiawan" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -14.84833, + "lon": 70.18898 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-22.61222°, -46.0575°)", + " Point B: (4.2168°, 100.6996°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -14.848330°", + " Longitude: 70.188980°", + "FINAL ANSWER: -14.848330, 70.188980" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 45.33319, + "lon": 122.78464, + "name": "Taonan" + }, + "point_b": { + "lat": 13.88724, + "lon": 100.5792, + "name": "Lak Si" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 37.873512, + "lon": 115.663106 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (45.33319°, 122.78464°)", + " Point B: (13.88724°, 100.5792°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 37.873512°", + " Longitude: 115.663106°", + "FINAL ANSWER: 37.873512, 115.663106" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 48.20172, + "lon": 16.34715, + "name": "Neubau" + }, + "point_b": { + "lat": 12.11451, + "lon": 12.8262, + "name": "Magumeri" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 39.190189, + "lon": 15.164826 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (48.20172°, 16.34715°)", + " Point B: (12.11451°, 12.8262°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 39.190189°", + " Longitude: 15.164826°", + "FINAL ANSWER: 39.190189, 15.164826" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 32.71007, + "lon": 13.96713, + "name": "Al-'Alūaṣ" + }, + "point_b": { + "lat": 24.66051, + "lon": 97.18923, + "name": "Lakang" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 36.449801, + "lon": 35.27599 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (32.71007°, 13.96713°)", + " Point B: (24.66051°, 97.18923°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 36.449801°", + " Longitude: 35.275990°", + "FINAL ANSWER: 36.449801, 35.275990" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 51.87113, + "lon": 0.15868, + "name": "Bishops Stortford" + }, + "point_b": { + "lat": 47.99597, + "lon": -4.09795, + "name": "Quimper" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 48.978988, + "lon": -3.096666 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (51.87113°, 0.15868°)", + " Point B: (47.99597°, -4.09795°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 48.978988°", + " Longitude: -3.096666°", + "FINAL ANSWER: 48.978988, -3.096666" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 16.60175, + "lon": -15.34866, + "name": "Tékane" + }, + "point_b": { + "lat": 32.8043, + "lon": 21.86605, + "name": "Shahhat" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 21.466972, + "lon": -6.952294 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (16.60175°, -15.34866°)", + " Point B: (32.8043°, 21.86605°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 21.466972°", + " Longitude: -6.952294°", + "FINAL ANSWER: 21.466972, -6.952294" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -25.81015, + "lon": 28.74248, + "name": "Bronkhorstspruit" + }, + "point_b": { + "lat": -12.1201, + "lon": -58.00274, + "name": "Brasnorte" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -25.285872, + "lon": -16.861938 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-25.81015°, 28.74248°)", + " Point B: (-12.1201°, -58.00274°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -25.285872°", + " Longitude: -16.861938°", + "FINAL ANSWER: -25.285872, -16.861938" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -1.36553, + "lon": -79.90507, + "name": "Balzar" + }, + "point_b": { + "lat": 39.23583, + "lon": 122.72361, + "name": "Xiaochangshan" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 62.019951, + "lon": 165.127443 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-1.36553°, -79.90507°)", + " Point B: (39.23583°, 122.72361°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 62.019951°", + " Longitude: 165.127443°", + "FINAL ANSWER: 62.019951, 165.127443" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -12.55708, + "lon": 16.33805, + "name": "Chinguar" + }, + "point_b": { + "lat": 21.4538, + "lon": 76.39335, + "name": "Nepānagar" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -3.83534, + "lon": 31.108816 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-12.55708°, 16.33805°)", + " Point B: (21.4538°, 76.39335°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -3.835340°", + " Longitude: 31.108816°", + "FINAL ANSWER: -3.835340, 31.108816" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 52.21173, + "lon": 24.3563, + "name": "Kobryn" + }, + "point_b": { + "lat": -3.89, + "lon": -38.45056, + "name": "Eusébio" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 27.477892, + "lon": -15.349521 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (52.21173°, 24.3563°)", + " Point B: (-3.89°, -38.45056°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 27.477892°", + " Longitude: -15.349521°", + "FINAL ANSWER: 27.477892, -15.349521" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 47.37398, + "lon": 8.49007, + "name": "Zürich (Kreis 9) / Albisrieden" + }, + "point_b": { + "lat": 43.43925, + "lon": -70.77422, + "name": "Sanford" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 51.929212, + "lon": -10.935095 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (47.37398°, 8.49007°)", + " Point B: (43.43925°, -70.77422°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 51.929212°", + " Longitude: -10.935095°", + "FINAL ANSWER: 51.929212, -10.935095" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 8.79577, + "lon": -75.69947, + "name": "San Carlos" + }, + "point_b": { + "lat": 11.44495, + "lon": 77.71102, + "name": "Kumarapalayam" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 28.525076, + "lon": -42.79861 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (8.79577°, -75.69947°)", + " Point B: (11.44495°, 77.71102°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 28.525076°", + " Longitude: -42.798610°", + "FINAL ANSWER: 28.525076, -42.798610" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 15.16222, + "lon": 120.5675, + "name": "Santol" + }, + "point_b": { + "lat": 35.27306, + "lon": 7.75194, + "name": "Cheria" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 29.942716, + "lon": 98.998835 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (15.16222°, 120.5675°)", + " Point B: (35.27306°, 7.75194°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 29.942716°", + " Longitude: 98.998835°", + "FINAL ANSWER: 29.942716, 98.998835" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 24.10287, + "lon": 90.09841, + "name": "Mirzāpur" + }, + "point_b": { + "lat": 47.93596, + "lon": 29.62225, + "name": "Balta" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 45.331573, + "lon": 48.522057 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (24.10287°, 90.09841°)", + " Point B: (47.93596°, 29.62225°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 45.331573°", + " Longitude: 48.522057°", + "FINAL ANSWER: 45.331573, 48.522057" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 51.26667, + "lon": 0.51667, + "name": "Maidstone" + }, + "point_b": { + "lat": 36.59634, + "lon": -119.4504, + "name": "Reedley" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 51.65052, + "lon": -102.160507 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (51.26667°, 0.51667°)", + " Point B: (36.59634°, -119.4504°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 51.650520°", + " Longitude: -102.160507°", + "FINAL ANSWER: 51.650520, -102.160507" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -13.83333, + "lon": -171.76666, + "name": "Apia" + }, + "point_b": { + "lat": 13.65, + "lon": 79.42, + "name": "Akkarampalle" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 7.574792, + "lon": 107.029192 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-13.83333°, -171.76666°)", + " Point B: (13.65°, 79.42°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 7.574792°", + " Longitude: 107.029192°", + "FINAL ANSWER: 7.574792, 107.029192" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 10.48421, + "lon": 76.10445, + "name": "Karamuck" + }, + "point_b": { + "lat": 26.97579, + "lon": 83.10995, + "name": "Mehndāwal" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 22.879703, + "lon": 81.216746 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (10.48421°, 76.10445°)", + " Point B: (26.97579°, 83.10995°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 22.879703°", + " Longitude: 81.216746°", + "FINAL ANSWER: 22.879703, 81.216746" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 5.2118, + "lon": -3.73884, + "name": "Grand-Bassam" + }, + "point_b": { + "lat": 33.37362, + "lon": -7.99462, + "name": "Bir Jdid" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 19.304943, + "lon": -5.679809 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (5.2118°, -3.73884°)", + " Point B: (33.37362°, -7.99462°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 19.304943°", + " Longitude: -5.679809°", + "FINAL ANSWER: 19.304943, -5.679809" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 27.26881, + "lon": 31.15232, + "name": "Abnūb" + }, + "point_b": { + "lat": 36.50921, + "lon": -86.885, + "name": "Springfield" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 50.299039, + "lon": -23.079449 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (27.26881°, 31.15232°)", + " Point B: (36.50921°, -86.885°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 50.299039°", + " Longitude: -23.079449°", + "FINAL ANSWER: 50.299039, -23.079449" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 32.8343, + "lon": -97.2289, + "name": "North Richland Hills" + }, + "point_b": { + "lat": 41.56667, + "lon": 23.73333, + "name": "Gotse Delchev" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 48.066239, + "lon": -76.155704 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (32.8343°, -97.2289°)", + " Point B: (41.56667°, 23.73333°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 48.066239°", + " Longitude: -76.155704°", + "FINAL ANSWER: 48.066239, -76.155704" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 1.37222, + "lon": 103.94778, + "name": "Pasir Ris New Town" + }, + "point_b": { + "lat": 43.53692, + "lon": 6.46458, + "name": "Draguignan" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 31.658733, + "lon": 65.500259 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (1.37222°, 103.94778°)", + " Point B: (43.53692°, 6.46458°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 31.658733°", + " Longitude: 65.500259°", + "FINAL ANSWER: 31.658733, 65.500259" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -13.81333, + "lon": -41.29667, + "name": "Ituaçu" + }, + "point_b": { + "lat": 52.53129, + "lon": 24.9782, + "name": "Byaroza" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 39.334362, + "lon": -0.332221 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-13.81333°, -41.29667°)", + " Point B: (52.53129°, 24.9782°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 39.334362°", + " Longitude: -0.332221°", + "FINAL ANSWER: 39.334362, -0.332221" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 15.60811, + "lon": 39.47455, + "name": "Massawa" + }, + "point_b": { + "lat": 34.67139, + "lon": 70.20944, + "name": "Mehtar Lām" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 30.571957, + "lon": 61.532473 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (15.60811°, 39.47455°)", + " Point B: (34.67139°, 70.20944°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 30.571957°", + " Longitude: 61.532473°", + "FINAL ANSWER: 30.571957, 61.532473" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 35.88889, + "lon": 2.74905, + "name": "Ksar el Boukhari" + }, + "point_b": { + "lat": 60.2052, + "lon": 24.6522, + "name": "Espoo" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 42.288253, + "lon": 6.479325 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (35.88889°, 2.74905°)", + " Point B: (60.2052°, 24.6522°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 42.288253°", + " Longitude: 6.479325°", + "FINAL ANSWER: 42.288253, 6.479325" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -10.2621, + "lon": 29.92712, + "name": "Luwingu" + }, + "point_b": { + "lat": 16.8722, + "lon": 79.56247, + "name": "Miryalaguda" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 10.503456, + "lon": 66.700383 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-10.2621°, 29.92712°)", + " Point B: (16.8722°, 79.56247°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 10.503456°", + " Longitude: 66.700383°", + "FINAL ANSWER: 10.503456, 66.700383" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -33.95, + "lon": 151.23333, + "name": "Maroubra" + }, + "point_b": { + "lat": 30.9616, + "lon": 31.24069, + "name": "Samannūd" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 15.910351, + "lon": 62.846844 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-33.95°, 151.23333°)", + " Point B: (30.9616°, 31.24069°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 15.910351°", + " Longitude: 62.846844°", + "FINAL ANSWER: 15.910351, 62.846844" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 18.38865, + "lon": 78.81048, + "name": "Sirsilla" + }, + "point_b": { + "lat": -2.27169, + "lon": 40.90201, + "name": "Lamu" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 13.640092, + "lon": 68.876442 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (18.38865°, 78.81048°)", + " Point B: (-2.27169°, 40.90201°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 13.640092°", + " Longitude: 68.876442°", + "FINAL ANSWER: 13.640092, 68.876442" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 14.72775, + "lon": 32.26928, + "name": "Al-Quṭaynah" + }, + "point_b": { + "lat": 30.0445, + "lon": 72.3556, + "name": "Vihari" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 19.442912, + "lon": 41.452613 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (14.72775°, 32.26928°)", + " Point B: (30.0445°, 72.3556°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 19.442912°", + " Longitude: 41.452613°", + "FINAL ANSWER: 19.442912, 41.452613" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 64.75067, + "lon": 20.95279, + "name": "Skellefteå" + }, + "point_b": { + "lat": 30.19846, + "lon": 75.6819, + "name": "Longowal" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 50.410308, + "lon": 58.271848 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (64.75067°, 20.95279°)", + " Point B: (30.19846°, 75.6819°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 50.410308°", + " Longitude: 58.271848°", + "FINAL ANSWER: 50.410308, 58.271848" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 24.41339, + "lon": 74.47331, + "name": "Bari Sādri" + }, + "point_b": { + "lat": 6.29164, + "lon": -6.27945, + "name": "Dignago" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 19.806492, + "lon": 31.964668 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (24.41339°, 74.47331°)", + " Point B: (6.29164°, -6.27945°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 19.806492°", + " Longitude: 31.964668°", + "FINAL ANSWER: 19.806492, 31.964668" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 42.30008, + "lon": -83.01654, + "name": "Windsor" + }, + "point_b": { + "lat": -32.33083, + "lon": 28.14981, + "name": "Butterworth" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 28.913434, + "lon": -47.594622 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (42.30008°, -83.01654°)", + " Point B: (-32.33083°, 28.14981°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 28.913434°", + " Longitude: -47.594622°", + "FINAL ANSWER: 28.913434, -47.594622" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 9.87648, + "lon": -84.07479, + "name": "San Rafael Arriba" + }, + "point_b": { + "lat": 8.9, + "lon": 39.91667, + "name": "Metahāra" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 16.374748, + "lon": 9.789569 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (9.87648°, -84.07479°)", + " Point B: (8.9°, 39.91667°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 16.374748°", + " Longitude: 9.789569°", + "FINAL ANSWER: 16.374748, 9.789569" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 38.16143, + "lon": 106.58502, + "name": "Ningdong" + }, + "point_b": { + "lat": 5.55874, + "lon": 7.63359, + "name": "Bende" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 38.378576, + "lon": 76.664704 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (38.16143°, 106.58502°)", + " Point B: (5.55874°, 7.63359°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 38.378576°", + " Longitude: 76.664704°", + "FINAL ANSWER: 38.378576, 76.664704" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 53.23157, + "lon": 7.461, + "name": "Leer" + }, + "point_b": { + "lat": 11.43522, + "lon": 5.23494, + "name": "Zuru" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 21.887142, + "lon": 5.625662 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (53.23157°, 7.461°)", + " Point B: (11.43522°, 5.23494°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 21.887142°", + " Longitude: 5.625662°", + "FINAL ANSWER: 21.887142, 5.625662" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 36.84666, + "lon": 136.98355, + "name": "Himi" + }, + "point_b": { + "lat": 21.36373, + "lon": -157.84294, + "name": "Kalihi Valley" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 28.200122, + "lon": -171.916641 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (36.84666°, 136.98355°)", + " Point B: (21.36373°, -157.84294°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 28.200122°", + " Longitude: -171.916641°", + "FINAL ANSWER: 28.200122, -171.916641" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -8.1181, + "lon": 111.8935, + "name": "Boyolangu" + }, + "point_b": { + "lat": 41.24591, + "lon": -75.88131, + "name": "Wilkes-Barre" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 62.885539, + "lon": 134.439645 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-8.1181°, 111.8935°)", + " Point B: (41.24591°, -75.88131°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 62.885539°", + " Longitude: 134.439645°", + "FINAL ANSWER: 62.885539, 134.439645" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -26.08111, + "lon": -53.055, + "name": "Francisco Beltrão" + }, + "point_b": { + "lat": -25.699, + "lon": 27.47475, + "name": "Marikana" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -30.630275, + "lon": 8.069957 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-26.08111°, -53.055°)", + " Point B: (-25.699°, 27.47475°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -30.630275°", + " Longitude: 8.069957°", + "FINAL ANSWER: -30.630275, 8.069957" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 39.55223, + "lon": -8.97749, + "name": "Alcobaça" + }, + "point_b": { + "lat": 52.5514, + "lon": -2.02355, + "name": "Wednesbury" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 49.343848, + "lon": -4.095243 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (39.55223°, -8.97749°)", + " Point B: (52.5514°, -2.02355°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 49.343848°", + " Longitude: -4.095243°", + "FINAL ANSWER: 49.343848, -4.095243" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 54.09242, + "lon": 18.77787, + "name": "Tczew" + }, + "point_b": { + "lat": -23.87444, + "lon": -53.90167, + "name": "Altônia" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -2.861974, + "lon": -40.037733 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (54.09242°, 18.77787°)", + " Point B: (-23.87444°, -53.90167°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -2.861974°", + " Longitude: -40.037733°", + "FINAL ANSWER: -2.861974, -40.037733" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 22.80979, + "lon": 89.56439, + "name": "Khulna" + }, + "point_b": { + "lat": 18.37035, + "lon": -97.29966, + "name": "Altepexi" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 56.574619, + "lon": 99.674891 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (22.80979°, 89.56439°)", + " Point B: (18.37035°, -97.29966°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 56.574619°", + " Longitude: 99.674891°", + "FINAL ANSWER: 56.574619, 99.674891" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 24.20645, + "lon": 84.87085, + "name": "Chatrā" + }, + "point_b": { + "lat": 48.83864, + "lon": 2.41579, + "name": "Saint-Mandé" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 49.271637, + "lon": 28.168016 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (24.20645°, 84.87085°)", + " Point B: (48.83864°, 2.41579°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 49.271637°", + " Longitude: 28.168016°", + "FINAL ANSWER: 49.271637, 28.168016" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -1.71464, + "lon": -49.53152, + "name": "São Sebastião da Boa Vista" + }, + "point_b": { + "lat": 36.65, + "lon": 138.18333, + "name": "Nagano" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 33.670816, + "lon": -57.04544 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-1.71464°, -49.53152°)", + " Point B: (36.65°, 138.18333°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 33.670816°", + " Longitude: -57.045440°", + "FINAL ANSWER: 33.670816, -57.045440" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 35.74381, + "lon": -0.7693, + "name": "’Aïn el Turk" + }, + "point_b": { + "lat": -38.03333, + "lon": 145.3, + "name": "Narre Warren" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 19.170806, + "lon": 38.475559 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (35.74381°, -0.7693°)", + " Point B: (-38.03333°, 145.3°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 19.170806°", + " Longitude: 38.475559°", + "FINAL ANSWER: 19.170806, 38.475559" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 40.81108, + "lon": 69.19417, + "name": "Bo‘ka" + }, + "point_b": { + "lat": -1.66506, + "lon": -78.65887, + "name": "Riobamba" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 49.185477, + "lon": -30.35358 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (40.81108°, 69.19417°)", + " Point B: (-1.66506°, -78.65887°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 49.185477°", + " Longitude: -30.353580°", + "FINAL ANSWER: 49.185477, -30.353580" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -13.08271, + "lon": -62.27726, + "name": "Rolim de Moura do Guaporé" + }, + "point_b": { + "lat": -22.81639, + "lon": -45.1925, + "name": "Guaratinguetá" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -20.532235, + "lon": -49.649484 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-13.08271°, -62.27726°)", + " Point B: (-22.81639°, -45.1925°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -20.532235°", + " Longitude: -49.649484°", + "FINAL ANSWER: -20.532235, -49.649484" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 56.37328, + "lon": 38.58321, + "name": "Strunino" + }, + "point_b": { + "lat": 38.5106, + "lon": -1.70096, + "name": "Hellín" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 44.143281, + "lon": 5.826544 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (56.37328°, 38.58321°)", + " Point B: (38.5106°, -1.70096°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 44.143281°", + " Longitude: 5.826544°", + "FINAL ANSWER: 44.143281, 5.826544" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -20.7725, + "lon": -49.71417, + "name": "Monte Aprazível" + }, + "point_b": { + "lat": 37.36605, + "lon": -121.82718, + "name": "Alum Rock" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 10.207734, + "lon": -82.393083 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-20.7725°, -49.71417°)", + " Point B: (37.36605°, -121.82718°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 10.207734°", + " Longitude: -82.393083°", + "FINAL ANSWER: 10.207734, -82.393083" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 51.03951, + "lon": -114.07087, + "name": "Beltline" + }, + "point_b": { + "lat": -33.60047, + "lon": 22.19955, + "name": "Oudtshoorn" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 21.253176, + "lon": -26.746843 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (51.03951°, -114.07087°)", + " Point B: (-33.60047°, 22.19955°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 21.253176°", + " Longitude: -26.746843°", + "FINAL ANSWER: 21.253176, -26.746843" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -19.65, + "lon": 47.31667, + "name": "Antanifotsy" + }, + "point_b": { + "lat": 21.32855, + "lon": 71.02645, + "name": "Dhāri" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 0.857563, + "lon": 59.105725 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-19.65°, 47.31667°)", + " Point B: (21.32855°, 71.02645°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 0.857563°", + " Longitude: 59.105725°", + "FINAL ANSWER: 0.857563, 59.105725" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 22.48898, + "lon": 90.06273, + "name": "Bhāndāria" + }, + "point_b": { + "lat": 49.23839, + "lon": -122.86676, + "name": "Maillardville" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 65.603591, + "lon": 133.416202 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (22.48898°, 90.06273°)", + " Point B: (49.23839°, -122.86676°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 65.603591°", + " Longitude: 133.416202°", + "FINAL ANSWER: 65.603591, 133.416202" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 36.81006, + "lon": 10.09557, + "name": "Manouba" + }, + "point_b": { + "lat": 14.68698, + "lon": -17.22808, + "name": "Bargny Guèdj" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 26.391715, + "lon": -4.879173 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (36.81006°, 10.09557°)", + " Point B: (14.68698°, -17.22808°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 26.391715°", + " Longitude: -4.879173°", + "FINAL ANSWER: 26.391715, -4.879173" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 7.36983, + "lon": 4.1863, + "name": "Ikire" + }, + "point_b": { + "lat": 51.31889, + "lon": -2.20861, + "name": "Trowbridge" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 18.379156, + "lon": 3.03044 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (7.36983°, 4.1863°)", + " Point B: (51.31889°, -2.20861°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 18.379156°", + " Longitude: 3.030440°", + "FINAL ANSWER: 18.379156, 3.030440" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 41.82392, + "lon": -87.85173, + "name": "Brookfield" + }, + "point_b": { + "lat": 12.95772, + "lon": 99.90555, + "name": "Tha Yang" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 72.061891, + "lon": -103.467915 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (41.82392°, -87.85173°)", + " Point B: (12.95772°, 99.90555°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 72.061891°", + " Longitude: -103.467915°", + "FINAL ANSWER: 72.061891, -103.467915" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 43.35689, + "lon": -3.01146, + "name": "Getxo" + }, + "point_b": { + "lat": 9.62376, + "lon": -0.82705, + "name": "Savelugu" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 26.494386, + "lon": -1.754204 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (43.35689°, -3.01146°)", + " Point B: (9.62376°, -0.82705°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 26.494386°", + " Longitude: -1.754204°", + "FINAL ANSWER: 26.494386, -1.754204" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 36.37227, + "lon": 119.58208, + "name": "Kanjia" + }, + "point_b": { + "lat": 4.70592, + "lon": -74.23021, + "name": "Mosquera" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 66.186944, + "lon": 148.630877 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (36.37227°, 119.58208°)", + " Point B: (4.70592°, -74.23021°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 66.186944°", + " Longitude: 148.630877°", + "FINAL ANSWER: 66.186944, 148.630877" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 10.48666, + "lon": -66.73799, + "name": "Caucagüito" + }, + "point_b": { + "lat": -27.09028, + "lon": -48.61139, + "name": "Itapema" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -8.405019, + "lon": -58.128385 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (10.48666°, -66.73799°)", + " Point B: (-27.09028°, -48.61139°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -8.405019°", + " Longitude: -58.128385°", + "FINAL ANSWER: -8.405019, -58.128385" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 11.86819, + "lon": 3.38327, + "name": "Malanville" + }, + "point_b": { + "lat": 5.82417, + "lon": 125.20333, + "name": "Glan" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 17.119831, + "lon": 33.796114 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (11.86819°, 3.38327°)", + " Point B: (5.82417°, 125.20333°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 17.119831°", + " Longitude: 33.796114°", + "FINAL ANSWER: 17.119831, 33.796114" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 6.58333, + "lon": 1.5, + "name": "Tabligbo" + }, + "point_b": { + "lat": -34.4279, + "lon": 150.89268, + "name": "Wollongong city centre" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -19.637794, + "lon": 25.190045 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (6.58333°, 1.5°)", + " Point B: (-34.4279°, 150.89268°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -19.637794°", + " Longitude: 25.190045°", + "FINAL ANSWER: -19.637794, 25.190045" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -38.76081, + "lon": -72.5982, + "name": "Padre Las Casas" + }, + "point_b": { + "lat": 11.42599, + "lon": 77.57074, + "name": "Salangaippālaiyam" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -51.911903, + "lon": -24.55312 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-38.76081°, -72.5982°)", + " Point B: (11.42599°, 77.57074°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -51.911903°", + " Longitude: -24.553120°", + "FINAL ANSWER: -51.911903, -24.553120" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 5.0234, + "lon": -6.56157, + "name": "Gabiadji" + }, + "point_b": { + "lat": 51.93, + "lon": 6.07083, + "name": "Zevenaar" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 16.833206, + "lon": -4.301876 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (5.0234°, -6.56157°)", + " Point B: (51.93°, 6.07083°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 16.833206°", + " Longitude: -4.301876°", + "FINAL ANSWER: 16.833206, -4.301876" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -22.74389, + "lon": -43.7075, + "name": "Seropédica" + }, + "point_b": { + "lat": 52.33645, + "lon": 13.41316, + "name": "Blankenfelde-Mahlow" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 35.69163, + "lon": -7.992576 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-22.74389°, -43.7075°)", + " Point B: (52.33645°, 13.41316°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 35.691630°", + " Longitude: -7.992576°", + "FINAL ANSWER: 35.691630, -7.992576" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 43.83193, + "lon": 11.19924, + "name": "Sesto Fiorentino" + }, + "point_b": { + "lat": 51.76338, + "lon": -0.22419, + "name": "Hatfield" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 45.915602, + "lon": 8.660008 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (43.83193°, 11.19924°)", + " Point B: (51.76338°, -0.22419°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 45.915602°", + " Longitude: 8.660008°", + "FINAL ANSWER: 45.915602, 8.660008" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 30.31768, + "lon": 76.86596, + "name": "Kardhān" + }, + "point_b": { + "lat": -14.67806, + "lon": -39.375, + "name": "Itajuípe" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 14.518252, + "lon": 13.520054 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (30.31768°, 76.86596°)", + " Point B: (-14.67806°, -39.375°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 14.518252°", + " Longitude: 13.520054°", + "FINAL ANSWER: 14.518252, 13.520054" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 29.55718, + "lon": -95.80856, + "name": "Rosenberg" + }, + "point_b": { + "lat": 19.43332, + "lon": -99.19919, + "name": "Polanco" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 24.5047, + "lon": -97.572315 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (29.55718°, -95.80856°)", + " Point B: (19.43332°, -99.19919°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 24.504700°", + " Longitude: -97.572315°", + "FINAL ANSWER: 24.504700, -97.572315" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 54.12588, + "lon": 20.57954, + "name": "Lidzbark Warmiński" + }, + "point_b": { + "lat": 58.07756, + "lon": 60.7202, + "name": "Nizhnyaya Salda" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 57.738455, + "lon": 39.575208 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (54.12588°, 20.57954°)", + " Point B: (58.07756°, 60.7202°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 57.738455°", + " Longitude: 39.575208°", + "FINAL ANSWER: 57.738455, 39.575208" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 55.95206, + "lon": -3.19648, + "name": "Edinburgh" + }, + "point_b": { + "lat": 12.49187, + "lon": 109.12495, + "name": "Ninh Hòa" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 48.551594, + "lon": 74.979593 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (55.95206°, -3.19648°)", + " Point B: (12.49187°, 109.12495°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 48.551594°", + " Longitude: 74.979593°", + "FINAL ANSWER: 48.551594, 74.979593" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 43.1689, + "lon": -86.26395, + "name": "Norton Shores" + }, + "point_b": { + "lat": 15.95923, + "lon": 76.11351, + "name": "Ilkal" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 69.235108, + "lon": -58.657883 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (43.1689°, -86.26395°)", + " Point B: (15.95923°, 76.11351°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 69.235108°", + " Longitude: -58.657883°", + "FINAL ANSWER: 69.235108, -58.657883" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -7.11799, + "lon": 39.20782, + "name": "Mkuranga" + }, + "point_b": { + "lat": 51.41334, + "lon": -0.36701, + "name": "Hampton" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 23.321805, + "lon": 24.111687 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-7.11799°, 39.20782°)", + " Point B: (51.41334°, -0.36701°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 23.321805°", + " Longitude: 24.111687°", + "FINAL ANSWER: 23.321805, 24.111687" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -26.33639, + "lon": -49.90639, + "name": "Itaiópolis" + }, + "point_b": { + "lat": 35.35, + "lon": 137.18333, + "name": "Toki" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 10.463881, + "lon": -71.330517 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-26.33639°, -49.90639°)", + " Point B: (35.35°, 137.18333°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 10.463881°", + " Longitude: -71.330517°", + "FINAL ANSWER: 10.463881, -71.330517" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 21.16516, + "lon": 77.3091, + "name": "Anjangaon" + }, + "point_b": { + "lat": 36.365, + "lon": 6.61472, + "name": "Constantine" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 33.905818, + "lon": 44.93586 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (21.16516°, 77.3091°)", + " Point B: (36.365°, 6.61472°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 33.905818°", + " Longitude: 44.935860°", + "FINAL ANSWER: 33.905818, 44.935860" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 37.75, + "lon": 140.46667, + "name": "Fukushima" + }, + "point_b": { + "lat": 35.85, + "lon": 117.7, + "name": "Dongdu" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 37.689087, + "lon": 134.687837 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (37.75°, 140.46667°)", + " Point B: (35.85°, 117.7°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 37.689087°", + " Longitude: 134.687837°", + "FINAL ANSWER: 37.689087, 134.687837" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 8.36319, + "lon": 77.29777, + "name": "Kulasegaram" + }, + "point_b": { + "lat": -32.05251, + "lon": 115.88782, + "name": "Willetton" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -22.622725, + "lon": 104.722961 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (8.36319°, 77.29777°)", + " Point B: (-32.05251°, 115.88782°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -22.622725°", + " Longitude: 104.722961°", + "FINAL ANSWER: -22.622725, 104.722961" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 30.17599, + "lon": 106.17168, + "name": "Gulou" + }, + "point_b": { + "lat": -37.96667, + "lon": 145.16667, + "name": "Noble Park" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -21.353222, + "lon": 133.742377 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (30.17599°, 106.17168°)", + " Point B: (-37.96667°, 145.16667°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -21.353222°", + " Longitude: 133.742377°", + "FINAL ANSWER: -21.353222, 133.742377" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 8.1843, + "lon": 77.24805, + "name": "Reethapuram" + }, + "point_b": { + "lat": 11.55444, + "lon": -1.77361, + "name": "Sapouy" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 12.874647, + "lon": 18.057905 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (8.1843°, 77.24805°)", + " Point B: (11.55444°, -1.77361°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 12.874647°", + " Longitude: 18.057905°", + "FINAL ANSWER: 12.874647, 18.057905" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 37.52966, + "lon": -122.04024, + "name": "Newark" + }, + "point_b": { + "lat": 16.68317, + "lon": 74.58892, + "name": "Kurandvād" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 46.019943, + "lon": 86.207937 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (37.52966°, -122.04024°)", + " Point B: (16.68317°, 74.58892°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 46.019943°", + " Longitude: 86.207937°", + "FINAL ANSWER: 46.019943, 86.207937" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 14.78412, + "lon": 78.5729, + "name": "Gopavaram" + }, + "point_b": { + "lat": -25.67031, + "lon": 31.86288, + "name": "Kamaqhekeza" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 4.515923, + "lon": 67.168475 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (14.78412°, 78.5729°)", + " Point B: (-25.67031°, 31.86288°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 4.515923°", + " Longitude: 67.168475°", + "FINAL ANSWER: 4.515923, 67.168475" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -9.44112, + "lon": 159.97002, + "name": "Kola'a" + }, + "point_b": { + "lat": -31.76737, + "lon": 115.96936, + "name": "Ellenbrook" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -15.989133, + "lon": 150.148043 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-9.44112°, 159.97002°)", + " Point B: (-31.76737°, 115.96936°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -15.989133°", + " Longitude: 150.148043°", + "FINAL ANSWER: -15.989133, 150.148043" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 50.0088, + "lon": -119.39672, + "name": "Lake Country" + }, + "point_b": { + "lat": 51.95109, + "lon": 7.98756, + "name": "Warendorf" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 70.228021, + "lon": -58.127321 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (50.0088°, -119.39672°)", + " Point B: (51.95109°, 7.98756°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 70.228021°", + " Longitude: -58.127321°", + "FINAL ANSWER: 70.228021, -58.127321" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -33.9209, + "lon": 151.12506, + "name": "Earlwood" + }, + "point_b": { + "lat": 52.60252, + "lon": 4.68815, + "name": "Heiloo" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -3.825214, + "lon": 127.222803 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-33.9209°, 151.12506°)", + " Point B: (52.60252°, 4.68815°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -3.825214°", + " Longitude: 127.222803°", + "FINAL ANSWER: -3.825214, 127.222803" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -23.84861, + "lon": -50.18778, + "name": "Ibaiti" + }, + "point_b": { + "lat": 35.70307, + "lon": 139.70436, + "name": "Ōkubo" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 11.534142, + "lon": -72.069507 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-23.84861°, -50.18778°)", + " Point B: (35.70307°, 139.70436°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 11.534142°", + " Longitude: -72.069507°", + "FINAL ANSWER: 11.534142, -72.069507" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 50.43109, + "lon": 7.40425, + "name": "Andernach" + }, + "point_b": { + "lat": -16.47583, + "lon": -43.48833, + "name": "Francisco Sá" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 35.469054, + "lon": -11.165446 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (50.43109°, 7.40425°)", + " Point B: (-16.47583°, -43.48833°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 35.469054°", + " Longitude: -11.165446°", + "FINAL ANSWER: 35.469054, -11.165446" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 49.6, + "lon": 117.43333, + "name": "Manzhouli" + }, + "point_b": { + "lat": 42.89799, + "lon": 71.37334, + "name": "Taraz" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 49.757643, + "lon": 105.049395 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (49.6°, 117.43333°)", + " Point B: (42.89799°, 71.37334°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 49.757643°", + " Longitude: 105.049395°", + "FINAL ANSWER: 49.757643, 105.049395" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -30.31002, + "lon": 30.66275, + "name": "eMuziwezinto" + }, + "point_b": { + "lat": 8.39925, + "lon": -71.64082, + "name": "Santa Cruz de Mora" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -4.726212, + "lon": -48.899252 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-30.31002°, 30.66275°)", + " Point B: (8.39925°, -71.64082°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -4.726212°", + " Longitude: -48.899252°", + "FINAL ANSWER: -4.726212, -48.899252" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 10.02737, + "lon": 77.47815, + "name": "Allinagaram" + }, + "point_b": { + "lat": -11.27389, + "lon": -37.79, + "name": "Itabaianinha" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 5.050431, + "lon": 48.515155 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (10.02737°, 77.47815°)", + " Point B: (-11.27389°, -37.79°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 5.050431°", + " Longitude: 48.515155°", + "FINAL ANSWER: 5.050431, 48.515155" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -4.96667, + "lon": 34.88333, + "name": "Mungaa" + }, + "point_b": { + "lat": 23.47917, + "lon": 120.44889, + "name": "Chiayi City" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 12.510723, + "lon": 75.476855 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-4.96667°, 34.88333°)", + " Point B: (23.47917°, 120.44889°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 12.510723°", + " Longitude: 75.476855°", + "FINAL ANSWER: 12.510723, 75.476855" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 11.93018, + "lon": 75.57152, + "name": "Mattanur" + }, + "point_b": { + "lat": 36.55528, + "lon": 2.79028, + "name": "Oued el Alleug" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 34.543962, + "lon": 23.940333 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (11.93018°, 75.57152°)", + " Point B: (36.55528°, 2.79028°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 34.543962°", + " Longitude: 23.940333°", + "FINAL ANSWER: 34.543962, 23.940333" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -12.48602, + "lon": 130.9833, + "name": "Palmerston" + }, + "point_b": { + "lat": -16.2325, + "lon": 39.90861, + "name": "Angoche" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -20.075691, + "lon": 85.934744 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-12.48602°, 130.9833°)", + " Point B: (-16.2325°, 39.90861°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -20.075691°", + " Longitude: 85.934744°", + "FINAL ANSWER: -20.075691, 85.934744" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 33.95015, + "lon": -118.03917, + "name": "South Whittier" + }, + "point_b": { + "lat": 10.30416, + "lon": 1.37962, + "name": "Natitingou" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 26.733538, + "lon": -21.174853 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (33.95015°, -118.03917°)", + " Point B: (10.30416°, 1.37962°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 26.733538°", + " Longitude: -21.174853°", + "FINAL ANSWER: 26.733538, -21.174853" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 53.0, + "lon": -1.3, + "name": "Eastwood" + }, + "point_b": { + "lat": -3.33984, + "lon": 128.91975, + "name": "Amahai" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 58.652684, + "lon": 50.622031 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (53.0°, -1.3°)", + " Point B: (-3.33984°, 128.91975°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 58.652684°", + " Longitude: 50.622031°", + "FINAL ANSWER: 58.652684, 50.622031" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 29.79712, + "lon": 107.45755, + "name": "Qingxi" + }, + "point_b": { + "lat": -21.78778, + "lon": -46.56139, + "name": "Poços de Caldas" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 17.126393, + "lon": 22.104913 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (29.79712°, 107.45755°)", + " Point B: (-21.78778°, -46.56139°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 17.126393°", + " Longitude: 22.104913°", + "FINAL ANSWER: 17.126393, 22.104913" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 48.15344, + "lon": 17.05522, + "name": "Karlova Ves" + }, + "point_b": { + "lat": -34.89791, + "lon": -54.95021, + "name": "Maldonado" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -13.878065, + "lon": -37.560382 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (48.15344°, 17.05522°)", + " Point B: (-34.89791°, -54.95021°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -13.878065°", + " Longitude: -37.560382°", + "FINAL ANSWER: -13.878065, -37.560382" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 25.60962, + "lon": 85.48076, + "name": "Mahnar Bazar" + }, + "point_b": { + "lat": 38.66314, + "lon": -9.0724, + "name": "Barreiro" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 42.710285, + "lon": 42.654006 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (25.60962°, 85.48076°)", + " Point B: (38.66314°, -9.0724°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 42.710285°", + " Longitude: 42.654006°", + "FINAL ANSWER: 42.710285, 42.654006" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 13.5503, + "lon": 78.50288, + "name": "Madanapalle" + }, + "point_b": { + "lat": -30.25833, + "lon": -54.91417, + "name": "Rosário do Sul" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -30.613811, + "lon": -15.848477 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (13.5503°, 78.50288°)", + " Point B: (-30.25833°, -54.91417°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -30.613811°", + " Longitude: -15.848477°", + "FINAL ANSWER: -30.613811, -15.848477" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 2.98056, + "lon": 34.13306, + "name": "Kotido" + }, + "point_b": { + "lat": 30.57556, + "lon": 2.88417, + "name": "El Menia" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 17.380199, + "lon": 19.694859 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (2.98056°, 34.13306°)", + " Point B: (30.57556°, 2.88417°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 17.380199°", + " Longitude: 19.694859°", + "FINAL ANSWER: 17.380199, 19.694859" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -23.65639, + "lon": -47.2225, + "name": "Ibiúna" + }, + "point_b": { + "lat": -13.34333, + "lon": -44.63667, + "name": "Correntina" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -21.081617, + "lon": -46.544969 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-23.65639°, -47.2225°)", + " Point B: (-13.34333°, -44.63667°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -21.081617°", + " Longitude: -46.544969°", + "FINAL ANSWER: -21.081617, -46.544969" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 34.1463, + "lon": 73.21168, + "name": "Abbottabad" + }, + "point_b": { + "lat": 52.49631, + "lon": 82.77466, + "name": "Aleysk" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 43.418695, + "lon": 77.263201 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (34.1463°, 73.21168°)", + " Point B: (52.49631°, 82.77466°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 43.418695°", + " Longitude: 77.263201°", + "FINAL ANSWER: 43.418695, 77.263201" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -8.90889, + "lon": -35.725, + "name": "Colônia Leopoldina" + }, + "point_b": { + "lat": 53.46723, + "lon": -2.68166, + "name": "Haydock" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 38.713198, + "lon": -15.290324 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-8.90889°, -35.725°)", + " Point B: (53.46723°, -2.68166°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 38.713198°", + " Longitude: -15.290324°", + "FINAL ANSWER: 38.713198, -15.290324" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -17.38195, + "lon": -66.15995, + "name": "Cochabamba" + }, + "point_b": { + "lat": 6.79519, + "lon": -6.2355, + "name": "Zaliohouan" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 0.357322, + "lon": -20.89914 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-17.38195°, -66.15995°)", + " Point B: (6.79519°, -6.2355°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 0.357322°", + " Longitude: -20.899140°", + "FINAL ANSWER: 0.357322, -20.899140" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 33.62594, + "lon": -97.13335, + "name": "Gainesville" + }, + "point_b": { + "lat": 31.12624, + "lon": 31.64313, + "name": "Minyat an Naşr" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 55.703573, + "lon": -31.092212 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (33.62594°, -97.13335°)", + " Point B: (31.12624°, 31.64313°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 55.703573°", + " Longitude: -31.092212°", + "FINAL ANSWER: 55.703573, -31.092212" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 7.71393, + "lon": 3.91665, + "name": "Fiditi" + }, + "point_b": { + "lat": 47.05048, + "lon": 8.30635, + "name": "Luzern" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 37.231625, + "lon": 6.834488 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (7.71393°, 3.91665°)", + " Point B: (47.05048°, 8.30635°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 37.231625°", + " Longitude: 6.834488°", + "FINAL ANSWER: 37.231625, 6.834488" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 32.45861, + "lon": 130.19306, + "name": "Amakusa" + }, + "point_b": { + "lat": 26.33338, + "lon": 88.55777, + "name": "Panchagarh" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 29.082002, + "lon": 98.407259 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (32.45861°, 130.19306°)", + " Point B: (26.33338°, 88.55777°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 29.082002°", + " Longitude: 98.407259°", + "FINAL ANSWER: 29.082002, 98.407259" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 10.26478, + "lon": 105.26676, + "name": "Núi Sập" + }, + "point_b": { + "lat": 38.2125, + "lon": 106.225, + "name": "Wanghong" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 31.226213, + "lon": 105.938808 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (10.26478°, 105.26676°)", + " Point B: (38.2125°, 106.225°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 31.226213°", + " Longitude: 105.938808°", + "FINAL ANSWER: 31.226213, 105.938808" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 30.85711, + "lon": 32.31183, + "name": "Al Qanţarah" + }, + "point_b": { + "lat": 11.5579, + "lon": 75.75964, + "name": "Mennānyam" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 17.363822, + "lon": 65.956267 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (30.85711°, 32.31183°)", + " Point B: (11.5579°, 75.75964°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 17.363822°", + " Longitude: 65.956267°", + "FINAL ANSWER: 17.363822, 65.956267" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -35.73167, + "lon": 174.32391, + "name": "Whangarei" + }, + "point_b": { + "lat": -34.71247, + "lon": -71.0434, + "name": "Chimbarongo" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -52.587261, + "lon": -127.798986 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-35.73167°, 174.32391°)", + " Point B: (-34.71247°, -71.0434°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -52.587261°", + " Longitude: -127.798986°", + "FINAL ANSWER: -52.587261, -127.798986" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 40.81056, + "lon": 111.65222, + "name": "Hohhot" + }, + "point_b": { + "lat": -17.39321, + "lon": 15.89107, + "name": "Helao Nafidi" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 17.041755, + "lon": 56.500771 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (40.81056°, 111.65222°)", + " Point B: (-17.39321°, 15.89107°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 17.041755°", + " Longitude: 56.500771°", + "FINAL ANSWER: 17.041755, 56.500771" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 8.61565, + "lon": 6.4185, + "name": "Baro" + }, + "point_b": { + "lat": -4.77609, + "lon": 11.86352, + "name": "Pointe-Noire" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 5.270289, + "lon": 7.792487 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (8.61565°, 6.4185°)", + " Point B: (-4.77609°, 11.86352°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 5.270289°", + " Longitude: 7.792487°", + "FINAL ANSWER: 5.270289, 7.792487" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 43.65783, + "lon": 6.92537, + "name": "Grasse" + }, + "point_b": { + "lat": -9.66583, + "lon": -35.73528, + "name": "Maceió" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 4.287028, + "lon": -26.950319 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (43.65783°, 6.92537°)", + " Point B: (-9.66583°, -35.73528°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 4.287028°", + " Longitude: -26.950319°", + "FINAL ANSWER: 4.287028, -26.950319" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 26.02301, + "lon": 76.34408, + "name": "Sawai Madhopur" + }, + "point_b": { + "lat": -7.16177, + "lon": 23.70057, + "name": "Luputa" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 1.706993, + "lon": 36.102959 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (26.02301°, 76.34408°)", + " Point B: (-7.16177°, 23.70057°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 1.706993°", + " Longitude: 36.102959°", + "FINAL ANSWER: 1.706993, 36.102959" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -5.26667, + "lon": -80.68333, + "name": "Catacaos" + }, + "point_b": { + "lat": 28.55778, + "lon": -81.4534, + "name": "Pine Hills" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 20.101912, + "lon": -81.237687 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-5.26667°, -80.68333°)", + " Point B: (28.55778°, -81.4534°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 20.101912°", + " Longitude: -81.237687°", + "FINAL ANSWER: 20.101912, -81.237687" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -26.67313, + "lon": 27.92615, + "name": "Vereeniging" + }, + "point_b": { + "lat": 13.16417, + "lon": -0.8225, + "name": "Pissila" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -6.970234, + "lon": 12.921667 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-26.67313°, 27.92615°)", + " Point B: (13.16417°, -0.8225°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -6.970234°", + " Longitude: 12.921667°", + "FINAL ANSWER: -6.970234, 12.921667" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 5.28515, + "lon": -2.76658, + "name": "Elubo" + }, + "point_b": { + "lat": 40.69149, + "lon": -73.80569, + "name": "Jamaica" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 16.895444, + "lon": -16.884753 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (5.28515°, -2.76658°)", + " Point B: (40.69149°, -73.80569°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 16.895444°", + " Longitude: -16.884753°", + "FINAL ANSWER: 16.895444, -16.884753" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 10.15951, + "lon": -68.89453, + "name": "Chivacoa" + }, + "point_b": { + "lat": -17.5347, + "lon": -149.56843, + "name": "Papeete" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -11.922523, + "lon": -128.540735 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (10.15951°, -68.89453°)", + " Point B: (-17.5347°, -149.56843°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -11.922523°", + " Longitude: -128.540735°", + "FINAL ANSWER: -11.922523, -128.540735" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -9.43056, + "lon": 159.92103, + "name": "Nggosi" + }, + "point_b": { + "lat": 6.87341, + "lon": -6.84829, + "name": "Belleville" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -13.704803, + "lon": 117.565137 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-9.43056°, 159.92103°)", + " Point B: (6.87341°, -6.84829°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -13.704803°", + " Longitude: 117.565137°", + "FINAL ANSWER: -13.704803, 117.565137" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 29.66578, + "lon": -95.01937, + "name": "La Porte" + }, + "point_b": { + "lat": 43.24622, + "lon": 5.39788, + "name": "Mazargues" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 48.940529, + "lon": -50.839506 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (29.66578°, -95.01937°)", + " Point B: (43.24622°, 5.39788°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 48.940529°", + " Longitude: -50.839506°", + "FINAL ANSWER: 48.940529, -50.839506" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 13.43528, + "lon": -16.67639, + "name": "Ibo Town" + }, + "point_b": { + "lat": 34.83033, + "lon": 0.15171, + "name": "Saïda" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 18.93892, + "lon": -12.954198 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (13.43528°, -16.67639°)", + " Point B: (34.83033°, 0.15171°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 18.938920°", + " Longitude: -12.954198°", + "FINAL ANSWER: 18.938920, -12.954198" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 32.2341, + "lon": 34.95023, + "name": "Eṭ Ṭīra" + }, + "point_b": { + "lat": -33.95222, + "lon": 150.89949, + "name": "Casula" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -20.195202, + "lon": 118.460825 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (32.2341°, 34.95023°)", + " Point B: (-33.95222°, 150.89949°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -20.195202°", + " Longitude: 118.460825°", + "FINAL ANSWER: -20.195202, 118.460825" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 11.05915, + "lon": -12.39498, + "name": "Pita" + }, + "point_b": { + "lat": 20.78613, + "lon": 78.5936, + "name": "Pipri" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 22.139225, + "lon": 31.684569 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (11.05915°, -12.39498°)", + " Point B: (20.78613°, 78.5936°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 22.139225°", + " Longitude: 31.684569°", + "FINAL ANSWER: 22.139225, 31.684569" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -22.94667, + "lon": -47.31583, + "name": "Monte Mor" + }, + "point_b": { + "lat": -11.60389, + "lon": -38.58313, + "name": "Sátiro Dias" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -17.322515, + "lon": -42.814367 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-22.94667°, -47.31583°)", + " Point B: (-11.60389°, -38.58313°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -17.322515°", + " Longitude: -42.814367°", + "FINAL ANSWER: -17.322515, -42.814367" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 37.00972, + "lon": 37.79417, + "name": "Nizip" + }, + "point_b": { + "lat": -16.18361, + "lon": -40.69444, + "name": "Almenara" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 13.312574, + "lon": -5.748489 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (37.00972°, 37.79417°)", + " Point B: (-16.18361°, -40.69444°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 13.312574°", + " Longitude: -5.748489°", + "FINAL ANSWER: 13.312574, -5.748489" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 38.67618, + "lon": 16.10094, + "name": "Vibo Valentia" + }, + "point_b": { + "lat": 9.8, + "lon": 38.73333, + "name": "Fichē" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 17.289663, + "lon": 33.942031 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (38.67618°, 16.10094°)", + " Point B: (9.8°, 38.73333°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 17.289663°", + " Longitude: 33.942031°", + "FINAL ANSWER: 17.289663, 33.942031" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 48.89672, + "lon": 2.25666, + "name": "Courbevoie" + }, + "point_b": { + "lat": -37.2463, + "lon": -73.31752, + "name": "Arauco" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 29.710574, + "lon": -23.203744 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (48.89672°, 2.25666°)", + " Point B: (-37.2463°, -73.31752°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 29.710574°", + " Longitude: -23.203744°", + "FINAL ANSWER: 29.710574, -23.203744" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 30.17582, + "lon": 106.48624, + "name": "Laitan" + }, + "point_b": { + "lat": 41.52311, + "lon": -81.51846, + "name": "South Euclid" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 82.120484, + "lon": 146.750307 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (30.17582°, 106.48624°)", + " Point B: (41.52311°, -81.51846°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 82.120484°", + " Longitude: 146.750307°", + "FINAL ANSWER: 82.120484, 146.750307" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 35.9441, + "lon": 5.03107, + "name": "Râs el Oued" + }, + "point_b": { + "lat": 41.23506, + "lon": 1.81193, + "name": "Sitges" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 38.600589, + "lon": 3.480863 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (35.9441°, 5.03107°)", + " Point B: (41.23506°, 1.81193°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 38.600589°", + " Longitude: 3.480863°", + "FINAL ANSWER: 38.600589, 3.480863" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 9.62512, + "lon": 78.62434, + "name": "Ilaiyankudi" + }, + "point_b": { + "lat": 38.00437, + "lon": -122.29886, + "name": "Pinole" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 64.326274, + "lon": 127.014831 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (9.62512°, 78.62434°)", + " Point B: (38.00437°, -122.29886°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 64.326274°", + " Longitude: 127.014831°", + "FINAL ANSWER: 64.326274, 127.014831" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 43.56722, + "lon": 43.58528, + "name": "Chegem" + }, + "point_b": { + "lat": 59.83333, + "lon": 10.43721, + "name": "Asker" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 48.398066, + "lon": 37.454139 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (43.56722°, 43.58528°)", + " Point B: (59.83333°, 10.43721°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 48.398066°", + " Longitude: 37.454139°", + "FINAL ANSWER: 48.398066, 37.454139" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 24.07821, + "lon": 89.63262, + "name": "Bera" + }, + "point_b": { + "lat": -7.83306, + "lon": -35.75472, + "name": "Surubim" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 5.373212, + "lon": -7.249811 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (24.07821°, 89.63262°)", + " Point B: (-7.83306°, -35.75472°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 5.373212°", + " Longitude: -7.249811°", + "FINAL ANSWER: 5.373212, -7.249811" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 52.72247, + "lon": -1.3702, + "name": "Coalville" + }, + "point_b": { + "lat": 18.44134, + "lon": -66.11822, + "name": "Cataño" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 29.772993, + "lon": -55.232114 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (52.72247°, -1.3702°)", + " Point B: (18.44134°, -66.11822°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 29.772993°", + " Longitude: -55.232114°", + "FINAL ANSWER: 29.772993, -55.232114" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 6.74177, + "lon": -7.11742, + "name": "Guézon" + }, + "point_b": { + "lat": 49.81667, + "lon": -119.48333, + "name": "Okanagan Mission" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 25.951337, + "lon": -23.427359 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (6.74177°, -7.11742°)", + " Point B: (49.81667°, -119.48333°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 25.951337°", + " Longitude: -23.427359°", + "FINAL ANSWER: 25.951337, -23.427359" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 50.85023, + "lon": 0.47095, + "name": "Bexhill-on-Sea" + }, + "point_b": { + "lat": 41.40585, + "lon": 2.13243, + "name": "La Bonanova" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 46.131027, + "lon": 1.373075 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (50.85023°, 0.47095°)", + " Point B: (41.40585°, 2.13243°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 46.131027°", + " Longitude: 1.373075°", + "FINAL ANSWER: 46.131027, 1.373075" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 50.58727, + "lon": 8.67554, + "name": "Gießen" + }, + "point_b": { + "lat": -22.38754, + "lon": 26.71077, + "name": "Serowe" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -4.070455, + "lon": 22.96003 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (50.58727°, 8.67554°)", + " Point B: (-22.38754°, 26.71077°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -4.070455°", + " Longitude: 22.960030°", + "FINAL ANSWER: -4.070455, 22.960030" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 14.03507, + "lon": -83.38882, + "name": "Puerto Cabezas" + }, + "point_b": { + "lat": 13.41778, + "lon": -16.66667, + "name": "Faji Kunda" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 15.479846, + "lon": -33.207905 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (14.03507°, -83.38882°)", + " Point B: (13.41778°, -16.66667°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 15.479846°", + " Longitude: -33.207905°", + "FINAL ANSWER: 15.479846, -33.207905" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 39.98483, + "lon": -75.14712, + "name": "Hartranft" + }, + "point_b": { + "lat": 1.40096, + "lon": 34.45038, + "name": "Kapchorwa" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 18.348209, + "lon": 14.366741 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (39.98483°, -75.14712°)", + " Point B: (1.40096°, 34.45038°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 18.348209°", + " Longitude: 14.366741°", + "FINAL ANSWER: 18.348209, 14.366741" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -22.41278, + "lon": -50.57583, + "name": "Paraguaçu Paulista" + }, + "point_b": { + "lat": 11.90112, + "lon": 75.38924, + "name": "Puzhathi" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 0.271405, + "lon": 45.463963 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-22.41278°, -50.57583°)", + " Point B: (11.90112°, 75.38924°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 0.271405°", + " Longitude: 45.463963°", + "FINAL ANSWER: 0.271405, 45.463963" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -31.49285, + "lon": 25.00633, + "name": "Middelburg" + }, + "point_b": { + "lat": 6.09106, + "lon": -75.63569, + "name": "Caldas" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -19.365905, + "lon": -30.596165 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-31.49285°, 25.00633°)", + " Point B: (6.09106°, -75.63569°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -19.365905°", + " Longitude: -30.596165°", + "FINAL ANSWER: -19.365905, -30.596165" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 36.88527, + "lon": 81.52298, + "name": "Siyeke" + }, + "point_b": { + "lat": 40.49014, + "lon": -3.96383, + "name": "Villanueva del Pardillo" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 44.070873, + "lon": 62.635011 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (36.88527°, 81.52298°)", + " Point B: (40.49014°, -3.96383°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 44.070873°", + " Longitude: 62.635011°", + "FINAL ANSWER: 44.070873, 62.635011" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -3.74167, + "lon": -43.36028, + "name": "Chapadinha" + }, + "point_b": { + "lat": -9.58333, + "lon": 33.85, + "name": "Kyela" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -9.579041, + "lon": 14.38072 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-3.74167°, -43.36028°)", + " Point B: (-9.58333°, 33.85°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -9.579041°", + " Longitude: 14.380720°", + "FINAL ANSWER: -9.579041, 14.380720" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -21.2075, + "lon": -159.77546, + "name": "Avarua" + }, + "point_b": { + "lat": -30.3875, + "lon": -56.45139, + "name": "Quaraí" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -31.891203, + "lon": -137.511653 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-21.2075°, -159.77546°)", + " Point B: (-30.3875°, -56.45139°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -31.891203°", + " Longitude: -137.511653°", + "FINAL ANSWER: -31.891203, -137.511653" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -15.61532, + "lon": -43.59187, + "name": "Barreiro do Jaíba" + }, + "point_b": { + "lat": 22.76843, + "lon": -102.58141, + "name": "Zacatecas" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 4.107075, + "lon": -72.381568 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-15.61532°, -43.59187°)", + " Point B: (22.76843°, -102.58141°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 4.107075°", + " Longitude: -72.381568°", + "FINAL ANSWER: 4.107075, -72.381568" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 9.62512, + "lon": 78.62434, + "name": "Ilaiyankudi" + }, + "point_b": { + "lat": -37.9, + "lon": 144.66667, + "name": "Werribee" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -28.544731, + "lon": 124.235029 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (9.62512°, 78.62434°)", + " Point B: (-37.9°, 144.66667°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -28.544731°", + " Longitude: 124.235029°", + "FINAL ANSWER: -28.544731, 124.235029" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -27.25204, + "lon": 152.99226, + "name": "Kallangur" + }, + "point_b": { + "lat": 42.59981, + "lon": -71.36728, + "name": "Chelmsford" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 37.999587, + "lon": -117.801592 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-27.25204°, 152.99226°)", + " Point B: (42.59981°, -71.36728°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 37.999587°", + " Longitude: -117.801592°", + "FINAL ANSWER: 37.999587, -117.801592" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 40.80357, + "lon": 140.40299, + "name": "Tsugaru" + }, + "point_b": { + "lat": -24.80645, + "lon": -65.41999, + "name": "Salta" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 30.321729, + "lon": -120.949548 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (40.80357°, 140.40299°)", + " Point B: (-24.80645°, -65.41999°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 30.321729°", + " Longitude: -120.949548°", + "FINAL ANSWER: 30.321729, -120.949548" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 6.23669, + "lon": 0.99578, + "name": "Dzodze" + }, + "point_b": { + "lat": 45.03341, + "lon": -79.31633, + "name": "Bracebridge" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 41.000475, + "lon": -52.829758 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (6.23669°, 0.99578°)", + " Point B: (45.03341°, -79.31633°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 41.000475°", + " Longitude: -52.829758°", + "FINAL ANSWER: 41.000475, -52.829758" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 44.9279, + "lon": -122.98371, + "name": "Four Corners" + }, + "point_b": { + "lat": -37.2, + "lon": 174.95, + "name": "Pukekohe East" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 25.618894, + "lon": -142.393346 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (44.9279°, -122.98371°)", + " Point B: (-37.2°, 174.95°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 25.618894°", + " Longitude: -142.393346°", + "FINAL ANSWER: 25.618894, -142.393346" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 43.15357, + "lon": -93.20104, + "name": "Mason City" + }, + "point_b": { + "lat": 23.89154, + "lon": 90.40232, + "name": "Tungi" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 71.251708, + "lon": -98.465317 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (43.15357°, -93.20104°)", + " Point B: (23.89154°, 90.40232°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 71.251708°", + " Longitude: -98.465317°", + "FINAL ANSWER: 71.251708, -98.465317" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 41.86505, + "lon": -80.78981, + "name": "Ashtabula" + }, + "point_b": { + "lat": -37.77988, + "lon": 144.92276, + "name": "Ascot Vale" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -18.865937, + "lon": -179.482637 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (41.86505°, -80.78981°)", + " Point B: (-37.77988°, 144.92276°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -18.865937°", + " Longitude: -179.482637°", + "FINAL ANSWER: -18.865937, -179.482637" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 51.65598, + "lon": 7.3453, + "name": "Datteln" + }, + "point_b": { + "lat": -3.36167, + "lon": -39.83167, + "name": "Amontada" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 11.427564, + "lon": -31.415547 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (51.65598°, 7.3453°)", + " Point B: (-3.36167°, -39.83167°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 11.427564°", + " Longitude: -31.415547°", + "FINAL ANSWER: 11.427564, -31.415547" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -21.205, + "lon": -41.88778, + "name": "Itaperuna" + }, + "point_b": { + "lat": 41.64454, + "lon": -0.93349, + "name": "Oliver-Valdefierro" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 10.884123, + "lon": -23.766142 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-21.205°, -41.88778°)", + " Point B: (41.64454°, -0.93349°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 10.884123°", + " Longitude: -23.766142°", + "FINAL ANSWER: 10.884123, -23.766142" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 38.4774, + "lon": 47.0699, + "name": "Ahar" + }, + "point_b": { + "lat": 2.5142, + "lon": -76.84939, + "name": "Villa Rica" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 21.943821, + "lon": -55.33786 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (38.4774°, 47.0699°)", + " Point B: (2.5142°, -76.84939°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 21.943821°", + " Longitude: -55.337860°", + "FINAL ANSWER: 21.943821, -55.337860" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 22.38161, + "lon": 107.3683, + "name": "Chongzuo" + }, + "point_b": { + "lat": -18.16583, + "lon": -47.94639, + "name": "Catalão" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 9.751326, + "lon": 26.155515 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (22.38161°, 107.3683°)", + " Point B: (-18.16583°, -47.94639°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 9.751326°", + " Longitude: 26.155515°", + "FINAL ANSWER: 9.751326, 26.155515" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 38.96667, + "lon": -0.18333, + "name": "Gandia" + }, + "point_b": { + "lat": 30.16356, + "lon": 73.56858, + "name": "Minchianabad" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 40.714695, + "lon": 38.970767 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (38.96667°, -0.18333°)", + " Point B: (30.16356°, 73.56858°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 40.714695°", + " Longitude: 38.970767°", + "FINAL ANSWER: 40.714695, 38.970767" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 40.42386, + "lon": -3.53261, + "name": "San Fernando de Henares" + }, + "point_b": { + "lat": 16.54092, + "lon": 80.80213, + "name": "Gannavaram" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 36.058015, + "lon": 44.567951 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (40.42386°, -3.53261°)", + " Point B: (16.54092°, 80.80213°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 36.058015°", + " Longitude: 44.567951°", + "FINAL ANSWER: 36.058015, 44.567951" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -15.96528, + "lon": -54.96833, + "name": "Jaciara" + }, + "point_b": { + "lat": 6.17591, + "lon": -75.59174, + "name": "Envigado" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -4.974616, + "lon": -65.454704 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-15.96528°, -54.96833°)", + " Point B: (6.17591°, -75.59174°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -4.974616°", + " Longitude: -65.454704°", + "FINAL ANSWER: -4.974616, -65.454704" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 54.11287, + "lon": 102.17773, + "name": "Sayansk" + }, + "point_b": { + "lat": 43.91971, + "lon": 5.05141, + "name": "L'Isle-sur-la-Sorgue" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 60.081344, + "lon": 76.926284 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (54.11287°, 102.17773°)", + " Point B: (43.91971°, 5.05141°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 60.081344°", + " Longitude: 76.926284°", + "FINAL ANSWER: 60.081344, 76.926284" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -0.45275, + "lon": 39.64601, + "name": "Garissa" + }, + "point_b": { + "lat": 32.23341, + "lon": 106.30126, + "name": "Donghe" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 9.489065, + "lon": 54.316177 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-0.45275°, 39.64601°)", + " Point B: (32.23341°, 106.30126°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 9.489065°", + " Longitude: 54.316177°", + "FINAL ANSWER: 9.489065, 54.316177" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 37.29548, + "lon": 14.84058, + "name": "Scordia" + }, + "point_b": { + "lat": 29.45679, + "lon": 119.88872, + "name": "Puyang" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 40.968986, + "lon": 98.547766 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (37.29548°, 14.84058°)", + " Point B: (29.45679°, 119.88872°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 40.968986°", + " Longitude: 98.547766°", + "FINAL ANSWER: 40.968986, 98.547766" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -16.43389, + "lon": -41.00333, + "name": "Jequitinhonha" + }, + "point_b": { + "lat": 35.75647, + "lon": -83.97046, + "name": "Maryville" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -3.080789, + "lon": -50.930363 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-16.43389°, -41.00333°)", + " Point B: (35.75647°, -83.97046°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -3.080789°", + " Longitude: -50.930363°", + "FINAL ANSWER: -3.080789, -50.930363" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -13.83333, + "lon": -171.76666, + "name": "Apia" + }, + "point_b": { + "lat": -3.35, + "lon": 37.33333, + "name": "Moshi" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -28.00647, + "lon": 151.889236 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-13.83333°, -171.76666°)", + " Point B: (-3.35°, 37.33333°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -28.006470°", + " Longitude: 151.889236°", + "FINAL ANSWER: -28.006470, 151.889236" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 34.37002, + "lon": 73.47082, + "name": "Muzaffarābād" + }, + "point_b": { + "lat": 13.35861, + "lon": 123.73361, + "name": "Tabaco" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 30.917104, + "lon": 87.729932 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (34.37002°, 73.47082°)", + " Point B: (13.35861°, 123.73361°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 30.917104°", + " Longitude: 87.729932°", + "FINAL ANSWER: 30.917104, 87.729932" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 0.06968, + "lon": 42.74497, + "name": "Jamaame" + }, + "point_b": { + "lat": -3.13901, + "lon": -44.32519, + "name": "Santa Rita" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -2.829575, + "lon": -22.527845 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (0.06968°, 42.74497°)", + " Point B: (-3.13901°, -44.32519°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -2.829575°", + " Longitude: -22.527845°", + "FINAL ANSWER: -2.829575, -22.527845" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 53.14118, + "lon": 8.21467, + "name": "Oldenburg" + }, + "point_b": { + "lat": -9.44666, + "lon": 159.94549, + "name": "Tandai" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 68.197528, + "lon": 71.889522 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (53.14118°, 8.21467°)", + " Point B: (-9.44666°, 159.94549°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 68.197528°", + " Longitude: 71.889522°", + "FINAL ANSWER: 68.197528, 71.889522" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 6.97647, + "lon": -7.79834, + "name": "Zou" + }, + "point_b": { + "lat": 10.3121, + "lon": 39.65888, + "name": "Mehal Mēda" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 9.428779, + "lon": 15.818786 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (6.97647°, -7.79834°)", + " Point B: (10.3121°, 39.65888°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 9.428779°", + " Longitude: 15.818786°", + "FINAL ANSWER: 9.428779, 15.818786" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -8.23333, + "lon": -35.79694, + "name": "Bezerros" + }, + "point_b": { + "lat": 6.80619, + "lon": 29.67742, + "name": "Rumbek" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -0.848298, + "lon": -2.999199 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-8.23333°, -35.79694°)", + " Point B: (6.80619°, 29.67742°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -0.848298°", + " Longitude: -2.999199°", + "FINAL ANSWER: -0.848298, -2.999199" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -12.56598, + "lon": 16.22589, + "name": "Catchiungo" + }, + "point_b": { + "lat": 10.85009, + "lon": 8.199, + "name": "Dutsen Wai" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 4.998049, + "lon": 10.217422 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-12.56598°, 16.22589°)", + " Point B: (10.85009°, 8.199°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 4.998049°", + " Longitude: 10.217422°", + "FINAL ANSWER: 4.998049, 10.217422" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -13.45836, + "lon": 25.8338, + "name": "Kasempa" + }, + "point_b": { + "lat": -46.4, + "lon": 168.35, + "name": "Invercargill" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -62.75257, + "lon": 127.969201 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-13.45836°, 25.8338°)", + " Point B: (-46.4°, 168.35°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -62.752570°", + " Longitude: 127.969201°", + "FINAL ANSWER: -62.752570, 127.969201" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 29.96207, + "lon": 105.88678, + "name": "Xiaodu" + }, + "point_b": { + "lat": 30.42881, + "lon": -87.17997, + "name": "East Pensacola Heights" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 58.367148, + "lon": 117.921782 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (29.96207°, 105.88678°)", + " Point B: (30.42881°, -87.17997°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 58.367148°", + " Longitude: 117.921782°", + "FINAL ANSWER: 58.367148, 117.921782" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 26.74134, + "lon": 83.88689, + "name": "Kushinagar" + }, + "point_b": { + "lat": 6.76229, + "lon": -6.8638, + "name": "Zoukougbeu" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 27.03223, + "lon": 59.287323 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (26.74134°, 83.88689°)", + " Point B: (6.76229°, -6.8638°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 27.032230°", + " Longitude: 59.287323°", + "FINAL ANSWER: 27.032230, 59.287323" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -7.35833, + "lon": -35.89833, + "name": "Queimadas" + }, + "point_b": { + "lat": 19.2366, + "lon": -104.56512, + "name": "Cihuatlán" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 7.179284, + "lon": -69.269646 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-7.35833°, -35.89833°)", + " Point B: (19.2366°, -104.56512°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 7.179284°", + " Longitude: -69.269646°", + "FINAL ANSWER: 7.179284, -69.269646" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 38.91144, + "lon": -90.15066, + "name": "Upper Alton" + }, + "point_b": { + "lat": 9.67813, + "lon": -68.97278, + "name": "San Rafael de Onoto" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 24.660652, + "lon": -78.300972 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (38.91144°, -90.15066°)", + " Point B: (9.67813°, -68.97278°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 24.660652°", + " Longitude: -78.300972°", + "FINAL ANSWER: 24.660652, -78.300972" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 55.66613, + "lon": 12.51388, + "name": "Valby" + }, + "point_b": { + "lat": -31.88822, + "lon": 115.87186, + "name": "Dianella" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 41.491154, + "lon": 54.911492 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (55.66613°, 12.51388°)", + " Point B: (-31.88822°, 115.87186°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 41.491154°", + " Longitude: 54.911492°", + "FINAL ANSWER: 41.491154, 54.911492" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 36.12232, + "lon": 0.89865, + "name": "Mazouna" + }, + "point_b": { + "lat": 40.00989, + "lon": -75.16387, + "name": "Nicetown-Tioga" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 44.125138, + "lon": -56.337589 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (36.12232°, 0.89865°)", + " Point B: (40.00989°, -75.16387°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 44.125138°", + " Longitude: -56.337589°", + "FINAL ANSWER: 44.125138, -56.337589" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 28.13328, + "lon": 82.29803, + "name": "Tulsi̇̄pur" + }, + "point_b": { + "lat": -23.54771, + "lon": -46.63145, + "name": "Se" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 5.302142, + "lon": 15.509056 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (28.13328°, 82.29803°)", + " Point B: (-23.54771°, -46.63145°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 5.302142°", + " Longitude: 15.509056°", + "FINAL ANSWER: 5.302142, 15.509056" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 24.80418, + "lon": 88.94875, + "name": "Pār Naogaon" + }, + "point_b": { + "lat": -19.61806, + "lon": -44.04306, + "name": "Pedro Leopoldo" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -7.738582, + "lon": -11.055643 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (24.80418°, 88.94875°)", + " Point B: (-19.61806°, -44.04306°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -7.738582°", + " Longitude: -11.055643°", + "FINAL ANSWER: -7.738582, -11.055643" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 31.89385, + "lon": 35.01504, + "name": "Modi‘in Makkabbim Re‘ut" + }, + "point_b": { + "lat": 51.14942, + "lon": 15.00835, + "name": "Zgorzelec" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 41.947659, + "lon": 26.529254 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (31.89385°, 35.01504°)", + " Point B: (51.14942°, 15.00835°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 41.947659°", + " Longitude: 26.529254°", + "FINAL ANSWER: 41.947659, 26.529254" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 38.82378, + "lon": -9.09719, + "name": "São João da Talha" + }, + "point_b": { + "lat": 49.98111, + "lon": 92.06667, + "name": "Ulaangom" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 56.893223, + "lon": 65.988449 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (38.82378°, -9.09719°)", + " Point B: (49.98111°, 92.06667°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 56.893223°", + " Longitude: 65.988449°", + "FINAL ANSWER: 56.893223, 65.988449" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 2.35, + "lon": 102.876, + "name": "Kampung Selang" + }, + "point_b": { + "lat": 26.31008, + "lon": -80.23727, + "name": "Parkland" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 63.651213, + "lon": -89.179904 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (2.35°, 102.876°)", + " Point B: (26.31008°, -80.23727°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 63.651213°", + " Longitude: -89.179904°", + "FINAL ANSWER: 63.651213, -89.179904" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 14.78869, + "lon": 120.99889, + "name": "Loma de Gato" + }, + "point_b": { + "lat": 18.47186, + "lon": -69.89232, + "name": "Santo Domingo" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 51.924033, + "lon": -87.703003 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (14.78869°, 120.99889°)", + " Point B: (18.47186°, -69.89232°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 51.924033°", + " Longitude: -87.703003°", + "FINAL ANSWER: 51.924033, -87.703003" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -6.63889, + "lon": -79.78889, + "name": "Ferreñafe" + }, + "point_b": { + "lat": 36.53628, + "lon": 3.8334, + "name": "Draa el Mizan" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 19.62727, + "lon": -43.37569 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-6.63889°, -79.78889°)", + " Point B: (36.53628°, 3.8334°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 19.627270°", + " Longitude: -43.375690°", + "FINAL ANSWER: 19.627270, -43.375690" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 40.79944, + "lon": 30.74806, + "name": "Hendek" + }, + "point_b": { + "lat": 19.42155, + "lon": -98.95038, + "name": "Santa María Chimalhuacán" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 53.03816, + "lon": -47.224579 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (40.79944°, 30.74806°)", + " Point B: (19.42155°, -98.95038°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 53.038160°", + " Longitude: -47.224579°", + "FINAL ANSWER: 53.038160, -47.224579" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 53.70177, + "lon": 9.99328, + "name": "Norderstedt" + }, + "point_b": { + "lat": 40.94149, + "lon": -73.10594, + "name": "East Setauket" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 56.848522, + "lon": -13.373339 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (53.70177°, 9.99328°)", + " Point B: (40.94149°, -73.10594°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 56.848522°", + " Longitude: -13.373339°", + "FINAL ANSWER: 56.848522, -13.373339" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 33.27362, + "lon": 129.87877, + "name": "Imarichō-kō" + }, + "point_b": { + "lat": -34.7302, + "lon": -56.21915, + "name": "Las Piedras" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -13.276273, + "lon": -152.315466 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (33.27362°, 129.87877°)", + " Point B: (-34.7302°, -56.21915°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -13.276273°", + " Longitude: -152.315466°", + "FINAL ANSWER: -13.276273, -152.315466" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 33.78333, + "lon": 130.98333, + "name": "Kanda" + }, + "point_b": { + "lat": 11.46077, + "lon": -69.5657, + "name": "La Vela de Coro" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 40.967886, + "lon": -85.540226 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (33.78333°, 130.98333°)", + " Point B: (11.46077°, -69.5657°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 40.967886°", + " Longitude: -85.540226°", + "FINAL ANSWER: 40.967886, -85.540226" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 32.62639, + "lon": 116.99694, + "name": "Huainan" + }, + "point_b": { + "lat": 17.70217, + "lon": 33.98638, + "name": "Atbara" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 34.39207, + "lon": 94.612725 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (32.62639°, 116.99694°)", + " Point B: (17.70217°, 33.98638°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 34.392070°", + " Longitude: 94.612725°", + "FINAL ANSWER: 34.392070, 94.612725" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 19.58893, + "lon": -96.93727, + "name": "Banderilla" + }, + "point_b": { + "lat": 58.46151, + "lon": 8.77253, + "name": "Arendal" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 60.628279, + "lon": -31.72284 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (19.58893°, -96.93727°)", + " Point B: (58.46151°, 8.77253°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 60.628279°", + " Longitude: -31.722840°", + "FINAL ANSWER: 60.628279, -31.722840" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 34.13333, + "lon": 118.43333, + "name": "Shaodian" + }, + "point_b": { + "lat": -4.87778, + "lon": -80.70528, + "name": "Marcavelica" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 54.004142, + "lon": -132.395599 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (34.13333°, 118.43333°)", + " Point B: (-4.87778°, -80.70528°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 54.004142°", + " Longitude: -132.395599°", + "FINAL ANSWER: 54.004142, -132.395599" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 30.53629, + "lon": 120.68638, + "name": "Haining" + }, + "point_b": { + "lat": -16.3775, + "lon": -39.58028, + "name": "Eunápolis" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 34.694435, + "lon": 23.338317 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (30.53629°, 120.68638°)", + " Point B: (-16.3775°, -39.58028°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 34.694435°", + " Longitude: 23.338317°", + "FINAL ANSWER: 34.694435, 23.338317" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -37.57742, + "lon": 144.72607, + "name": "Sunbury" + }, + "point_b": { + "lat": 32.45861, + "lon": 130.19306, + "name": "Amakusa" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -2.580079, + "lon": 137.230751 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-37.57742°, 144.72607°)", + " Point B: (32.45861°, 130.19306°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -2.580079°", + " Longitude: 137.230751°", + "FINAL ANSWER: -2.580079, 137.230751" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 17.47531, + "lon": 103.45753, + "name": "Sawang Daen Din" + }, + "point_b": { + "lat": 38.84622, + "lon": -77.30637, + "name": "Fairfax" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 69.756962, + "lon": -78.606652 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (17.47531°, 103.45753°)", + " Point B: (38.84622°, -77.30637°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 69.756962°", + " Longitude: -78.606652°", + "FINAL ANSWER: 69.756962, -78.606652" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 27.67658, + "lon": 85.31417, + "name": "Pātan" + }, + "point_b": { + "lat": 59.73833, + "lon": 30.08944, + "name": "Krasnoye Selo" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 46.877211, + "lon": 65.876892 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (27.67658°, 85.31417°)", + " Point B: (59.73833°, 30.08944°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 46.877211°", + " Longitude: 65.876892°", + "FINAL ANSWER: 46.877211, 65.876892" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -8.3, + "lon": 31.51667, + "name": "Matai" + }, + "point_b": { + "lat": 53.14636, + "lon": 29.20552, + "name": "Bobruysk" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 7.063723, + "lon": 31.095441 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-8.3°, 31.51667°)", + " Point B: (53.14636°, 29.20552°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 7.063723°", + " Longitude: 31.095441°", + "FINAL ANSWER: 7.063723, 31.095441" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 43.8245, + "lon": 11.13027, + "name": "Campi Bisenzio" + }, + "point_b": { + "lat": -7.19722, + "lon": -59.89139, + "name": "Apuí" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 7.643782, + "lon": -45.854088 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (43.8245°, 11.13027°)", + " Point B: (-7.19722°, -59.89139°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 7.643782°", + " Longitude: -45.854088°", + "FINAL ANSWER: 7.643782, -45.854088" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -1.165, + "lon": 15.97, + "name": "Oyo" + }, + "point_b": { + "lat": -20.2215, + "lon": 57.53431, + "name": "Saint Pierre" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -6.388492, + "lon": 25.916107 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-1.165°, 15.97°)", + " Point B: (-20.2215°, 57.53431°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -6.388492°", + " Longitude: 25.916107°", + "FINAL ANSWER: -6.388492, 25.916107" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 24.56924, + "lon": 80.58809, + "name": "Nāgod" + }, + "point_b": { + "lat": 14.70413, + "lon": -91.86426, + "name": "Coatepeque" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 48.86385, + "lon": -82.528514 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (24.56924°, 80.58809°)", + " Point B: (14.70413°, -91.86426°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 48.863850°", + " Longitude: -82.528514°", + "FINAL ANSWER: 48.863850, -82.528514" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -24.56694, + "lon": -51.33333, + "name": "Cândido de Abreu" + }, + "point_b": { + "lat": 40.4084, + "lon": -80.53924, + "name": "Weirton Heights" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 8.179469, + "lon": -64.61403 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-24.56694°, -51.33333°)", + " Point B: (40.4084°, -80.53924°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 8.179469°", + " Longitude: -64.614030°", + "FINAL ANSWER: 8.179469, -64.614030" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 35.84562, + "lon": -86.39027, + "name": "Murfreesboro" + }, + "point_b": { + "lat": 7.07306, + "lon": 125.61278, + "name": "Davao" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 53.374638, + "lon": -179.760146 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (35.84562°, -86.39027°)", + " Point B: (7.07306°, 125.61278°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 53.374638°", + " Longitude: -179.760146°", + "FINAL ANSWER: 53.374638, -179.760146" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 27.17749, + "lon": 82.93442, + "name": "Bānsi" + }, + "point_b": { + "lat": 44.39982, + "lon": 131.14775, + "name": "Suifenhe" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 38.268582, + "lon": 104.244374 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (27.17749°, 82.93442°)", + " Point B: (44.39982°, 131.14775°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 38.268582°", + " Longitude: 104.244374°", + "FINAL ANSWER: 38.268582, 104.244374" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 39.92083, + "lon": 33.23083, + "name": "Elmadağ" + }, + "point_b": { + "lat": 50.79899, + "lon": -1.09125, + "name": "Portsmouth" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 43.546073, + "lon": 25.933642 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (39.92083°, 33.23083°)", + " Point B: (50.79899°, -1.09125°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 43.546073°", + " Longitude: 25.933642°", + "FINAL ANSWER: 43.546073, 25.933642" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 21.47831, + "lon": -101.21566, + "name": "San Felipe" + }, + "point_b": { + "lat": 20.52933, + "lon": 76.18457, + "name": "Buldāna" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 86.585621, + "lon": -4.538804 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (21.47831°, -101.21566°)", + " Point B: (20.52933°, 76.18457°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 86.585621°", + " Longitude: -4.538804°", + "FINAL ANSWER: 86.585621, -4.538804" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 29.44964, + "lon": 74.10093, + "name": "Pilibangan" + }, + "point_b": { + "lat": 4.80048, + "lon": 18.12747, + "name": "Boali" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 19.223681, + "lon": 44.065357 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (29.44964°, 74.10093°)", + " Point B: (4.80048°, 18.12747°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 19.223681°", + " Longitude: 44.065357°", + "FINAL ANSWER: 19.223681, 44.065357" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 47.79941, + "lon": 13.04399, + "name": "Salzburg" + }, + "point_b": { + "lat": 40.43553, + "lon": 71.76721, + "name": "Kirguli" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 48.032824, + "lon": 44.416112 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (47.79941°, 13.04399°)", + " Point B: (40.43553°, 71.76721°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 48.032824°", + " Longitude: 44.416112°", + "FINAL ANSWER: 48.032824, 44.416112" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 13.40417, + "lon": -16.65583, + "name": "Abuko" + }, + "point_b": { + "lat": -13.85875, + "lon": -40.08512, + "name": "Jequié" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -7.082103, + "lon": -34.135204 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (13.40417°, -16.65583°)", + " Point B: (-13.85875°, -40.08512°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -7.082103°", + " Longitude: -34.135204°", + "FINAL ANSWER: -7.082103, -34.135204" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -8.85, + "lon": 34.83333, + "name": "Makumbako" + }, + "point_b": { + "lat": 7.66638, + "lon": -76.68106, + "name": "Chigorodó" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -5.600185, + "lon": 6.71221 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-8.85°, 34.83333°)", + " Point B: (7.66638°, -76.68106°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -5.600185°", + " Longitude: 6.712210°", + "FINAL ANSWER: -5.600185, 6.712210" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 48.62605, + "lon": 2.60125, + "name": "Moissy-Cramayel" + }, + "point_b": { + "lat": 40.53694, + "lon": 17.43723, + "name": "Grottaglie" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 42.730718, + "lon": 14.107237 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (48.62605°, 2.60125°)", + " Point B: (40.53694°, 17.43723°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 42.730718°", + " Longitude: 14.107237°", + "FINAL ANSWER: 42.730718, 14.107237" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 50.25926, + "lon": 14.51759, + "name": "Neratovice" + }, + "point_b": { + "lat": 19.03833, + "lon": 109.84, + "name": "Yinggen" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 45.109649, + "lon": 74.144078 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (50.25926°, 14.51759°)", + " Point B: (19.03833°, 109.84°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 45.109649°", + " Longitude: 74.144078°", + "FINAL ANSWER: 45.109649, 74.144078" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 40.20686, + "lon": -8.41996, + "name": "Coimbra" + }, + "point_b": { + "lat": 21.88262, + "lon": -102.2843, + "name": "Aguascalientes" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 43.87179, + "lon": -34.629156 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (40.20686°, -8.41996°)", + " Point B: (21.88262°, -102.2843°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 43.871790°", + " Longitude: -34.629156°", + "FINAL ANSWER: 43.871790, -34.629156" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 17.50914, + "lon": -91.98125, + "name": "Palenque" + }, + "point_b": { + "lat": -23.68889, + "lon": -49.83389, + "name": "Siqueira Campos" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -3.310764, + "lon": -71.355509 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (17.50914°, -91.98125°)", + " Point B: (-23.68889°, -49.83389°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -3.310764°", + " Longitude: -71.355509°", + "FINAL ANSWER: -3.310764, -71.355509" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -22.43194, + "lon": -46.95778, + "name": "Mogi Mirim" + }, + "point_b": { + "lat": -5.4854, + "lon": 28.21601, + "name": "Kalima" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -12.017507, + "lon": 10.631994 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-22.43194°, -46.95778°)", + " Point B: (-5.4854°, 28.21601°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -12.017507°", + " Longitude: 10.631994°", + "FINAL ANSWER: -12.017507, 10.631994" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 6.98918, + "lon": 79.89167, + "name": "Wattala" + }, + "point_b": { + "lat": 30.26361, + "lon": 78.00862, + "name": "Clement Town" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 12.809315, + "lon": 79.46374 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (6.98918°, 79.89167°)", + " Point B: (30.26361°, 78.00862°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 12.809315°", + " Longitude: 79.463740°", + "FINAL ANSWER: 12.809315, 79.463740" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 36.3012, + "lon": 127.568, + "name": "Okcheon" + }, + "point_b": { + "lat": -6.6922, + "lon": 111.4527, + "name": "Lasem" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 25.689582, + "lon": 122.71372 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (36.3012°, 127.568°)", + " Point B: (-6.6922°, 111.4527°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 25.689582°", + " Longitude: 122.713720°", + "FINAL ANSWER: 25.689582, 122.713720" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 41.84559, + "lon": -87.75394, + "name": "Cicero" + }, + "point_b": { + "lat": -0.75333, + "lon": -48.51667, + "name": "Salvaterra" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 32.25619, + "lon": -75.193219 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (41.84559°, -87.75394°)", + " Point B: (-0.75333°, -48.51667°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 32.256190°", + " Longitude: -75.193219°", + "FINAL ANSWER: 32.256190, -75.193219" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 14.17309, + "lon": -16.84929, + "name": "Joal" + }, + "point_b": { + "lat": -6.55833, + "lon": -35.74167, + "name": "Araruna" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 9.047278, + "lon": -21.69903 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (14.17309°, -16.84929°)", + " Point B: (-6.55833°, -35.74167°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 9.047278°", + " Longitude: -21.699030°", + "FINAL ANSWER: 9.047278, -21.699030" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 33.09179, + "lon": -97.04668, + "name": "Highland Village" + }, + "point_b": { + "lat": -23.2325, + "lon": -51.66556, + "name": "Astorga" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 5.339911, + "lon": -73.250094 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (33.09179°, -97.04668°)", + " Point B: (-23.2325°, -51.66556°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 5.339911°", + " Longitude: -73.250094°", + "FINAL ANSWER: 5.339911, -73.250094" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 10.88606, + "lon": -72.8487, + "name": "Fonseca" + }, + "point_b": { + "lat": 59.46529, + "lon": 24.98215, + "name": "Maardu" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 28.798128, + "lon": -60.838181 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (10.88606°, -72.8487°)", + " Point B: (59.46529°, 24.98215°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 28.798128°", + " Longitude: -60.838181°", + "FINAL ANSWER: 28.798128, -60.838181" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 23.83238, + "lon": 71.6047, + "name": "Rādhanpur" + }, + "point_b": { + "lat": 12.47554, + "lon": 15.43647, + "name": "Massaguet" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 20.384874, + "lon": 42.523913 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (23.83238°, 71.6047°)", + " Point B: (12.47554°, 15.43647°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 20.384874°", + " Longitude: 42.523913°", + "FINAL ANSWER: 20.384874, 42.523913" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 1.53333, + "lon": 103.66667, + "name": "Mukim Pulai" + }, + "point_b": { + "lat": 43.75503, + "lon": -79.33018, + "name": "Parkwoods-Donalda" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 68.643973, + "lon": 111.393264 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (1.53333°, 103.66667°)", + " Point B: (43.75503°, -79.33018°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 68.643973°", + " Longitude: 111.393264°", + "FINAL ANSWER: 68.643973, 111.393264" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 36.2126, + "lon": 57.68191, + "name": "Sabzevar" + }, + "point_b": { + "lat": 7.46478, + "lon": 5.42333, + "name": "Ise-Ekiti" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 24.027686, + "lon": 28.668597 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (36.2126°, 57.68191°)", + " Point B: (7.46478°, 5.42333°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 24.027686°", + " Longitude: 28.668597°", + "FINAL ANSWER: 24.027686, 28.668597" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 42.85842, + "lon": -70.93005, + "name": "Amesbury" + }, + "point_b": { + "lat": 21.16813, + "lon": -102.46097, + "name": "Jalostotitlán" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 32.993982, + "lon": -88.632181 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (42.85842°, -70.93005°)", + " Point B: (21.16813°, -102.46097°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 32.993982°", + " Longitude: -88.632181°", + "FINAL ANSWER: 32.993982, -88.632181" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 52.58514, + "lon": -2.05934, + "name": "Willenhall" + }, + "point_b": { + "lat": 35.87278, + "lon": 10.53722, + "name": "Kelaa Kebira" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 40.166954, + "lon": 8.009777 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (52.58514°, -2.05934°)", + " Point B: (35.87278°, 10.53722°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 40.166954°", + " Longitude: 8.009777°", + "FINAL ANSWER: 40.166954, 8.009777" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 38.23532, + "lon": 125.76244, + "name": "Sinwŏn-ŭp" + }, + "point_b": { + "lat": 52.20333, + "lon": 4.39861, + "name": "Katwijk aan Zee" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 63.072798, + "lon": 34.251819 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (38.23532°, 125.76244°)", + " Point B: (52.20333°, 4.39861°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 63.072798°", + " Longitude: 34.251819°", + "FINAL ANSWER: 63.072798, 34.251819" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 42.52565, + "lon": -71.09533, + "name": "Reading" + }, + "point_b": { + "lat": 34.31, + "lon": -2.16, + "name": "Jerada" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 43.867853, + "lon": -34.388577 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (42.52565°, -71.09533°)", + " Point B: (34.31°, -2.16°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 43.867853°", + " Longitude: -34.388577°", + "FINAL ANSWER: 43.867853, -34.388577" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 37.28766, + "lon": -6.0541, + "name": "Coria del Río" + }, + "point_b": { + "lat": -37.70462, + "lon": 145.10302, + "name": "Greensborough" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -0.836988, + "lon": 68.902484 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (37.28766°, -6.0541°)", + " Point B: (-37.70462°, 145.10302°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -0.836988°", + " Longitude: 68.902484°", + "FINAL ANSWER: -0.836988, 68.902484" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 42.97096, + "lon": 132.41035, + "name": "Fokino" + }, + "point_b": { + "lat": 33.5594, + "lon": 75.23222, + "name": "Dooru Verinag" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 43.475196, + "lon": 116.970427 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (42.97096°, 132.41035°)", + " Point B: (33.5594°, 75.23222°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 43.475196°", + " Longitude: 116.970427°", + "FINAL ANSWER: 43.475196, 116.970427" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 11.84326, + "lon": 75.54368, + "name": "Mangattidam" + }, + "point_b": { + "lat": 6.90418, + "lon": -6.24347, + "name": "Gonaté" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 10.232829, + "lon": 13.85725 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (11.84326°, 75.54368°)", + " Point B: (6.90418°, -6.24347°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 10.232829°", + " Longitude: 13.857250°", + "FINAL ANSWER: 10.232829, 13.857250" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -26.9033, + "lon": 27.45727, + "name": "Parys" + }, + "point_b": { + "lat": 53.54899, + "lon": -2.52464, + "name": "Westhoughton" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 33.963296, + "lon": 8.698963 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-26.9033°, 27.45727°)", + " Point B: (53.54899°, -2.52464°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 33.963296°", + " Longitude: 8.698963°", + "FINAL ANSWER: 33.963296, 8.698963" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -12.24667, + "lon": 40.12083, + "name": "Macomia" + }, + "point_b": { + "lat": 45.64789, + "lon": 10.26487, + "name": "Lumezzane" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 31.731666, + "lon": 20.357112 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-12.24667°, 40.12083°)", + " Point B: (45.64789°, 10.26487°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 31.731666°", + " Longitude: 20.357112°", + "FINAL ANSWER: 31.731666, 20.357112" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 22.24411, + "lon": 114.14616, + "name": "South Horizons (Estate)" + }, + "point_b": { + "lat": 13.77678, + "lon": 100.579, + "name": "Huai Khwang" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 15.978216, + "lon": 103.852783 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (22.24411°, 114.14616°)", + " Point B: (13.77678°, 100.579°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 15.978216°", + " Longitude: 103.852783°", + "FINAL ANSWER: 15.978216, 103.852783" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 22.00265, + "lon": 100.7697, + "name": "Jinghong" + }, + "point_b": { + "lat": -37.80639, + "lon": 145.03086, + "name": "Kew" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 6.8486, + "lon": 111.235689 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (22.00265°, 100.7697°)", + " Point B: (-37.80639°, 145.03086°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 6.848600°", + " Longitude: 111.235689°", + "FINAL ANSWER: 6.848600, 111.235689" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -7.31111, + "lon": -39.30417, + "name": "Barbalha" + }, + "point_b": { + "lat": 5.44266, + "lon": 100.42972, + "name": "Sungai Dua" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 1.662154, + "lon": 65.571032 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-7.31111°, -39.30417°)", + " Point B: (5.44266°, 100.42972°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 1.662154°", + " Longitude: 65.571032°", + "FINAL ANSWER: 1.662154, 65.571032" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 38.21741, + "lon": 27.64744, + "name": "Bayındır" + }, + "point_b": { + "lat": -28.64397, + "lon": -53.60633, + "name": "Cruz Alta" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 23.740979, + "lon": 3.313319 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (38.21741°, 27.64744°)", + " Point B: (-28.64397°, -53.60633°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 23.740979°", + " Longitude: 3.313319°", + "FINAL ANSWER: 23.740979, 3.313319" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 26.8912, + "lon": 80.21149, + "name": "Bāngarmau" + }, + "point_b": { + "lat": 22.20179, + "lon": -84.08484, + "name": "Guane" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 52.048867, + "lon": -68.579978 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (26.8912°, 80.21149°)", + " Point B: (22.20179°, -84.08484°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 52.048867°", + " Longitude: -68.579978°", + "FINAL ANSWER: 52.048867, -68.579978" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 42.46806, + "lon": 140.86806, + "name": "Date" + }, + "point_b": { + "lat": 28.69919, + "lon": 30.7673, + "name": "Al ‘Idwah" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 51.105734, + "lon": 78.771357 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (42.46806°, 140.86806°)", + " Point B: (28.69919°, 30.7673°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 51.105734°", + " Longitude: 78.771357°", + "FINAL ANSWER: 51.105734, 78.771357" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 30.17922, + "lon": 31.2056, + "name": "Qalyub" + }, + "point_b": { + "lat": 11.72745, + "lon": 75.55509, + "name": "Chockli" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 17.359611, + "lon": 65.496389 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (30.17922°, 31.2056°)", + " Point B: (11.72745°, 75.55509°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 17.359611°", + " Longitude: 65.496389°", + "FINAL ANSWER: 17.359611, 65.496389" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 10.65, + "lon": -9.88333, + "name": "Kouroussa" + }, + "point_b": { + "lat": -8.35806, + "lon": -42.24667, + "name": "São João do Piauí" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 5.981127, + "lon": -18.072126 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (10.65°, -9.88333°)", + " Point B: (-8.35806°, -42.24667°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 5.981127°", + " Longitude: -18.072126°", + "FINAL ANSWER: 5.981127, -18.072126" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 9.91246, + "lon": -67.35398, + "name": "San Juan de los Morros" + }, + "point_b": { + "lat": -7.1872, + "lon": 113.2394, + "name": "Sampang" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 36.016118, + "lon": 123.674895 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (9.91246°, -67.35398°)", + " Point B: (-7.1872°, 113.2394°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 36.016118°", + " Longitude: 123.674895°", + "FINAL ANSWER: 36.016118, 123.674895" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -12.41713, + "lon": -41.77049, + "name": "Seabra" + }, + "point_b": { + "lat": 45.66651, + "lon": -122.56093, + "name": "Orchards" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 35.852819, + "lon": -94.666674 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-12.41713°, -41.77049°)", + " Point B: (45.66651°, -122.56093°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 35.852819°", + " Longitude: -94.666674°", + "FINAL ANSWER: 35.852819, -94.666674" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 21.00153, + "lon": -100.38416, + "name": "San José Iturbide" + }, + "point_b": { + "lat": 6.98789, + "lon": -73.04953, + "name": "Piedecuesta" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 17.819635, + "lon": -93.206516 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (21.00153°, -100.38416°)", + " Point B: (6.98789°, -73.04953°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 17.819635°", + " Longitude: -93.206516°", + "FINAL ANSWER: 17.819635, -93.206516" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 48.79993, + "lon": 2.33256, + "name": "Arcueil" + }, + "point_b": { + "lat": -1.77111, + "lon": -47.43806, + "name": "Irituia" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 25.523552, + "lon": -27.999166 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (48.79993°, 2.33256°)", + " Point B: (-1.77111°, -47.43806°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 25.523552°", + " Longitude: -27.999166°", + "FINAL ANSWER: 25.523552, -27.999166" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -7.00906, + "lon": 23.45278, + "name": "Mwene-Ditu" + }, + "point_b": { + "lat": -19.33018, + "lon": 48.97791, + "name": "Vatomandry" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -10.309356, + "lon": 29.606262 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-7.00906°, 23.45278°)", + " Point B: (-19.33018°, 48.97791°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -10.309356°", + " Longitude: 29.606262°", + "FINAL ANSWER: -10.309356, 29.606262" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 40.24147, + "lon": -3.69999, + "name": "Pinto" + }, + "point_b": { + "lat": 17.03795, + "lon": 81.77597, + "name": "Katheru" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 40.978791, + "lon": 21.298362 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (40.24147°, -3.69999°)", + " Point B: (17.03795°, 81.77597°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 40.978791°", + " Longitude: 21.298362°", + "FINAL ANSWER: 40.978791, 21.298362" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 0.9592, + "lon": -79.65397, + "name": "Esmeraldas" + }, + "point_b": { + "lat": -7.58333, + "lon": 31.26667, + "name": "Chala" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -2.745213, + "lon": -52.17905 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (0.9592°, -79.65397°)", + " Point B: (-7.58333°, 31.26667°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -2.745213°", + " Longitude: -52.179050°", + "FINAL ANSWER: -2.745213, -52.179050" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 25.26328, + "lon": 87.23264, + "name": "Colgong" + }, + "point_b": { + "lat": 12.561, + "lon": 75.38741, + "name": "Sullya" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 19.006227, + "lon": 81.083363 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (25.26328°, 87.23264°)", + " Point B: (12.561°, 75.38741°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 19.006227°", + " Longitude: 81.083363°", + "FINAL ANSWER: 19.006227, 81.083363" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 7.7782, + "lon": 81.6038, + "name": "Eravur Town" + }, + "point_b": { + "lat": 2.74899, + "lon": 98.3127, + "name": "Sidikalang" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 6.566397, + "lon": 85.808397 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (7.7782°, 81.6038°)", + " Point B: (2.74899°, 98.3127°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 6.566397°", + " Longitude: 85.808397°", + "FINAL ANSWER: 6.566397, 85.808397" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 41.14389, + "lon": -8.64639, + "name": "Afurada de Baixo" + }, + "point_b": { + "lat": 10.215, + "lon": 123.03528, + "name": "Tinongan" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 52.772104, + "lon": 29.383133 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (41.14389°, -8.64639°)", + " Point B: (10.215°, 123.03528°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 52.772104°", + " Longitude: 29.383133°", + "FINAL ANSWER: 52.772104, 29.383133" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -24.18472, + "lon": -53.0275, + "name": "Goioerê" + }, + "point_b": { + "lat": 14.4605, + "lon": 5.2437, + "name": "Illéla" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -5.561527, + "lon": -22.93941 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-24.18472°, -53.0275°)", + " Point B: (14.4605°, 5.2437°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -5.561527°", + " Longitude: -22.939410°", + "FINAL ANSWER: -5.561527, -22.939410" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 1.46083, + "lon": 33.93611, + "name": "Kumi" + }, + "point_b": { + "lat": 35.96124, + "lon": 0.91896, + "name": "Oued Rhiou" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 19.447455, + "lon": 19.212847 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (1.46083°, 33.93611°)", + " Point B: (35.96124°, 0.91896°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 19.447455°", + " Longitude: 19.212847°", + "FINAL ANSWER: 19.447455, 19.212847" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 9.04059, + "lon": -79.44083, + "name": "Juan Díaz" + }, + "point_b": { + "lat": 30.20921, + "lon": 107.2589, + "name": "Chengxi" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 76.055518, + "lon": -117.389549 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (9.04059°, -79.44083°)", + " Point B: (30.20921°, 107.2589°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 76.055518°", + " Longitude: -117.389549°", + "FINAL ANSWER: 76.055518, -117.389549" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 0.4, + "lon": 32.63333, + "name": "Kira" + }, + "point_b": { + "lat": 40.23417, + "lon": 69.69481, + "name": "Buston" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 10.958832, + "lon": 40.327197 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (0.4°, 32.63333°)", + " Point B: (40.23417°, 69.69481°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 10.958832°", + " Longitude: 40.327197°", + "FINAL ANSWER: 10.958832, 40.327197" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 39.93484, + "lon": -75.03073, + "name": "Cherry Hill" + }, + "point_b": { + "lat": -20.23333, + "lon": 47.38333, + "name": "Fandriana" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -0.391617, + "lon": 21.905067 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (39.93484°, -75.03073°)", + " Point B: (-20.23333°, 47.38333°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -0.391617°", + " Longitude: 21.905067°", + "FINAL ANSWER: -0.391617, 21.905067" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -10.9, + "lon": 38.5, + "name": "Nangomba" + }, + "point_b": { + "lat": 31.1608, + "lon": 52.6506, + "name": "Abadeh" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 10.206142, + "lon": 45.086785 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-10.9°, 38.5°)", + " Point B: (31.1608°, 52.6506°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 10.206142°", + " Longitude: 45.086785°", + "FINAL ANSWER: 10.206142, 45.086785" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -20.46444, + "lon": -45.42639, + "name": "Formiga" + }, + "point_b": { + "lat": -34.22997, + "lon": 19.4265, + "name": "Caledon" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -31.476448, + "lon": -15.27102 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-20.46444°, -45.42639°)", + " Point B: (-34.22997°, 19.4265°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -31.476448°", + " Longitude: -15.271020°", + "FINAL ANSWER: -31.476448, -15.271020" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 52.65303, + "lon": 90.09454, + "name": "Abaza" + }, + "point_b": { + "lat": 49.00875, + "lon": 2.39819, + "name": "Villiers-le-Bel" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 56.064655, + "lon": 20.452064 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (52.65303°, 90.09454°)", + " Point B: (49.00875°, 2.39819°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 56.064655°", + " Longitude: 20.452064°", + "FINAL ANSWER: 56.064655, 20.452064" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -33.9677, + "lon": 151.10149, + "name": "Hurstville" + }, + "point_b": { + "lat": 58.36319, + "lon": 25.59159, + "name": "Viljandi" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 23.395264, + "lon": 111.963294 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-33.9677°, 151.10149°)", + " Point B: (58.36319°, 25.59159°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 23.395264°", + " Longitude: 111.963294°", + "FINAL ANSWER: 23.395264, 111.963294" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 13.2923, + "lon": 123.4855, + "name": "Polangui" + }, + "point_b": { + "lat": 41.80614, + "lon": -88.3273, + "name": "North Aurora" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 38.940875, + "lon": 139.734627 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (13.2923°, 123.4855°)", + " Point B: (41.80614°, -88.3273°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 38.940875°", + " Longitude: 139.734627°", + "FINAL ANSWER: 38.940875, 139.734627" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 39.70056, + "lon": 125.89333, + "name": "Kaech’ŏn" + }, + "point_b": { + "lat": 6.65166, + "lon": -5.60501, + "name": "Konéfla" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 50.295085, + "lon": 87.26691 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (39.70056°, 125.89333°)", + " Point B: (6.65166°, -5.60501°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 50.295085°", + " Longitude: 87.266910°", + "FINAL ANSWER: 50.295085, 87.266910" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -23.065, + "lon": -54.19056, + "name": "Naviraí" + }, + "point_b": { + "lat": 50.88898, + "lon": 3.42756, + "name": "Waregem" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -3.754064, + "lon": -42.45089 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-23.065°, -54.19056°)", + " Point B: (50.88898°, 3.42756°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -3.754064°", + " Longitude: -42.450890°", + "FINAL ANSWER: -3.754064, -42.450890" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -2.63861, + "lon": 30.46778, + "name": "Kabanga" + }, + "point_b": { + "lat": -33.7457, + "lon": 151.04764, + "name": "West Pennant Hills" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -19.715813, + "lon": 53.63436 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-2.63861°, 30.46778°)", + " Point B: (-33.7457°, 151.04764°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -19.715813°", + " Longitude: 53.634360°", + "FINAL ANSWER: -19.715813, 53.634360" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 26.26541, + "lon": 88.18982, + "name": "Islāmpur" + }, + "point_b": { + "lat": -7.39083, + "lon": 112.72667, + "name": "Gedangan" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 1.137035, + "lon": 106.922914 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (26.26541°, 88.18982°)", + " Point B: (-7.39083°, 112.72667°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 1.137035°", + " Longitude: 106.922914°", + "FINAL ANSWER: 1.137035, 106.922914" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -12.36333, + "lon": -44.97333, + "name": "São Desidério" + }, + "point_b": { + "lat": 35.74922, + "lon": 1.54778, + "name": "Lardjem" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 12.685546, + "lon": -23.987 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-12.36333°, -44.97333°)", + " Point B: (35.74922°, 1.54778°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 12.685546°", + " Longitude: -23.987000°", + "FINAL ANSWER: 12.685546, -23.987000" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -13.40985, + "lon": -76.13235, + "name": "Chincha Alta" + }, + "point_b": { + "lat": 37.08819, + "lon": -8.2503, + "name": "Albufeira" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 0.383515, + "lon": -61.089559 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-13.40985°, -76.13235°)", + " Point B: (37.08819°, -8.2503°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 0.383515°", + " Longitude: -61.089559°", + "FINAL ANSWER: 0.383515, -61.089559" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 31.75872, + "lon": -106.48693, + "name": "El Paso" + }, + "point_b": { + "lat": 39.71611, + "lon": 66.66417, + "name": "Juma Shahri" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 66.488024, + "lon": 59.671186 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (31.75872°, -106.48693°)", + " Point B: (39.71611°, 66.66417°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 66.488024°", + " Longitude: 59.671186°", + "FINAL ANSWER: 66.488024, 59.671186" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -37.81992, + "lon": 145.0358, + "name": "Hawthorn" + }, + "point_b": { + "lat": 49.12624, + "lon": -122.67995, + "name": "Willoughby" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 8.092597, + "lon": -174.400208 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-37.81992°, 145.0358°)", + " Point B: (49.12624°, -122.67995°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 8.092597°", + " Longitude: -174.400208°", + "FINAL ANSWER: 8.092597, -174.400208" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -28.4602, + "lon": -62.83354, + "name": "Añatuya" + }, + "point_b": { + "lat": -34.15152, + "lon": 19.01509, + "name": "Grabouw" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -38.424309, + "lon": -1.527248 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-28.4602°, -62.83354°)", + " Point B: (-34.15152°, 19.01509°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -38.424309°", + " Longitude: -1.527248°", + "FINAL ANSWER: -38.424309, -1.527248" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 5.61637, + "lon": -73.81748, + "name": "Chiquinquirá" + }, + "point_b": { + "lat": 31.78199, + "lon": 35.21961, + "name": "West Jerusalem" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 34.799859, + "lon": 4.515386 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (5.61637°, -73.81748°)", + " Point B: (31.78199°, 35.21961°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 34.799859°", + " Longitude: 4.515386°", + "FINAL ANSWER: 34.799859, 4.515386" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 31.41648, + "lon": 31.81332, + "name": "Damietta" + }, + "point_b": { + "lat": 37.54557, + "lon": -97.26893, + "name": "Derby" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 48.521997, + "lon": 9.407926 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (31.41648°, 31.81332°)", + " Point B: (37.54557°, -97.26893°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 48.521997°", + " Longitude: 9.407926°", + "FINAL ANSWER: 48.521997, 9.407926" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 13.30867, + "lon": 7.15602, + "name": "Madarounfa" + }, + "point_b": { + "lat": 40.36709, + "lon": -3.74608, + "name": "Buenavista" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 20.140991, + "lon": 4.868166 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (13.30867°, 7.15602°)", + " Point B: (40.36709°, -3.74608°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 20.140991°", + " Longitude: 4.868166°", + "FINAL ANSWER: 20.140991, 4.868166" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 32.54193, + "lon": 44.22469, + "name": "Al Hindīyah" + }, + "point_b": { + "lat": -37.86667, + "lon": 145.06667, + "name": "Glen Iris" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 15.464432, + "lon": 70.444818 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (32.54193°, 44.22469°)", + " Point B: (-37.86667°, 145.06667°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 15.464432°", + " Longitude: 70.444818°", + "FINAL ANSWER: 15.464432, 70.444818" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 10.8293, + "lon": -75.03346, + "name": "Juan de Acosta" + }, + "point_b": { + "lat": -28.91588, + "lon": 27.56957, + "name": "Hlohlolwane" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -24.066108, + "lon": -1.666358 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (10.8293°, -75.03346°)", + " Point B: (-28.91588°, 27.56957°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -24.066108°", + " Longitude: -1.666358°", + "FINAL ANSWER: -24.066108, -1.666358" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 19.9381, + "lon": 79.11192, + "name": "Ghugus" + }, + "point_b": { + "lat": 40.97926, + "lon": -74.11653, + "name": "Ridgewood" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 63.58788, + "lon": -44.1949 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (19.9381°, 79.11192°)", + " Point B: (40.97926°, -74.11653°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 63.587880°", + " Longitude: -44.194900°", + "FINAL ANSWER: 63.587880, -44.194900" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 60.4664, + "lon": 26.94582, + "name": "Kotka" + }, + "point_b": { + "lat": -38.07018, + "lon": 145.47411, + "name": "Pakenham" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -9.617016, + "lon": 124.656128 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (60.4664°, 26.94582°)", + " Point B: (-38.07018°, 145.47411°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -9.617016°", + " Longitude: 124.656128°", + "FINAL ANSWER: -9.617016, 124.656128" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 41.97263, + "lon": -71.32474, + "name": "North Attleborough Center" + }, + "point_b": { + "lat": 26.5503, + "lon": 84.6801, + "name": "Areraj" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 65.192161, + "lon": -46.884824 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (41.97263°, -71.32474°)", + " Point B: (26.5503°, 84.6801°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 65.192161°", + " Longitude: -46.884824°", + "FINAL ANSWER: 65.192161, -46.884824" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 5.95753, + "lon": 6.85305, + "name": "Ozubulu" + }, + "point_b": { + "lat": 37.33813, + "lon": 40.81739, + "name": "Yeşilli" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 30.271065, + "lon": 30.636353 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (5.95753°, 6.85305°)", + " Point B: (37.33813°, 40.81739°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 30.271065°", + " Longitude: 30.636353°", + "FINAL ANSWER: 30.271065, 30.636353" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 0.17124, + "lon": 34.59466, + "name": "Khwisero" + }, + "point_b": { + "lat": 11.84828, + "lon": -86.19916, + "name": "Jinotepe" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 7.010612, + "lon": 5.300975 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (0.17124°, 34.59466°)", + " Point B: (11.84828°, -86.19916°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 7.010612°", + " Longitude: 5.300975°", + "FINAL ANSWER: 7.010612, 5.300975" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 38.29674, + "lon": -85.75996, + "name": "Clarksville" + }, + "point_b": { + "lat": 45.33619, + "lon": -75.7225, + "name": "Nepean" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 41.925519, + "lon": -81.018099 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (38.29674°, -85.75996°)", + " Point B: (45.33619°, -75.7225°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 41.925519°", + " Longitude: -81.018099°", + "FINAL ANSWER: 41.925519, -81.018099" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -24.61778, + "lon": -53.32, + "name": "Cafelândia" + }, + "point_b": { + "lat": 18.47186, + "lon": -69.89232, + "name": "Santo Domingo" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 7.702315, + "lon": -65.733264 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-24.61778°, -53.32°)", + " Point B: (18.47186°, -69.89232°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 7.702315°", + " Longitude: -65.733264°", + "FINAL ANSWER: 7.702315, -65.733264" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 40.39162, + "lon": -111.85077, + "name": "Lehi" + }, + "point_b": { + "lat": -6.59444, + "lon": 106.78917, + "name": "Bogor" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 50.737475, + "lon": -157.387309 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (40.39162°, -111.85077°)", + " Point B: (-6.59444°, 106.78917°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 50.737475°", + " Longitude: -157.387309°", + "FINAL ANSWER: 50.737475, -157.387309" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 33.14782, + "lon": 73.75187, + "name": "New Mirpur City" + }, + "point_b": { + "lat": 8.76667, + "lon": -8.61667, + "name": "Moussadou" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 26.911789, + "lon": 28.426827 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (33.14782°, 73.75187°)", + " Point B: (8.76667°, -8.61667°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 26.911789°", + " Longitude: 28.426827°", + "FINAL ANSWER: 26.911789, 28.426827" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 41.06022, + "lon": -111.97105, + "name": "Layton" + }, + "point_b": { + "lat": 53.49642, + "lon": -2.51973, + "name": "Leigh" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 53.426528, + "lon": -94.734604 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (41.06022°, -111.97105°)", + " Point B: (53.49642°, -2.51973°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 53.426528°", + " Longitude: -94.734604°", + "FINAL ANSWER: 53.426528, -94.734604" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 42.06975, + "lon": -87.78784, + "name": "Glenview" + }, + "point_b": { + "lat": 11.26667, + "lon": 75.91667, + "name": "Mavoor" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 69.2809, + "lon": -58.524705 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (42.06975°, -87.78784°)", + " Point B: (11.26667°, 75.91667°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 69.280900°", + " Longitude: -58.524705°", + "FINAL ANSWER: 69.280900, -58.524705" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 6.64738, + "lon": -75.46031, + "name": "Santa Rosa de Osos" + }, + "point_b": { + "lat": 12.98417, + "lon": 37.04417, + "name": "Tikil Dingay" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 13.469475, + "lon": -48.339677 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (6.64738°, -75.46031°)", + " Point B: (12.98417°, 37.04417°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 13.469475°", + " Longitude: -48.339677°", + "FINAL ANSWER: 13.469475, -48.339677" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 28.79304, + "lon": 76.13968, + "name": "Bhiwāni" + }, + "point_b": { + "lat": -15.67941, + "lon": -48.19667, + "name": "Brazlândia" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 13.778168, + "lon": 8.885209 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (28.79304°, 76.13968°)", + " Point B: (-15.67941°, -48.19667°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 13.778168°", + " Longitude: 8.885209°", + "FINAL ANSWER: 13.778168, 8.885209" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 27.29636, + "lon": 75.18665, + "name": "Danta" + }, + "point_b": { + "lat": 32.61889, + "lon": 36.10213, + "name": "Dar‘ā" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 29.71165, + "lon": 65.883531 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (27.29636°, 75.18665°)", + " Point B: (32.61889°, 36.10213°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 29.711650°", + " Longitude: 65.883531°", + "FINAL ANSWER: 29.711650, 65.883531" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 41.43763, + "lon": 22.64288, + "name": "Strumica" + }, + "point_b": { + "lat": 40.44289, + "lon": -3.71124, + "name": "Vallehermoso" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 41.25582, + "lon": 2.764088 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (41.43763°, 22.64288°)", + " Point B: (40.44289°, -3.71124°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 41.255820°", + " Longitude: 2.764088°", + "FINAL ANSWER: 41.255820, 2.764088" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 9.25385, + "lon": -70.25105, + "name": "Boconó" + }, + "point_b": { + "lat": 32.8043, + "lon": 21.86605, + "name": "Shahhat" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 28.903664, + "lon": -28.946217 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (9.25385°, -70.25105°)", + " Point B: (32.8043°, 21.86605°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 28.903664°", + " Longitude: -28.946217°", + "FINAL ANSWER: 28.903664, -28.946217" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 30.73629, + "lon": 76.7884, + "name": "Chandigarh" + }, + "point_b": { + "lat": 18.0554, + "lon": 120.56489, + "name": "Batac City" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 28.880277, + "lon": 88.571184 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (30.73629°, 76.7884°)", + " Point B: (18.0554°, 120.56489°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 28.880277°", + " Longitude: 88.571184°", + "FINAL ANSWER: 28.880277, 88.571184" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 33.56391, + "lon": 6.70326, + "name": "Reguiba" + }, + "point_b": { + "lat": 45.43713, + "lon": 12.33265, + "name": "Venice" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 36.555967, + "lon": 7.940128 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (33.56391°, 6.70326°)", + " Point B: (45.43713°, 12.33265°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 36.555967°", + " Longitude: 7.940128°", + "FINAL ANSWER: 36.555967, 7.940128" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -9.34213, + "lon": 32.745, + "name": "Nakonde" + }, + "point_b": { + "lat": 35.65087, + "lon": 139.79163, + "name": "Toyosu" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 32.164946, + "lon": 106.997764 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-9.34213°, 32.745°)", + " Point B: (35.65087°, 139.79163°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 32.164946°", + " Longitude: 106.997764°", + "FINAL ANSWER: 32.164946, 106.997764" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 23.74771, + "lon": 86.78804, + "name": "Chirkunda" + }, + "point_b": { + "lat": -4.44696, + "lon": -49.11556, + "name": "Jacundá" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 24.250657, + "lon": 12.817296 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (23.74771°, 86.78804°)", + " Point B: (-4.44696°, -49.11556°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 24.250657°", + " Longitude: 12.817296°", + "FINAL ANSWER: 24.250657, 12.817296" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -23.04972, + "lon": -47.83667, + "name": "Laranjal Paulista" + }, + "point_b": { + "lat": 26.85, + "lon": 104.23333, + "name": "Weining" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -9.413054, + "lon": -10.044732 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-23.04972°, -47.83667°)", + " Point B: (26.85°, 104.23333°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -9.413054°", + " Longitude: -10.044732°", + "FINAL ANSWER: -9.413054, -10.044732" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -38.97736, + "lon": -67.82714, + "name": "Allen" + }, + "point_b": { + "lat": 27.79449, + "lon": 77.4368, + "name": "Kosi" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 5.788537, + "lon": 45.709716 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-38.97736°, -67.82714°)", + " Point B: (27.79449°, 77.4368°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 5.788537°", + " Longitude: 45.709716°", + "FINAL ANSWER: 5.788537, 45.709716" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 48.06226, + "lon": 8.49358, + "name": "Villingen-Schwenningen" + }, + "point_b": { + "lat": -21.54, + "lon": -43.01056, + "name": "São João Nepomuceno" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -3.520228, + "lon": -32.181503 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (48.06226°, 8.49358°)", + " Point B: (-21.54°, -43.01056°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -3.520228°", + " Longitude: -32.181503°", + "FINAL ANSWER: -3.520228, -32.181503" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -25.61692, + "lon": 27.99471, + "name": "Ga-Rankuwa" + }, + "point_b": { + "lat": 43.02295, + "lon": 25.10364, + "name": "Sevlievo" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -8.456134, + "lon": 27.317773 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-25.61692°, 27.99471°)", + " Point B: (43.02295°, 25.10364°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -8.456134°", + " Longitude: 27.317773°", + "FINAL ANSWER: -8.456134, 27.317773" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -10.73366, + "lon": 14.97995, + "name": "Quibala" + }, + "point_b": { + "lat": 45.46005, + "lon": -73.57058, + "name": "Verdun" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 37.407939, + "lon": -42.947318 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-10.73366°, 14.97995°)", + " Point B: (45.46005°, -73.57058°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 37.407939°", + " Longitude: -42.947318°", + "FINAL ANSWER: 37.407939, -42.947318" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 39.25066, + "lon": -76.52052, + "name": "Dundalk" + }, + "point_b": { + "lat": 52.22096, + "lon": 20.98526, + "name": "Ochota" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 49.959276, + "lon": -59.688732 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (39.25066°, -76.52052°)", + " Point B: (52.22096°, 20.98526°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 49.959276°", + " Longitude: -59.688732°", + "FINAL ANSWER: 49.959276, -59.688732" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 42.97086, + "lon": -82.42491, + "name": "Port Huron" + }, + "point_b": { + "lat": 14.0341, + "lon": -0.03261, + "name": "Dori" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 41.863719, + "lon": -56.98309 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (42.97086°, -82.42491°)", + " Point B: (14.0341°, -0.03261°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 41.863719°", + " Longitude: -56.983090°", + "FINAL ANSWER: 41.863719, -56.983090" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 26.30328, + "lon": 127.79396, + "name": "Kishaba" + }, + "point_b": { + "lat": 44.27262, + "lon": -121.17392, + "name": "Redmond" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 52.363439, + "lon": -151.227836 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (26.30328°, 127.79396°)", + " Point B: (44.27262°, -121.17392°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 52.363439°", + " Longitude: -151.227836°", + "FINAL ANSWER: 52.363439, -151.227836" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 36.11667, + "lon": 139.96667, + "name": "Ishige" + }, + "point_b": { + "lat": 33.72835, + "lon": -117.14642, + "name": "Menifee" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 43.797146, + "lon": -139.365747 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (36.11667°, 139.96667°)", + " Point B: (33.72835°, -117.14642°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 43.797146°", + " Longitude: -139.365747°", + "FINAL ANSWER: 43.797146, -139.365747" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 10.05896, + "lon": -65.03698, + "name": "Puerto Píritu" + }, + "point_b": { + "lat": 41.49109, + "lon": 2.14079, + "name": "Cerdanyola del Vallès" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 37.333288, + "lon": -18.690649 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (10.05896°, -65.03698°)", + " Point B: (41.49109°, 2.14079°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 37.333288°", + " Longitude: -18.690649°", + "FINAL ANSWER: 37.333288, -18.690649" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -6.7674, + "lon": 110.8541, + "name": "Baekrajan" + }, + "point_b": { + "lat": 5.93876, + "lon": -6.59826, + "name": "Yabayo" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -0.798068, + "lon": 52.05197 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-6.7674°, 110.8541°)", + " Point B: (5.93876°, -6.59826°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -0.798068°", + " Longitude: 52.051970°", + "FINAL ANSWER: -0.798068, 52.051970" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 49.13645, + "lon": 8.91229, + "name": "Eppingen" + }, + "point_b": { + "lat": 36.37285, + "lon": -94.20882, + "name": "Bentonville" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 48.214113, + "lon": -76.279636 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (49.13645°, 8.91229°)", + " Point B: (36.37285°, -94.20882°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 48.214113°", + " Longitude: -76.279636°", + "FINAL ANSWER: 48.214113, -76.279636" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -3.54306, + "lon": -43.91583, + "name": "Vargem Grande" + }, + "point_b": { + "lat": -19.35278, + "lon": -47.29278, + "name": "Perdizes" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -7.498669, + "lon": -44.728856 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-3.54306°, -43.91583°)", + " Point B: (-19.35278°, -47.29278°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -7.498669°", + " Longitude: -44.728856°", + "FINAL ANSWER: -7.498669, -44.728856" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -37.81501, + "lon": 144.96657, + "name": "Melbourne City Centre" + }, + "point_b": { + "lat": 54.37978, + "lon": 18.59539, + "name": "Wrzeszcz Górny" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 42.643197, + "lon": 69.990844 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-37.81501°, 144.96657°)", + " Point B: (54.37978°, 18.59539°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 42.643197°", + " Longitude: 69.990844°", + "FINAL ANSWER: 42.643197, 69.990844" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 42.34491, + "lon": -71.10017, + "name": "Fenway/Kenmore" + }, + "point_b": { + "lat": 34.45, + "lon": 135.76667, + "name": "Kashiwara" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 63.9962, + "lon": -92.316449 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (42.34491°, -71.10017°)", + " Point B: (34.45°, 135.76667°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 63.996200°", + " Longitude: -92.316449°", + "FINAL ANSWER: 63.996200, -92.316449" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 47.76291, + "lon": 27.92854, + "name": "Bălţi" + }, + "point_b": { + "lat": 5.54167, + "lon": 95.33333, + "name": "Banda Aceh" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 41.153012, + "lon": 51.067381 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (47.76291°, 27.92854°)", + " Point B: (5.54167°, 95.33333°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 41.153012°", + " Longitude: 51.067381°", + "FINAL ANSWER: 41.153012, 51.067381" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 33.50921, + "lon": -111.89903, + "name": "Scottsdale" + }, + "point_b": { + "lat": -28.61961, + "lon": 28.20966, + "name": "Fouriesburg" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 24.836336, + "lon": -71.095373 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (33.50921°, -111.89903°)", + " Point B: (-28.61961°, 28.20966°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 24.836336°", + " Longitude: -71.095373°", + "FINAL ANSWER: 24.836336, -71.095373" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -10.89481, + "lon": 17.76402, + "name": "Cambundi" + }, + "point_b": { + "lat": 43.27083, + "lon": 5.3821, + "name": "Marseille 08" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 29.820131, + "lon": 9.427869 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-10.89481°, 17.76402°)", + " Point B: (43.27083°, 5.3821°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 29.820131°", + " Longitude: 9.427869°", + "FINAL ANSWER: 29.820131, 9.427869" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -9.34213, + "lon": 32.745, + "name": "Nakonde" + }, + "point_b": { + "lat": 11.52639, + "lon": 42.85194, + "name": "Arta" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 1.096391, + "lon": 37.780683 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-9.34213°, 32.745°)", + " Point B: (11.52639°, 42.85194°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 1.096391°", + " Longitude: 37.780683°", + "FINAL ANSWER: 1.096391, 37.780683" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 52.28927, + "lon": -0.60184, + "name": "Rushden" + }, + "point_b": { + "lat": 37.81667, + "lon": 140.5, + "name": "Date" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 68.169123, + "lon": 28.051288 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (52.28927°, -0.60184°)", + " Point B: (37.81667°, 140.5°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 68.169123°", + " Longitude: 28.051288°", + "FINAL ANSWER: 68.169123, 28.051288" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 29.44631, + "lon": 107.10217, + "name": "Longtan" + }, + "point_b": { + "lat": 40.66599, + "lon": 16.60463, + "name": "Matera" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 38.963634, + "lon": 88.673075 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (29.44631°, 107.10217°)", + " Point B: (40.66599°, 16.60463°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 38.963634°", + " Longitude: 88.673075°", + "FINAL ANSWER: 38.963634, 88.673075" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 45.56628, + "lon": 5.92079, + "name": "Chambéry" + }, + "point_b": { + "lat": -26.93139, + "lon": -48.95889, + "name": "Gaspar" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 10.45395, + "lon": -25.093174 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (45.56628°, 5.92079°)", + " Point B: (-26.93139°, -48.95889°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 10.453950°", + " Longitude: -25.093174°", + "FINAL ANSWER: 10.453950, -25.093174" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 49.10465, + "lon": 6.70402, + "name": "Saint-Avold" + }, + "point_b": { + "lat": 34.70053, + "lon": 137.52253, + "name": "Kosai" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 64.462932, + "lon": 86.029485 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (49.10465°, 6.70402°)", + " Point B: (34.70053°, 137.52253°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 64.462932°", + " Longitude: 86.029485°", + "FINAL ANSWER: 64.462932, 86.029485" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 6.24924, + "lon": -57.51578, + "name": "New Amsterdam" + }, + "point_b": { + "lat": 39.54595, + "lon": -0.57069, + "name": "Ribarroja del Turia" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 33.633256, + "lon": -18.065497 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (6.24924°, -57.51578°)", + " Point B: (39.54595°, -0.57069°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 33.633256°", + " Longitude: -18.065497°", + "FINAL ANSWER: 33.633256, -18.065497" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 34.18667, + "lon": -118.44897, + "name": "Van Nuys" + }, + "point_b": { + "lat": 11.8235, + "lon": -70.25637, + "name": "Santa Cruz de los Taques" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 18.694002, + "lon": -80.805821 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (34.18667°, -118.44897°)", + " Point B: (11.8235°, -70.25637°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 18.694002°", + " Longitude: -80.805821°", + "FINAL ANSWER: 18.694002, -80.805821" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 43.9168, + "lon": -80.09967, + "name": "Orangeville" + }, + "point_b": { + "lat": -38.0965, + "lon": 145.26707, + "name": "Cranbourne West" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -17.616282, + "lon": 179.804291 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (43.9168°, -80.09967°)", + " Point B: (-38.0965°, 145.26707°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -17.616282°", + " Longitude: 179.804291°", + "FINAL ANSWER: -17.616282, 179.804291" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 12.66664, + "lon": -0.57469, + "name": "Boulsa" + }, + "point_b": { + "lat": 12.15889, + "lon": -86.34417, + "name": "Ciudad Sandino" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 16.719364, + "lon": -43.511327 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (12.66664°, -0.57469°)", + " Point B: (12.15889°, -86.34417°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 16.719364°", + " Longitude: -43.511327°", + "FINAL ANSWER: 16.719364, -43.511327" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 29.9253, + "lon": 106.4907, + "name": "Tuchang" + }, + "point_b": { + "lat": 6.51115, + "lon": 1.82831, + "name": "Sé" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 18.83917, + "lon": 23.966714 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (29.9253°, 106.4907°)", + " Point B: (6.51115°, 1.82831°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 18.839170°", + " Longitude: 23.966714°", + "FINAL ANSWER: 18.839170, 23.966714" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 55.71667, + "lon": 37.78333, + "name": "Novokuz’minki" + }, + "point_b": { + "lat": 9.87121, + "lon": -84.06084, + "name": "San Miguel" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 49.97061, + "lon": -49.242259 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (55.71667°, 37.78333°)", + " Point B: (9.87121°, -84.06084°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 49.970610°", + " Longitude: -49.242259°", + "FINAL ANSWER: 49.970610, -49.242259" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 51.10754, + "lon": 114.54173, + "name": "Aginskoye" + }, + "point_b": { + "lat": 19.92672, + "lon": 74.7275, + "name": "Vaijāpur" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 37.130724, + "lon": 90.509582 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (51.10754°, 114.54173°)", + " Point B: (19.92672°, 74.7275°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 37.130724°", + " Longitude: 90.509582°", + "FINAL ANSWER: 37.130724, 90.509582" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 44.53889, + "lon": 10.81166, + "name": "Fiorano" + }, + "point_b": { + "lat": 50.82882, + "lon": -0.32247, + "name": "Lancing" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 46.208331, + "lon": 8.274695 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (44.53889°, 10.81166°)", + " Point B: (50.82882°, -0.32247°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 46.208331°", + " Longitude: 8.274695°", + "FINAL ANSWER: 46.208331, 8.274695" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 45.2629, + "lon": -122.69259, + "name": "Canby" + }, + "point_b": { + "lat": 21.49837, + "lon": -158.06515, + "name": "Schofield Barracks" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 28.277981, + "lon": -150.955871 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (45.2629°, -122.69259°)", + " Point B: (21.49837°, -158.06515°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 28.277981°", + " Longitude: -150.955871°", + "FINAL ANSWER: 28.277981, -150.955871" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -19.00083, + "lon": -46.31611, + "name": "Carmo do Paranaíba" + }, + "point_b": { + "lat": 49.34737, + "lon": 8.68733, + "name": "Leimen" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 34.205888, + "lon": -11.016482 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-19.00083°, -46.31611°)", + " Point B: (49.34737°, 8.68733°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 34.205888°", + " Longitude: -11.016482°", + "FINAL ANSWER: 34.205888, -11.016482" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 42.90975, + "lon": -85.76309, + "name": "Grandville" + }, + "point_b": { + "lat": -23.59245, + "lon": -46.78561, + "name": "Raposo Tavares" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 10.225791, + "lon": -64.012906 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (42.90975°, -85.76309°)", + " Point B: (-23.59245°, -46.78561°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 10.225791°", + " Longitude: -64.012906°", + "FINAL ANSWER: 10.225791, -64.012906" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 13.43512, + "lon": 77.72787, + "name": "Chik Ballāpur" + }, + "point_b": { + "lat": 34.73333, + "lon": 136.51667, + "name": "Tsu" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 31.9458, + "lon": 119.807882 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (13.43512°, 77.72787°)", + " Point B: (34.73333°, 136.51667°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 31.945800°", + " Longitude: 119.807882°", + "FINAL ANSWER: 31.945800, 119.807882" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 56.87456, + "lon": 37.35957, + "name": "Kimry" + }, + "point_b": { + "lat": -26.37, + "lon": -48.72222, + "name": "Araquari" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -3.301521, + "lon": -33.206327 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (56.87456°, 37.35957°)", + " Point B: (-26.37°, -48.72222°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -3.301521°", + " Longitude: -33.206327°", + "FINAL ANSWER: -3.301521, -33.206327" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -26.53643, + "lon": -59.34138, + "name": "General José de San Martín" + }, + "point_b": { + "lat": 49.47783, + "lon": 20.03228, + "name": "Nowy Targ" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 14.651132, + "lon": -27.151214 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-26.53643°, -59.34138°)", + " Point B: (49.47783°, 20.03228°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 14.651132°", + " Longitude: -27.151214°", + "FINAL ANSWER: 14.651132, -27.151214" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -7.68386, + "lon": 112.25804, + "name": "Ngoro" + }, + "point_b": { + "lat": 9.3863, + "lon": -67.05818, + "name": "El Sombrero" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 66.793306, + "lon": 43.089489 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-7.68386°, 112.25804°)", + " Point B: (9.3863°, -67.05818°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 66.793306°", + " Longitude: 43.089489°", + "FINAL ANSWER: 66.793306, 43.089489" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 2.0442, + "lon": 102.5689, + "name": "Muar" + }, + "point_b": { + "lat": -9.31833, + "lon": -35.56111, + "name": "São Luís do Quitunde" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -4.849688, + "lon": 68.799167 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (2.0442°, 102.5689°)", + " Point B: (-9.31833°, -35.56111°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -4.849688°", + " Longitude: 68.799167°", + "FINAL ANSWER: -4.849688, 68.799167" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 21.90709, + "lon": 96.04894, + "name": "Amarapura" + }, + "point_b": { + "lat": -3.25886, + "lon": -79.95876, + "name": "Machala" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 36.069644, + "lon": -70.857236 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (21.90709°, 96.04894°)", + " Point B: (-3.25886°, -79.95876°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 36.069644°", + " Longitude: -70.857236°", + "FINAL ANSWER: 36.069644, -70.857236" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 18.42745, + "lon": -67.15407, + "name": "Aguadilla" + }, + "point_b": { + "lat": 5.20856, + "lon": -74.73584, + "name": "Honda" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 8.530245, + "lon": -72.902495 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (18.42745°, -67.15407°)", + " Point B: (5.20856°, -74.73584°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 8.530245°", + " Longitude: -72.902495°", + "FINAL ANSWER: 8.530245, -72.902495" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 33.66946, + "lon": -117.82311, + "name": "Irvine" + }, + "point_b": { + "lat": 40.01923, + "lon": -82.87934, + "name": "Gahanna" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 39.440416, + "lon": -92.111864 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (33.66946°, -117.82311°)", + " Point B: (40.01923°, -82.87934°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 39.440416°", + " Longitude: -92.111864°", + "FINAL ANSWER: 39.440416, -92.111864" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 26.45756, + "lon": 80.77403, + "name": "Purwā" + }, + "point_b": { + "lat": 12.90569, + "lon": 79.31897, + "name": "Arcot" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 16.294674, + "lon": 79.661246 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (26.45756°, 80.77403°)", + " Point B: (12.90569°, 79.31897°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 16.294674°", + " Longitude: 79.661246°", + "FINAL ANSWER: 16.294674, 79.661246" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 39.93484, + "lon": -75.03073, + "name": "Cherry Hill" + }, + "point_b": { + "lat": 30.40793, + "lon": 108.21732, + "name": "Xituo" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 84.715308, + "lon": 132.366033 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (39.93484°, -75.03073°)", + " Point B: (30.40793°, 108.21732°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 84.715308°", + " Longitude: 132.366033°", + "FINAL ANSWER: 84.715308, 132.366033" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 5.40733, + "lon": -75.48749, + "name": "Salamina" + }, + "point_b": { + "lat": 14.93152, + "lon": -23.51254, + "name": "Praia" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 8.555287, + "lon": -62.800352 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (5.40733°, -75.48749°)", + " Point B: (14.93152°, -23.51254°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 8.555287°", + " Longitude: -62.800352°", + "FINAL ANSWER: 8.555287, -62.800352" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 22.49487, + "lon": 114.13949, + "name": "Fanling" + }, + "point_b": { + "lat": -29.16806, + "lon": -51.17944, + "name": "Caxias do Sul" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -24.024145, + "lon": 43.837461 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (22.49487°, 114.13949°)", + " Point B: (-29.16806°, -51.17944°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -24.024145°", + " Longitude: 43.837461°", + "FINAL ANSWER: -24.024145, 43.837461" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 7.69385, + "lon": -5.03031, + "name": "Bouaké" + }, + "point_b": { + "lat": -10.06806, + "lon": -78.15222, + "name": "Huarmey" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -6.079903, + "lon": -59.658658 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (7.69385°, -5.03031°)", + " Point B: (-10.06806°, -78.15222°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -6.079903°", + " Longitude: -59.658658°", + "FINAL ANSWER: -6.079903, -59.658658" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 14.42038, + "lon": -16.70258, + "name": "Thiadiaye" + }, + "point_b": { + "lat": 48.19001, + "lon": 17.72747, + "name": "Galanta" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 40.76379, + "lon": 6.268236 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (14.42038°, -16.70258°)", + " Point B: (48.19001°, 17.72747°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 40.763790°", + " Longitude: 6.268236°", + "FINAL ANSWER: 40.763790, 6.268236" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -7.19111, + "lon": -48.20722, + "name": "Araguaína" + }, + "point_b": { + "lat": 31.93058, + "lon": 70.45959, + "name": "Kulachi" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 31.950397, + "lon": 35.528377 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-7.19111°, -48.20722°)", + " Point B: (31.93058°, 70.45959°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 31.950397°", + " Longitude: 35.528377°", + "FINAL ANSWER: 31.950397, 35.528377" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 7.10667, + "lon": 124.82917, + "name": "Kabacan" + }, + "point_b": { + "lat": 36.41097, + "lon": 138.99621, + "name": "Kanekomachi" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 14.528963, + "lon": 127.892786 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (7.10667°, 124.82917°)", + " Point B: (36.41097°, 138.99621°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 14.528963°", + " Longitude: 127.892786°", + "FINAL ANSWER: 14.528963, 127.892786" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -15.2567, + "lon": 48.54249, + "name": "Befandriana" + }, + "point_b": { + "lat": -5.95, + "lon": 34.13333, + "name": "Mgandu" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -8.33363, + "lon": 37.658967 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-15.2567°, 48.54249°)", + " Point B: (-5.95°, 34.13333°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -8.333630°", + " Longitude: 37.658967°", + "FINAL ANSWER: -8.333630, 37.658967" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 6.63883, + "lon": 100.42342, + "name": "Sadao" + }, + "point_b": { + "lat": 55.9, + "lon": 37.55, + "name": "Vagonoremont" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 35.055875, + "lon": 78.645723 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (6.63883°, 100.42342°)", + " Point B: (55.9°, 37.55°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 35.055875°", + " Longitude: 78.645723°", + "FINAL ANSWER: 35.055875, 78.645723" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 52.57682, + "lon": -1.31536, + "name": "Earl Shilton" + }, + "point_b": { + "lat": -4.87778, + "lon": -80.70528, + "name": "Marcavelica" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 43.811758, + "lon": -31.7153 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (52.57682°, -1.31536°)", + " Point B: (-4.87778°, -80.70528°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 43.811758°", + " Longitude: -31.715300°", + "FINAL ANSWER: 43.811758, -31.715300" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -29.32816, + "lon": 31.28954, + "name": "KwaDukuza" + }, + "point_b": { + "lat": 11.7404, + "lon": 78.959, + "name": "Kallakkurichchi" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -9.596084, + "lon": 56.590651 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-29.32816°, 31.28954°)", + " Point B: (11.7404°, 78.959°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -9.596084°", + " Longitude: 56.590651°", + "FINAL ANSWER: -9.596084, 56.590651" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 2.08333, + "lon": 111.61667, + "name": "Maradong" + }, + "point_b": { + "lat": 34.86971, + "lon": -117.05615, + "name": "Barstow Heights" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 38.391083, + "lon": 165.018243 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (2.08333°, 111.61667°)", + " Point B: (34.86971°, -117.05615°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 38.391083°", + " Longitude: 165.018243°", + "FINAL ANSWER: 38.391083, 165.018243" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 35.28275, + "lon": -120.65962, + "name": "San Luis Obispo" + }, + "point_b": { + "lat": 43.84686, + "lon": 46.70977, + "name": "Kizlyar" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 68.068523, + "lon": 34.869007 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (35.28275°, -120.65962°)", + " Point B: (43.84686°, 46.70977°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 68.068523°", + " Longitude: 34.869007°", + "FINAL ANSWER: 68.068523, 34.869007" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 37.6918, + "lon": 127.8857, + "name": "Hongch’ŏn" + }, + "point_b": { + "lat": 37.96939, + "lon": -1.21714, + "name": "Alcantarilla" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 53.694938, + "lon": 104.333506 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (37.6918°, 127.8857°)", + " Point B: (37.96939°, -1.21714°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 53.694938°", + " Longitude: 104.333506°", + "FINAL ANSWER: 53.694938, 104.333506" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 39.87534, + "lon": 20.00477, + "name": "Sarandë" + }, + "point_b": { + "lat": 44.32597, + "lon": 85.62009, + "name": "Sandaohezi" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 44.562268, + "lon": 34.797703 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (39.87534°, 20.00477°)", + " Point B: (44.32597°, 85.62009°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 44.562268°", + " Longitude: 34.797703°", + "FINAL ANSWER: 44.562268, 34.797703" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 55.75533, + "lon": 38.09578, + "name": "Zarya" + }, + "point_b": { + "lat": 41.58778, + "lon": 129.60611, + "name": "Kyŏngsŏng" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 59.92207, + "lon": 64.142115 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (55.75533°, 38.09578°)", + " Point B: (41.58778°, 129.60611°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 59.922070°", + " Longitude: 64.142115°", + "FINAL ANSWER: 59.922070, 64.142115" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 33.91371, + "lon": -98.49339, + "name": "Wichita Falls" + }, + "point_b": { + "lat": 35.35, + "lon": 137.18333, + "name": "Toki" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 55.933026, + "lon": -159.715833 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (33.91371°, -98.49339°)", + " Point B: (35.35°, 137.18333°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 55.933026°", + " Longitude: -159.715833°", + "FINAL ANSWER: 55.933026, -159.715833" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 8.36972, + "lon": 124.86444, + "name": "Manolo Fortich" + }, + "point_b": { + "lat": 27.89364, + "lon": -82.24037, + "name": "Bloomingdale" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 50.037977, + "lon": -115.940228 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (8.36972°, 124.86444°)", + " Point B: (27.89364°, -82.24037°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 50.037977°", + " Longitude: -115.940228°", + "FINAL ANSWER: 50.037977, -115.940228" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 10.27284, + "lon": 76.17475, + "name": "Panangad" + }, + "point_b": { + "lat": -28.93575, + "lon": -49.49538, + "name": "Araranguá" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -19.676842, + "lon": 19.846164 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (10.27284°, 76.17475°)", + " Point B: (-28.93575°, -49.49538°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -19.676842°", + " Longitude: 19.846164°", + "FINAL ANSWER: -19.676842, 19.846164" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -28.65083, + "lon": -49.21, + "name": "Morro da Fumaça" + }, + "point_b": { + "lat": 33.50398, + "lon": 11.11215, + "name": "Zarzis" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 2.805659, + "lon": -19.899236 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-28.65083°, -49.21°)", + " Point B: (33.50398°, 11.11215°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 2.805659°", + " Longitude: -19.899236°", + "FINAL ANSWER: 2.805659, -19.899236" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 5.62657, + "lon": -0.25807, + "name": "New Achimota" + }, + "point_b": { + "lat": 25.58399, + "lon": 100.31181, + "name": "Fengyi" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 27.13937, + "lon": 73.243949 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (5.62657°, -0.25807°)", + " Point B: (25.58399°, 100.31181°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 27.139370°", + " Longitude: 73.243949°", + "FINAL ANSWER: 27.139370, 73.243949" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 35.68313, + "lon": -5.32871, + "name": "Mdiq" + }, + "point_b": { + "lat": 30.98352, + "lon": -110.29758, + "name": "Cananea" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 47.185614, + "lon": -59.826435 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (35.68313°, -5.32871°)", + " Point B: (30.98352°, -110.29758°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 47.185614°", + " Longitude: -59.826435°", + "FINAL ANSWER: 47.185614, -59.826435" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -3.38193, + "lon": 29.36142, + "name": "Bujumbura" + }, + "point_b": { + "lat": -19.53944, + "lon": -40.63056, + "name": "Colatina" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -17.534334, + "lon": -22.278726 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-3.38193°, 29.36142°)", + " Point B: (-19.53944°, -40.63056°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -17.534334°", + " Longitude: -22.278726°", + "FINAL ANSWER: -17.534334, -22.278726" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 37.67748, + "lon": -113.06189, + "name": "Cedar City" + }, + "point_b": { + "lat": 22.65361, + "lon": 86.35595, + "name": "Jadugora" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 50.066171, + "lon": 99.338976 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (37.67748°, -113.06189°)", + " Point B: (22.65361°, 86.35595°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 50.066171°", + " Longitude: 99.338976°", + "FINAL ANSWER: 50.066171, 99.338976" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 6.13833, + "lon": -75.26417, + "name": "Santuario" + }, + "point_b": { + "lat": 17.94979, + "lon": -94.91386, + "name": "Acayucan" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 15.139294, + "lon": -89.824012 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (6.13833°, -75.26417°)", + " Point B: (17.94979°, -94.91386°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 15.139294°", + " Longitude: -89.824012°", + "FINAL ANSWER: 15.139294, -89.824012" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 33.43532, + "lon": -112.35821, + "name": "Goodyear" + }, + "point_b": { + "lat": -17.70306, + "lon": -40.76639, + "name": "Carlos Chagas" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 22.688269, + "lon": -91.43169 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (33.43532°, -112.35821°)", + " Point B: (-17.70306°, -40.76639°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 22.688269°", + " Longitude: -91.431690°", + "FINAL ANSWER: 22.688269, -91.431690" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 42.12509, + "lon": -72.74954, + "name": "Westfield" + }, + "point_b": { + "lat": 10.36676, + "lon": -13.58253, + "name": "Fria" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 20.364274, + "lon": -25.322325 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (42.12509°, -72.74954°)", + " Point B: (10.36676°, -13.58253°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 20.364274°", + " Longitude: -25.322325°", + "FINAL ANSWER: 20.364274, -25.322325" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -1.8628, + "lon": 29.62541, + "name": "Ngororero" + }, + "point_b": { + "lat": 40.82566, + "lon": -73.69819, + "name": "Port Washington" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 14.651211, + "lon": 10.241821 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-1.8628°, 29.62541°)", + " Point B: (40.82566°, -73.69819°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 14.651211°", + " Longitude: 10.241821°", + "FINAL ANSWER: 14.651211, 10.241821" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 43.17959, + "lon": 70.4592, + "name": "Karatau" + }, + "point_b": { + "lat": 46.89028, + "lon": -71.37222, + "name": "La Haute-Saint-Charles" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 71.840921, + "lon": 4.898932 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (43.17959°, 70.4592°)", + " Point B: (46.89028°, -71.37222°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 71.840921°", + " Longitude: 4.898932°", + "FINAL ANSWER: 71.840921, 4.898932" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 47.3548, + "lon": 8.56097, + "name": "Zürich (Kreis 8)" + }, + "point_b": { + "lat": 51.43092, + "lon": -0.50606, + "name": "Staines" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 50.48004, + "lon": 1.903667 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (47.3548°, 8.56097°)", + " Point B: (51.43092°, -0.50606°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 50.480040°", + " Longitude: 1.903667°", + "FINAL ANSWER: 50.480040, 1.903667" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 33.96173, + "lon": -116.50353, + "name": "Desert Hot Springs" + }, + "point_b": { + "lat": 0.34881, + "lon": -78.12462, + "name": "Ibarra" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 9.324678, + "lon": -86.568812 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (33.96173°, -116.50353°)", + " Point B: (0.34881°, -78.12462°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 9.324678°", + " Longitude: -86.568812°", + "FINAL ANSWER: 9.324678, -86.568812" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -10.7525, + "lon": -39.20917, + "name": "Quijingue" + }, + "point_b": { + "lat": 44.17057, + "lon": 66.73376, + "name": "Shiyeli" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 39.675019, + "lon": 30.34219 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-10.7525°, -39.20917°)", + " Point B: (44.17057°, 66.73376°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 39.675019°", + " Longitude: 30.342190°", + "FINAL ANSWER: 39.675019, 30.342190" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -5.5375, + "lon": -35.81972, + "name": "João Câmara" + }, + "point_b": { + "lat": 52.07936, + "lon": 7.01344, + "name": "Ahaus" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 24.70197, + "lon": -19.703164 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-5.5375°, -35.81972°)", + " Point B: (52.07936°, 7.01344°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 24.701970°", + " Longitude: -19.703164°", + "FINAL ANSWER: 24.701970, -19.703164" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 35.23338, + "lon": -106.66447, + "name": "Rio Rancho" + }, + "point_b": { + "lat": 53.20008, + "lon": -105.76772, + "name": "Prince Albert" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 39.725637, + "lon": -106.487153 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (35.23338°, -106.66447°)", + " Point B: (53.20008°, -105.76772°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 39.725637°", + " Longitude: -106.487153°", + "FINAL ANSWER: 39.725637, -106.487153" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -32.57076, + "lon": 27.42396, + "name": "Stutterheim" + }, + "point_b": { + "lat": -1.94995, + "lon": 30.05885, + "name": "Kigali" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -17.264617, + "lon": 28.853487 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-32.57076°, 27.42396°)", + " Point B: (-1.94995°, 30.05885°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -17.264617°", + " Longitude: 28.853487°", + "FINAL ANSWER: -17.264617, 28.853487" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 36.37227, + "lon": 119.58208, + "name": "Kanjia" + }, + "point_b": { + "lat": 1.5995, + "lon": 11.57933, + "name": "Oyem" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 17.093089, + "lon": 32.631401 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (36.37227°, 119.58208°)", + " Point B: (1.5995°, 11.57933°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 17.093089°", + " Longitude: 32.631401°", + "FINAL ANSWER: 17.093089, 32.631401" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 46.61797, + "lon": 7.0569, + "name": "Bulle" + }, + "point_b": { + "lat": -36.8582, + "lon": 174.62019, + "name": "Lincoln" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 32.862668, + "lon": 125.794692 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (46.61797°, 7.0569°)", + " Point B: (-36.8582°, 174.62019°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 32.862668°", + " Longitude: 125.794692°", + "FINAL ANSWER: 32.862668, 125.794692" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 26.22375, + "lon": 79.83739, + "name": "Pukhrāyān" + }, + "point_b": { + "lat": 47.81954, + "lon": -122.17624, + "name": "North Creek" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 70.3168, + "lon": -148.74032 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (26.22375°, 79.83739°)", + " Point B: (47.81954°, -122.17624°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 70.316800°", + " Longitude: -148.740320°", + "FINAL ANSWER: 70.316800, -148.740320" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -24.62694, + "lon": 25.86556, + "name": "Mogoditshane" + }, + "point_b": { + "lat": 38.77144, + "lon": -90.37095, + "name": "Hazelwood" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -6.369465, + "lon": -0.625341 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-24.62694°, 25.86556°)", + " Point B: (38.77144°, -90.37095°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -6.369465°", + " Longitude: -0.625341°", + "FINAL ANSWER: -6.369465, -0.625341" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -24.59165, + "lon": 27.41155, + "name": "Thabazimbi" + }, + "point_b": { + "lat": 34.30778, + "lon": -118.44925, + "name": "Sylmar" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -5.083157, + "lon": -5.610973 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-24.59165°, 27.41155°)", + " Point B: (34.30778°, -118.44925°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -5.083157°", + " Longitude: -5.610973°", + "FINAL ANSWER: -5.083157, -5.610973" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 38.81061, + "lon": -90.69985, + "name": "O'Fallon" + }, + "point_b": { + "lat": 1.36259, + "lon": 109.30093, + "name": "Kota Sambas" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 59.866652, + "lon": 154.196618 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (38.81061°, -90.69985°)", + " Point B: (1.36259°, 109.30093°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 59.866652°", + " Longitude: 154.196618°", + "FINAL ANSWER: 59.866652, 154.196618" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 41.10442, + "lon": 30.69664, + "name": "Karasu" + }, + "point_b": { + "lat": -21.69694, + "lon": -45.25333, + "name": "Três Corações" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 28.283779, + "lon": 6.490491 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (41.10442°, 30.69664°)", + " Point B: (-21.69694°, -45.25333°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 28.283779°", + " Longitude: 6.490491°", + "FINAL ANSWER: 28.283779, 6.490491" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 0.39241, + "lon": 9.45356, + "name": "Libreville" + }, + "point_b": { + "lat": 43.77233, + "lon": 41.91366, + "name": "Karachayevsk" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 11.717202, + "lon": 15.945358 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (0.39241°, 9.45356°)", + " Point B: (43.77233°, 41.91366°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 11.717202°", + " Longitude: 15.945358°", + "FINAL ANSWER: 11.717202, 15.945358" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -20.73306, + "lon": -42.02944, + "name": "Carangola" + }, + "point_b": { + "lat": 54.2279, + "lon": 28.505, + "name": "Barysaw" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 19.988774, + "lon": -16.029726 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-20.73306°, -42.02944°)", + " Point B: (54.2279°, 28.505°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 19.988774°", + " Longitude: -16.029726°", + "FINAL ANSWER: 19.988774, -16.029726" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 19.43332, + "lon": -99.19919, + "name": "Polanco" + }, + "point_b": { + "lat": 40.43285, + "lon": -3.69354, + "name": "Almagro" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 40.383311, + "lon": -58.147628 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (19.43332°, -99.19919°)", + " Point B: (40.43285°, -3.69354°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 40.383311°", + " Longitude: -58.147628°", + "FINAL ANSWER: 40.383311, -58.147628" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 5.53711, + "lon": -0.69984, + "name": "Swedru" + }, + "point_b": { + "lat": 22.61892, + "lon": -83.70694, + "name": "Viñales" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 21.985173, + "lon": -61.693471 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (5.53711°, -0.69984°)", + " Point B: (22.61892°, -83.70694°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 21.985173°", + " Longitude: -61.693471°", + "FINAL ANSWER: 21.985173, -61.693471" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 53.72861, + "lon": -0.57215, + "name": "Brough" + }, + "point_b": { + "lat": -18.14307, + "lon": 177.50691, + "name": "Sigatoka" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 88.140711, + "lon": 82.746369 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (53.72861°, -0.57215°)", + " Point B: (-18.14307°, 177.50691°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 88.140711°", + " Longitude: 82.746369°", + "FINAL ANSWER: 88.140711, 82.746369" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 5.01806, + "lon": -1.66437, + "name": "Shama Junction" + }, + "point_b": { + "lat": 41.00997, + "lon": 17.00558, + "name": "Rutigliano" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 14.184833, + "lon": 2.19031 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (5.01806°, -1.66437°)", + " Point B: (41.00997°, 17.00558°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 14.184833°", + " Longitude: 2.190310°", + "FINAL ANSWER: 14.184833, 2.190310" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 51.48158, + "lon": 11.97947, + "name": "Halle (Saale)" + }, + "point_b": { + "lat": 28.88305, + "lon": -81.30868, + "name": "DeBary" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 41.088589, + "lon": -66.035363 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (51.48158°, 11.97947°)", + " Point B: (28.88305°, -81.30868°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 41.088589°", + " Longitude: -66.035363°", + "FINAL ANSWER: 41.088589, -66.035363" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 31.41667, + "lon": 130.31667, + "name": "Kaseda-shirakame" + }, + "point_b": { + "lat": 5.12181, + "lon": 9.96143, + "name": "Melong" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 21.237208, + "lon": 33.742651 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (31.41667°, 130.31667°)", + " Point B: (5.12181°, 9.96143°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 21.237208°", + " Longitude: 33.742651°", + "FINAL ANSWER: 21.237208, 33.742651" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 11.28333, + "lon": 36.21667, + "name": "Mambuk" + }, + "point_b": { + "lat": 35.76514, + "lon": 139.86677, + "name": "Kanamachi" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 39.150994, + "lon": 110.369707 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (11.28333°, 36.21667°)", + " Point B: (35.76514°, 139.86677°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 39.150994°", + " Longitude: 110.369707°", + "FINAL ANSWER: 39.150994, 110.369707" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 8.4022, + "lon": 14.1698, + "name": "Tcholliré" + }, + "point_b": { + "lat": 40.65909, + "lon": -3.76762, + "name": "Colmenar Viejo" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 16.633807, + "lon": 10.449195 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (8.4022°, 14.1698°)", + " Point B: (40.65909°, -3.76762°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 16.633807°", + " Longitude: 10.449195°", + "FINAL ANSWER: 16.633807, 10.449195" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 37.58333, + "lon": 140.43333, + "name": "Nihommatsu" + }, + "point_b": { + "lat": -21.28861, + "lon": -50.34, + "name": "Birigui" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 63.657822, + "lon": -167.465556 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (37.58333°, 140.43333°)", + " Point B: (-21.28861°, -50.34°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 63.657822°", + " Longitude: -167.465556°", + "FINAL ANSWER: 63.657822, -167.465556" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 3.4537, + "lon": 101.6413, + "name": "Hulu Yam Lama" + }, + "point_b": { + "lat": 44.4834, + "lon": -80.21638, + "name": "Collingwood" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 77.394656, + "lon": -86.459606 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (3.4537°, 101.6413°)", + " Point B: (44.4834°, -80.21638°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 77.394656°", + " Longitude: -86.459606°", + "FINAL ANSWER: 77.394656, -86.459606" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 52.30881, + "lon": 45.38992, + "name": "Petrovsk" + }, + "point_b": { + "lat": -4.23246, + "lon": -44.78164, + "name": "Bacabal" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 31.558205, + "lon": -13.223307 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (52.30881°, 45.38992°)", + " Point B: (-4.23246°, -44.78164°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 31.558205°", + " Longitude: -13.223307°", + "FINAL ANSWER: 31.558205, -13.223307" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 41.39005, + "lon": -81.75958, + "name": "Parma Heights" + }, + "point_b": { + "lat": 42.26121, + "lon": -71.4634, + "name": "Ashland" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 42.13014, + "lon": -74.061558 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (41.39005°, -81.75958°)", + " Point B: (42.26121°, -71.4634°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 42.130140°", + " Longitude: -74.061558°", + "FINAL ANSWER: 42.130140, -74.061558" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -10.00055, + "lon": 14.89519, + "name": "Calulo" + }, + "point_b": { + "lat": -6.45, + "lon": 38.33333, + "name": "Lugoba" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -9.247145, + "lon": 20.79473 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-10.00055°, 14.89519°)", + " Point B: (-6.45°, 38.33333°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -9.247145°", + " Longitude: 20.794730°", + "FINAL ANSWER: -9.247145, 20.794730" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 30.43046, + "lon": 31.03679, + "name": "Al Bājūr" + }, + "point_b": { + "lat": -37.88264, + "lon": 144.7003, + "name": "Hoppers Crossing" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -6.772987, + "lon": 84.000919 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (30.43046°, 31.03679°)", + " Point B: (-37.88264°, 144.7003°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -6.772987°", + " Longitude: 84.000919°", + "FINAL ANSWER: -6.772987, 84.000919" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 31.5464, + "lon": 34.49514, + "name": "Bayt Lāhyā" + }, + "point_b": { + "lat": -0.21209, + "lon": 36.27248, + "name": "Upper Gilgil" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 7.728617, + "lon": 35.871339 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (31.5464°, 34.49514°)", + " Point B: (-0.21209°, 36.27248°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 7.728617°", + " Longitude: 35.871339°", + "FINAL ANSWER: 7.728617, 35.871339" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 51.75, + "lon": -2.2, + "name": "Stroud" + }, + "point_b": { + "lat": -27.35917, + "lon": -53.39444, + "name": "Frederico Westphalen" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 13.429224, + "lon": -32.684952 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (51.75°, -2.2°)", + " Point B: (-27.35917°, -53.39444°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 13.429224°", + " Longitude: -32.684952°", + "FINAL ANSWER: 13.429224, -32.684952" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -9.62361, + "lon": -37.75667, + "name": "Piranhas" + }, + "point_b": { + "lat": 7.45123, + "lon": 8.60805, + "name": "Igbor" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -1.181569, + "lon": -14.504475 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-9.62361°, -37.75667°)", + " Point B: (7.45123°, 8.60805°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -1.181569°", + " Longitude: -14.504475°", + "FINAL ANSWER: -1.181569, -14.504475" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 38.70245, + "lon": -9.22936, + "name": "Algés" + }, + "point_b": { + "lat": -14.3525, + "lon": 35.65056, + "name": "Mandimba" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -0.622353, + "lon": 25.677656 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (38.70245°, -9.22936°)", + " Point B: (-14.3525°, 35.65056°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -0.622353°", + " Longitude: 25.677656°", + "FINAL ANSWER: -0.622353, 25.677656" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 45.56093, + "lon": 25.31787, + "name": "Zărnești" + }, + "point_b": { + "lat": -14.75639, + "lon": -40.08917, + "name": "Iguaí" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 33.263357, + "lon": 2.990574 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (45.56093°, 25.31787°)", + " Point B: (-14.75639°, -40.08917°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 33.263357°", + " Longitude: 2.990574°", + "FINAL ANSWER: 33.263357, 2.990574" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 21.77463, + "lon": 78.25756, + "name": "Multai" + }, + "point_b": { + "lat": -7.03333, + "lon": -40.45, + "name": "Ipueiras" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 20.810509, + "lon": 46.229215 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (21.77463°, 78.25756°)", + " Point B: (-7.03333°, -40.45°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 20.810509°", + " Longitude: 46.229215°", + "FINAL ANSWER: 20.810509, 46.229215" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 38.78333, + "lon": 0.16667, + "name": "Javea" + }, + "point_b": { + "lat": 34.10834, + "lon": -117.28977, + "name": "San Bernardino" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 51.015896, + "lon": -25.493345 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (38.78333°, 0.16667°)", + " Point B: (34.10834°, -117.28977°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 51.015896°", + " Longitude: -25.493345°", + "FINAL ANSWER: 51.015896, -25.493345" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 13.20194, + "lon": -16.73389, + "name": "Gunjur" + }, + "point_b": { + "lat": 10.5042, + "lon": -63.41729, + "name": "Casanay" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 11.927204, + "lon": -51.857947 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (13.20194°, -16.73389°)", + " Point B: (10.5042°, -63.41729°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 11.927204°", + " Longitude: -51.857947°", + "FINAL ANSWER: 11.927204, -51.857947" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 36.4, + "lon": 10.61667, + "name": "Hammamet" + }, + "point_b": { + "lat": 10.1477, + "lon": 76.23, + "name": "Parūr" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 19.170911, + "lon": 62.420215 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (36.4°, 10.61667°)", + " Point B: (10.1477°, 76.23°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 19.170911°", + " Longitude: 62.420215°", + "FINAL ANSWER: 19.170911, 62.420215" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 10.43959, + "lon": 45.01432, + "name": "Berbera" + }, + "point_b": { + "lat": 26.15272, + "lon": 80.16803, + "name": "Ghātampur" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 14.93526, + "lon": 53.219671 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (10.43959°, 45.01432°)", + " Point B: (26.15272°, 80.16803°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 14.935260°", + " Longitude: 53.219671°", + "FINAL ANSWER: 14.935260, 53.219671" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -2.63861, + "lon": 30.46778, + "name": "Kabanga" + }, + "point_b": { + "lat": -36.35846, + "lon": 146.32056, + "name": "Wangaratta" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -39.952128, + "lon": 111.789108 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-2.63861°, 30.46778°)", + " Point B: (-36.35846°, 146.32056°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -39.952128°", + " Longitude: 111.789108°", + "FINAL ANSWER: -39.952128, 111.789108" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 52.98947, + "lon": 6.9504, + "name": "Stadskanaal" + }, + "point_b": { + "lat": 44.1171, + "lon": 27.26056, + "name": "Silistra" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 46.650815, + "lon": 22.842472 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (52.98947°, 6.9504°)", + " Point B: (44.1171°, 27.26056°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 46.650815°", + " Longitude: 22.842472°", + "FINAL ANSWER: 46.650815, 22.842472" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -7.88944, + "lon": -37.12, + "name": "Monteiro" + }, + "point_b": { + "lat": 10.3991, + "lon": 123.9992, + "name": "Liloan" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 7.604923, + "lon": 42.224807 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-7.88944°, -37.12°)", + " Point B: (10.3991°, 123.9992°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 7.604923°", + " Longitude: 42.224807°", + "FINAL ANSWER: 7.604923, 42.224807" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 52.70333, + "lon": 5.29167, + "name": "Enkhuizen" + }, + "point_b": { + "lat": 11.00703, + "lon": -74.24765, + "name": "Ciénaga" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 48.426424, + "lon": -23.644402 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (52.70333°, 5.29167°)", + " Point B: (11.00703°, -74.24765°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 48.426424°", + " Longitude: -23.644402°", + "FINAL ANSWER: 48.426424, -23.644402" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 49.24966, + "lon": -123.11934, + "name": "Vancouver" + }, + "point_b": { + "lat": -27.91828, + "lon": 153.33275, + "name": "Helensvale" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 34.051686, + "lon": -152.969834 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (49.24966°, -123.11934°)", + " Point B: (-27.91828°, 153.33275°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 34.051686°", + " Longitude: -152.969834°", + "FINAL ANSWER: 34.051686, -152.969834" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 33.81518, + "lon": -4.40717, + "name": "Ribat Al Khayr" + }, + "point_b": { + "lat": 9.11072, + "lon": 99.23208, + "name": "Tha Kham" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 32.303753, + "lon": 53.660854 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (33.81518°, -4.40717°)", + " Point B: (9.11072°, 99.23208°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 32.303753°", + " Longitude: 53.660854°", + "FINAL ANSWER: 32.303753, 53.660854" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 12.03427, + "lon": 75.23779, + "name": "Mādāyi" + }, + "point_b": { + "lat": 22.54987, + "lon": 120.54067, + "name": "Chaozhou" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 15.609277, + "lon": 86.045037 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (12.03427°, 75.23779°)", + " Point B: (22.54987°, 120.54067°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 15.609277°", + " Longitude: 86.045037°", + "FINAL ANSWER: 15.609277, 86.045037" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 40.53694, + "lon": 17.43723, + "name": "Grottaglie" + }, + "point_b": { + "lat": 59.53436, + "lon": 18.07758, + "name": "Vallentuna" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 50.036073, + "lon": 17.69348 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (40.53694°, 17.43723°)", + " Point B: (59.53436°, 18.07758°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 50.036073°", + " Longitude: 17.693480°", + "FINAL ANSWER: 50.036073, 17.693480" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 29.06423, + "lon": 105.94487, + "name": "Zhuyang" + }, + "point_b": { + "lat": 31.71599, + "lon": 35.79392, + "name": "Mādabā" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 33.548002, + "lon": 89.326385 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (29.06423°, 105.94487°)", + " Point B: (31.71599°, 35.79392°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 33.548002°", + " Longitude: 89.326385°", + "FINAL ANSWER: 33.548002, 89.326385" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 39.74025, + "lon": 116.32693, + "name": "Daxing" + }, + "point_b": { + "lat": 6.55799, + "lon": -5.01769, + "name": "Toumodi" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 46.386626, + "lon": 79.812467 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (39.74025°, 116.32693°)", + " Point B: (6.55799°, -5.01769°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 46.386626°", + " Longitude: 79.812467°", + "FINAL ANSWER: 46.386626, 79.812467" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 7.2, + "lon": 38.6, + "name": "Shashamane" + }, + "point_b": { + "lat": 9.11972, + "lon": 4.8236, + "name": "Jebba" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 8.522338, + "lon": 21.753589 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (7.2°, 38.6°)", + " Point B: (9.11972°, 4.8236°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 8.522338°", + " Longitude: 21.753589°", + "FINAL ANSWER: 8.522338, 21.753589" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 42.15696, + "lon": 21.58559, + "name": "Lipkovo" + }, + "point_b": { + "lat": 23.29908, + "lon": 72.33362, + "name": "Kadi" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 39.63414, + "lon": 36.406771 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (42.15696°, 21.58559°)", + " Point B: (23.29908°, 72.33362°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 39.634140°", + " Longitude: 36.406771°", + "FINAL ANSWER: 39.634140, 36.406771" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 10.92611, + "lon": 78.0941, + "name": "Tāndoni" + }, + "point_b": { + "lat": 46.16824, + "lon": 34.80861, + "name": "Henichesk" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 20.830298, + "lon": 69.806437 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (10.92611°, 78.0941°)", + " Point B: (46.16824°, 34.80861°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 20.830298°", + " Longitude: 69.806437°", + "FINAL ANSWER: 20.830298, 69.806437" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 29.14269, + "lon": 71.25771, + "name": "Ahmadpur East" + }, + "point_b": { + "lat": 52.20845, + "lon": 9.55416, + "name": "Springe" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 44.873613, + "lon": 46.385863 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (29.14269°, 71.25771°)", + " Point B: (52.20845°, 9.55416°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 44.873613°", + " Longitude: 46.385863°", + "FINAL ANSWER: 44.873613, 46.385863" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 36.41976, + "lon": -6.14367, + "name": "Chiclana de la Frontera" + }, + "point_b": { + "lat": -37.70462, + "lon": 145.10302, + "name": "Greensborough" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 20.753971, + "lon": 35.340057 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (36.41976°, -6.14367°)", + " Point B: (-37.70462°, 145.10302°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 20.753971°", + " Longitude: 35.340057°", + "FINAL ANSWER: 20.753971, 35.340057" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -6.7475, + "lon": -51.16111, + "name": "Tucumã" + }, + "point_b": { + "lat": -26.53333, + "lon": 29.06667, + "name": "eMbalenhle" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -14.79395, + "lon": -32.985254 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-6.7475°, -51.16111°)", + " Point B: (-26.53333°, 29.06667°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -14.793950°", + " Longitude: -32.985254°", + "FINAL ANSWER: -14.793950, -32.985254" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 41.97587, + "lon": -87.68922, + "name": "Lincoln Square" + }, + "point_b": { + "lat": -3.47222, + "lon": -51.19778, + "name": "Anapu" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 20.168973, + "lon": -66.682859 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (41.97587°, -87.68922°)", + " Point B: (-3.47222°, -51.19778°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 20.168973°", + " Longitude: -66.682859°", + "FINAL ANSWER: 20.168973, -66.682859" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -15.21194, + "lon": -75.11028, + "name": "Minas de Marcona" + }, + "point_b": { + "lat": 5.13825, + "lon": -5.02123, + "name": "Grand-Lahou" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -11.203929, + "lon": -56.99448 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-15.21194°, -75.11028°)", + " Point B: (5.13825°, -5.02123°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -11.203929°", + " Longitude: -56.994480°", + "FINAL ANSWER: -11.203929, -56.994480" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 24.67193, + "lon": 102.1613, + "name": "Longquan" + }, + "point_b": { + "lat": 52.64738, + "lon": -1.08647, + "name": "Humberstone" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 51.332359, + "lon": 64.66224 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (24.67193°, 102.1613°)", + " Point B: (52.64738°, -1.08647°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 51.332359°", + " Longitude: 64.662240°", + "FINAL ANSWER: 51.332359, 64.662240" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 35.03126, + "lon": 139.92651, + "name": "Minamibōsō" + }, + "point_b": { + "lat": 46.23424, + "lon": 6.08025, + "name": "Meyrin" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 53.078154, + "lon": 121.649546 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (35.03126°, 139.92651°)", + " Point B: (46.23424°, 6.08025°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 53.078154°", + " Longitude: 121.649546°", + "FINAL ANSWER: 53.078154, 121.649546" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 42.32139, + "lon": 21.35833, + "name": "Vitina" + }, + "point_b": { + "lat": 50.84378, + "lon": 16.48859, + "name": "Świdnica" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 48.73347, + "lon": 17.85729 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (42.32139°, 21.35833°)", + " Point B: (50.84378°, 16.48859°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 48.733470°", + " Longitude: 17.857290°", + "FINAL ANSWER: 48.733470, 17.857290" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 49.86085, + "lon": 8.5725, + "name": "Griesheim" + }, + "point_b": { + "lat": -20.43333, + "lon": -45.16667, + "name": "Água Rasa" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 16.33592, + "lon": -23.648522 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (49.86085°, 8.5725°)", + " Point B: (-20.43333°, -45.16667°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 16.335920°", + " Longitude: -23.648522°", + "FINAL ANSWER: 16.335920, -23.648522" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 31.6, + "lon": 117.86667, + "name": "Chaohu" + }, + "point_b": { + "lat": 30.08843, + "lon": 31.28351, + "name": "Ḩadā’iq al Qubbah" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 39.365555, + "lon": 74.149887 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (31.6°, 117.86667°)", + " Point B: (30.08843°, 31.28351°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 39.365555°", + " Longitude: 74.149887°", + "FINAL ANSWER: 39.365555, 74.149887" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 20.99104, + "lon": 74.31475, + "name": "Sakri" + }, + "point_b": { + "lat": 52.26059, + "lon": 21.16355, + "name": "Rembertów" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 47.072412, + "lon": 39.338334 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (20.99104°, 74.31475°)", + " Point B: (52.26059°, 21.16355°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 47.072412°", + " Longitude: 39.338334°", + "FINAL ANSWER: 47.072412, 39.338334" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 3.31667, + "lon": 101.4, + "name": "Ijok" + }, + "point_b": { + "lat": 39.24038, + "lon": -76.83942, + "name": "Columbia" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 71.916214, + "lon": 95.341492 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (3.31667°, 101.4°)", + " Point B: (39.24038°, -76.83942°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 71.916214°", + " Longitude: 95.341492°", + "FINAL ANSWER: 71.916214, 95.341492" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 13.73939, + "lon": 106.98727, + "name": "Banlung" + }, + "point_b": { + "lat": -9.72283, + "lon": -63.31022, + "name": "Alto Paraíso" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 24.802153, + "lon": 63.387206 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (13.73939°, 106.98727°)", + " Point B: (-9.72283°, -63.31022°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 24.802153°", + " Longitude: 63.387206°", + "FINAL ANSWER: 24.802153, 63.387206" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 36.31, + "lon": 119.3875, + "name": "Jingzhi" + }, + "point_b": { + "lat": 35.83318, + "lon": 139.54437, + "name": "Miyoshidai" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 36.510013, + "lon": 124.436066 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (36.31°, 119.3875°)", + " Point B: (35.83318°, 139.54437°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 36.510013°", + " Longitude: 124.436066°", + "FINAL ANSWER: 36.510013, 124.436066" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 11.14968, + "lon": 78.5987, + "name": "Turaiyūr" + }, + "point_b": { + "lat": 51.74297, + "lon": 7.18163, + "name": "Haltern am See" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 24.457745, + "lon": 66.710308 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (11.14968°, 78.5987°)", + " Point B: (51.74297°, 7.18163°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 24.457745°", + " Longitude: 66.710308°", + "FINAL ANSWER: 24.457745, 66.710308" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 31.22452, + "lon": 75.77387, + "name": "Phagwāra" + }, + "point_b": { + "lat": 39.37733, + "lon": -76.53969, + "name": "Parkville" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 54.664144, + "lon": 59.286716 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (31.22452°, 75.77387°)", + " Point B: (39.37733°, -76.53969°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 54.664144°", + " Longitude: 59.286716°", + "FINAL ANSWER: 54.664144, 59.286716" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 10.52885, + "lon": 76.04793, + "name": "Chetwayi" + }, + "point_b": { + "lat": -7.221, + "lon": 108.1896, + "name": "Rajapolah" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 6.185823, + "lon": 84.187717 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (10.52885°, 76.04793°)", + " Point B: (-7.221°, 108.1896°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 6.185823°", + " Longitude: 84.187717°", + "FINAL ANSWER: 6.185823, 84.187717" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 14.12286, + "lon": 15.31189, + "name": "Mao" + }, + "point_b": { + "lat": 56.36009, + "lon": 8.61607, + "name": "Holstebro" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 24.708384, + "lon": 14.199774 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (14.12286°, 15.31189°)", + " Point B: (56.36009°, 8.61607°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 24.708384°", + " Longitude: 14.199774°", + "FINAL ANSWER: 24.708384, 14.199774" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 11.73292, + "lon": 41.082, + "name": "Dubti" + }, + "point_b": { + "lat": 32.74583, + "lon": 105.24139, + "name": "Bikou" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 19.319206, + "lon": 55.136078 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (11.73292°, 41.082°)", + " Point B: (32.74583°, 105.24139°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 19.319206°", + " Longitude: 55.136078°", + "FINAL ANSWER: 19.319206, 55.136078" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -17.73648, + "lon": 168.31366, + "name": "Port-Vila" + }, + "point_b": { + "lat": 50.37069, + "lon": 3.07922, + "name": "Douai" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 51.298172, + "lon": 142.476669 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-17.73648°, 168.31366°)", + " Point B: (50.37069°, 3.07922°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 51.298172°", + " Longitude: 142.476669°", + "FINAL ANSWER: 51.298172, 142.476669" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 33.01512, + "lon": -96.53888, + "name": "Wylie" + }, + "point_b": { + "lat": -6.9425, + "lon": -38.9675, + "name": "Aurora" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 4.024281, + "lon": -51.86146 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (33.01512°, -96.53888°)", + " Point B: (-6.9425°, -38.9675°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 4.024281°", + " Longitude: -51.861460°", + "FINAL ANSWER: 4.024281, -51.861460" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 55.75533, + "lon": 38.09578, + "name": "Zarya" + }, + "point_b": { + "lat": 51.39872, + "lon": -0.34916, + "name": "East Molesey" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 55.861178, + "lon": 27.888489 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (55.75533°, 38.09578°)", + " Point B: (51.39872°, -0.34916°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 55.861178°", + " Longitude: 27.888489°", + "FINAL ANSWER: 55.861178, 27.888489" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -27.36541, + "lon": 29.88175, + "name": "Volksrust" + }, + "point_b": { + "lat": 52.30667, + "lon": 6.51806, + "name": "Rijssen" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -7.34913, + "lon": 24.909956 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-27.36541°, 29.88175°)", + " Point B: (52.30667°, 6.51806°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -7.349130°", + " Longitude: 24.909956°", + "FINAL ANSWER: -7.349130, 24.909956" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 40.71427, + "lon": -73.95347, + "name": "Williamsburg" + }, + "point_b": { + "lat": -23.45442, + "lon": -46.66209, + "name": "Cachoeirinha" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 24.978168, + "lon": -65.477289 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (40.71427°, -73.95347°)", + " Point B: (-23.45442°, -46.66209°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 24.978168°", + " Longitude: -65.477289°", + "FINAL ANSWER: 24.978168, -65.477289" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -20.55722, + "lon": -48.56778, + "name": "Barretos" + }, + "point_b": { + "lat": 31.57851, + "lon": -84.15574, + "name": "Albany" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -7.466427, + "lon": -57.289471 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-20.55722°, -48.56778°)", + " Point B: (31.57851°, -84.15574°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -7.466427°", + " Longitude: -57.289471°", + "FINAL ANSWER: -7.466427, -57.289471" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 47.3264, + "lon": 8.79779, + "name": "Wetzikon" + }, + "point_b": { + "lat": 38.95178, + "lon": 40.02706, + "name": "Karakoçan" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 44.209902, + "lon": 25.510866 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (47.3264°, 8.79779°)", + " Point B: (38.95178°, 40.02706°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 44.209902°", + " Longitude: 25.510866°", + "FINAL ANSWER: 44.209902, 25.510866" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -1.19583, + "lon": -47.18083, + "name": "Capanema" + }, + "point_b": { + "lat": 21.22305, + "lon": 81.45609, + "name": "Bhilai Charoda" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 22.115146, + "lon": 12.975618 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-1.19583°, -47.18083°)", + " Point B: (21.22305°, 81.45609°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 22.115146°", + " Longitude: 12.975618°", + "FINAL ANSWER: 22.115146, 12.975618" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 21.16772, + "lon": 75.69762, + "name": "Yāval" + }, + "point_b": { + "lat": 9.89206, + "lon": 43.38531, + "name": "Baki" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 18.835309, + "lon": 67.267813 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (21.16772°, 75.69762°)", + " Point B: (9.89206°, 43.38531°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 18.835309°", + " Longitude: 67.267813°", + "FINAL ANSWER: 18.835309, 67.267813" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 35.69222, + "lon": -0.49944, + "name": "Assi Bou Nif" + }, + "point_b": { + "lat": 50.54384, + "lon": 7.24639, + "name": "Sinzig" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 39.449654, + "lon": 1.108791 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (35.69222°, -0.49944°)", + " Point B: (50.54384°, 7.24639°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 39.449654°", + " Longitude: 1.108791°", + "FINAL ANSWER: 39.449654, 1.108791" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -24.55611, + "lon": -54.05667, + "name": "Marechal Cândido Rondon" + }, + "point_b": { + "lat": 57.72101, + "lon": 12.9401, + "name": "Borås" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -2.640513, + "lon": -41.97245 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-24.55611°, -54.05667°)", + " Point B: (57.72101°, 12.9401°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -2.640513°", + " Longitude: -41.972450°", + "FINAL ANSWER: -2.640513, -41.972450" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -8.45806, + "lon": -35.94472, + "name": "Agrestina" + }, + "point_b": { + "lat": 5.53449, + "lon": -0.41679, + "name": "Kasoa" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -1.534935, + "lon": -18.123272 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-8.45806°, -35.94472°)", + " Point B: (5.53449°, -0.41679°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -1.534935°", + " Longitude: -18.123272°", + "FINAL ANSWER: -1.534935, -18.123272" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 34.76143, + "lon": 135.51567, + "name": "Suita" + }, + "point_b": { + "lat": 29.76096, + "lon": 76.56034, + "name": "Pūndri" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 33.676713, + "lon": 90.34397 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (34.76143°, 135.51567°)", + " Point B: (29.76096°, 76.56034°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 33.676713°", + " Longitude: 90.343970°", + "FINAL ANSWER: 33.676713, 90.343970" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 35.35043, + "lon": 139.87029, + "name": "Kimitsu" + }, + "point_b": { + "lat": -10.12556, + "lon": -36.17556, + "name": "Coruripe" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 72.705173, + "lon": 120.519061 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (35.35043°, 139.87029°)", + " Point B: (-10.12556°, -36.17556°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 72.705173°", + " Longitude: 120.519061°", + "FINAL ANSWER: 72.705173, 120.519061" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 33.51667, + "lon": 6.95, + "name": "Debila" + }, + "point_b": { + "lat": -4.41594, + "lon": -40.90471, + "name": "Croatá" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 5.815182, + "lon": -30.27018 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (33.51667°, 6.95°)", + " Point B: (-4.41594°, -40.90471°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 5.815182°", + " Longitude: -30.270180°", + "FINAL ANSWER: 5.815182, -30.270180" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 30.6885, + "lon": 76.40111, + "name": "Basi" + }, + "point_b": { + "lat": 34.07034, + "lon": 72.62147, + "name": "Topi" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 32.393515, + "lon": 74.546679 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (30.6885°, 76.40111°)", + " Point B: (34.07034°, 72.62147°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 32.393515°", + " Longitude: 74.546679°", + "FINAL ANSWER: 32.393515, 74.546679" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 31.21114, + "lon": 31.05119, + "name": "Sīdī Ghāzī" + }, + "point_b": { + "lat": 21.68562, + "lon": 75.09622, + "name": "Sendhwa" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 28.215103, + "lon": 54.034159 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (31.21114°, 31.05119°)", + " Point B: (21.68562°, 75.09622°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 28.215103°", + " Longitude: 54.034159°", + "FINAL ANSWER: 28.215103, 54.034159" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 26.4673, + "lon": -81.80147, + "name": "San Carlos Park" + }, + "point_b": { + "lat": 33.63333, + "lon": 115.18333, + "name": "Xincheng" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 54.214511, + "lon": -95.161872 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (26.4673°, -81.80147°)", + " Point B: (33.63333°, 115.18333°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 54.214511°", + " Longitude: -95.161872°", + "FINAL ANSWER: 54.214511, -95.161872" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 9.26927, + "lon": -2.9951, + "name": "Bouna" + }, + "point_b": { + "lat": 22.38333, + "lon": 114.18333, + "name": "Sha Tin" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 21.131585, + "lon": 23.02357 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (9.26927°, -2.9951°)", + " Point B: (22.38333°, 114.18333°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 21.131585°", + " Longitude: 23.023570°", + "FINAL ANSWER: 21.131585, 23.023570" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 46.13544, + "lon": -64.90504, + "name": "Lutes Mountain" + }, + "point_b": { + "lat": 60.40338, + "lon": 25.105, + "name": "Kerava" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 63.888112, + "lon": -1.480943 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (46.13544°, -64.90504°)", + " Point B: (60.40338°, 25.105°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 63.888112°", + " Longitude: -1.480943°", + "FINAL ANSWER: 63.888112, -1.480943" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 40.67343, + "lon": -73.43651, + "name": "East Massapequa" + }, + "point_b": { + "lat": 53.82499, + "lon": 39.5531, + "name": "Skopin" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 53.73994, + "lon": -56.413316 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (40.67343°, -73.43651°)", + " Point B: (53.82499°, 39.5531°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 53.739940°", + " Longitude: -56.413316°", + "FINAL ANSWER: 53.739940, -56.413316" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 28.00311, + "lon": 79.00821, + "name": "Ujhāni" + }, + "point_b": { + "lat": 40.70621, + "lon": -73.30623, + "name": "West Islip" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 69.880783, + "lon": 20.010488 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (28.00311°, 79.00821°)", + " Point B: (40.70621°, -73.30623°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 69.880783°", + " Longitude: 20.010488°", + "FINAL ANSWER: 69.880783, 20.010488" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 31.06251, + "lon": 113.76545, + "name": "Yunmeng Chengguanzhen" + }, + "point_b": { + "lat": 48.20854, + "lon": 12.39893, + "name": "Waldkraiburg" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 54.128761, + "lon": 40.684697 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (31.06251°, 113.76545°)", + " Point B: (48.20854°, 12.39893°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 54.128761°", + " Longitude: 40.684697°", + "FINAL ANSWER: 54.128761, 40.684697" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 18.48511, + "lon": -69.84757, + "name": "Santo Domingo Este" + }, + "point_b": { + "lat": -11.31667, + "lon": -38.23333, + "name": "Itapicuru" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 3.724657, + "lon": -53.770088 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (18.48511°, -69.84757°)", + " Point B: (-11.31667°, -38.23333°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 3.724657°", + " Longitude: -53.770088°", + "FINAL ANSWER: 3.724657, -53.770088" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 17.69134, + "lon": 83.00395, + "name": "Anakapalle" + }, + "point_b": { + "lat": -40.95972, + "lon": 175.6575, + "name": "Masterton" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -31.462972, + "lon": 145.631965 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (17.69134°, 83.00395°)", + " Point B: (-40.95972°, 175.6575°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -31.462972°", + " Longitude: 145.631965°", + "FINAL ANSWER: -31.462972, 145.631965" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 5.285, + "lon": -0.746, + "name": "Apam" + }, + "point_b": { + "lat": 11.74099, + "lon": 78.04559, + "name": "Omalur" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 12.051544, + "lon": 58.120767 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (5.285°, -0.746°)", + " Point B: (11.74099°, 78.04559°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 12.051544°", + " Longitude: 58.120767°", + "FINAL ANSWER: 12.051544, 58.120767" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 49.27732, + "lon": -0.7039, + "name": "Bayeux" + }, + "point_b": { + "lat": 1.7471, + "lon": 40.05732, + "name": "Wajir" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 14.461965, + "lon": 32.555649 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (49.27732°, -0.7039°)", + " Point B: (1.7471°, 40.05732°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 14.461965°", + " Longitude: 32.555649°", + "FINAL ANSWER: 14.461965, 32.555649" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 19.06406, + "lon": -98.30352, + "name": "Cholula" + }, + "point_b": { + "lat": 18.03413, + "lon": 77.77284, + "name": "Nārāyankher" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 54.42454, + "lon": -92.124352 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (19.06406°, -98.30352°)", + " Point B: (18.03413°, 77.77284°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 54.424540°", + " Longitude: -92.124352°", + "FINAL ANSWER: 54.424540, -92.124352" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 37.88576, + "lon": -122.11802, + "name": "Lafayette" + }, + "point_b": { + "lat": 2.2594, + "lon": 102.1838, + "name": "Bukit Rambai" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 24.776785, + "lon": 123.778704 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (37.88576°, -122.11802°)", + " Point B: (2.2594°, 102.1838°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 24.776785°", + " Longitude: 123.778704°", + "FINAL ANSWER: 24.776785, 123.778704" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 37.224, + "lon": 49.3125, + "name": "Fūman" + }, + "point_b": { + "lat": -20.43278, + "lon": -51.3425, + "name": "Ilha Solteira" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -4.040666, + "lon": -28.513702 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (37.224°, 49.3125°)", + " Point B: (-20.43278°, -51.3425°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -4.040666°", + " Longitude: -28.513702°", + "FINAL ANSWER: -4.040666, -28.513702" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 31.97102, + "lon": 34.78939, + "name": "Rishon LeTsiyyon" + }, + "point_b": { + "lat": 34.68473, + "lon": -6.00344, + "name": "Souk El Arbaa" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 35.051472, + "lon": 14.724788 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (31.97102°, 34.78939°)", + " Point B: (34.68473°, -6.00344°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 35.051472°", + " Longitude: 14.724788°", + "FINAL ANSWER: 35.051472, 14.724788" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 4.7466, + "lon": 9.6705, + "name": "Tombel" + }, + "point_b": { + "lat": 29.92885, + "lon": 117.94638, + "name": "Biyang" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 32.50671, + "lon": 87.807691 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (4.7466°, 9.6705°)", + " Point B: (29.92885°, 117.94638°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 32.506710°", + " Longitude: 87.807691°", + "FINAL ANSWER: 32.506710, 87.807691" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 51.66166, + "lon": 6.96514, + "name": "Dorsten" + }, + "point_b": { + "lat": 55.83928, + "lon": 13.30393, + "name": "Eslöv" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 52.73645, + "lon": 8.43413 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (51.66166°, 6.96514°)", + " Point B: (55.83928°, 13.30393°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 52.736450°", + " Longitude: 8.434130°", + "FINAL ANSWER: 52.736450, 8.434130" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -25.74946, + "lon": -56.43518, + "name": "Villarrica" + }, + "point_b": { + "lat": -23.56742, + "lon": -46.43264, + "name": "Jose Bonifacio" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -24.741405, + "lon": -51.390074 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-25.74946°, -56.43518°)", + " Point B: (-23.56742°, -46.43264°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -24.741405°", + " Longitude: -51.390074°", + "FINAL ANSWER: -24.741405, -51.390074" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 36.89556, + "lon": 8.44333, + "name": "El Kala" + }, + "point_b": { + "lat": -36.88745, + "lon": 174.77059, + "name": "Epsom" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 0.034066, + "lon": 91.632348 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (36.89556°, 8.44333°)", + " Point B: (-36.88745°, 174.77059°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 0.034066°", + " Longitude: 91.632348°", + "FINAL ANSWER: 0.034066, 91.632348" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 50.79509, + "lon": -1.12902, + "name": "Gosport" + }, + "point_b": { + "lat": 42.39176, + "lon": -71.03283, + "name": "Chelsea" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 52.173937, + "lon": -39.188301 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (50.79509°, -1.12902°)", + " Point B: (42.39176°, -71.03283°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 52.173937°", + " Longitude: -39.188301°", + "FINAL ANSWER: 52.173937, -39.188301" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 40.41896, + "lon": -80.58952, + "name": "Weirton" + }, + "point_b": { + "lat": 48.10537, + "lon": 11.76825, + "name": "Vaterstetten" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 54.544293, + "lon": -38.313317 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (40.41896°, -80.58952°)", + " Point B: (48.10537°, 11.76825°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 54.544293°", + " Longitude: -38.313317°", + "FINAL ANSWER: 54.544293, -38.313317" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -22.95833, + "lon": -45.54944, + "name": "Tremembé" + }, + "point_b": { + "lat": -0.9575, + "lon": 29.78972, + "name": "Kanungu" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -20.057255, + "lon": -25.311073 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-22.95833°, -45.54944°)", + " Point B: (-0.9575°, 29.78972°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -20.057255°", + " Longitude: -25.311073°", + "FINAL ANSWER: -20.057255, -25.311073" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 51.04358, + "lon": 13.69444, + "name": "Löbtau" + }, + "point_b": { + "lat": 51.9225, + "lon": 4.47917, + "name": "Rotterdam" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 51.330643, + "lon": 11.42605 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (51.04358°, 13.69444°)", + " Point B: (51.9225°, 4.47917°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 51.330643°", + " Longitude: 11.426050°", + "FINAL ANSWER: 51.330643, 11.426050" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 44.05817, + "lon": -121.31531, + "name": "Bend" + }, + "point_b": { + "lat": 26.08657, + "lon": 32.42265, + "name": "Al Waqf" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 66.085884, + "lon": -94.30911 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (44.05817°, -121.31531°)", + " Point B: (26.08657°, 32.42265°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 66.085884°", + " Longitude: -94.309110°", + "FINAL ANSWER: 66.085884, -94.309110" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 29.76328, + "lon": -95.36327, + "name": "Houston" + }, + "point_b": { + "lat": 38.91667, + "lon": 141.13333, + "name": "Ichinoseki" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 55.148072, + "lon": -151.303108 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (29.76328°, -95.36327°)", + " Point B: (38.91667°, 141.13333°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 55.148072°", + " Longitude: -151.303108°", + "FINAL ANSWER: 55.148072, -151.303108" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -37.87822, + "lon": 175.4402, + "name": "Cambridge" + }, + "point_b": { + "lat": 19.11285, + "lon": 77.96336, + "name": "Bhaisa" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 2.74854, + "lon": 99.712693 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-37.87822°, 175.4402°)", + " Point B: (19.11285°, 77.96336°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 2.748540°", + " Longitude: 99.712693°", + "FINAL ANSWER: 2.748540, 99.712693" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 12.97389, + "lon": 123.99333, + "name": "Sorsogon" + }, + "point_b": { + "lat": -28.78389, + "lon": -51.61, + "name": "Nova Prata" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -26.750808, + "lon": 113.898938 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (12.97389°, 123.99333°)", + " Point B: (-28.78389°, -51.61°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -26.750808°", + " Longitude: 113.898938°", + "FINAL ANSWER: -26.750808, 113.898938" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 6.65915, + "lon": 7.75961, + "name": "Eha Amufu" + }, + "point_b": { + "lat": 59.75069, + "lon": 30.58856, + "name": "Kolpino" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 46.948934, + "lon": 21.115121 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (6.65915°, 7.75961°)", + " Point B: (59.75069°, 30.58856°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 46.948934°", + " Longitude: 21.115121°", + "FINAL ANSWER: 46.948934, 21.115121" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 51.66446, + "lon": 7.63421, + "name": "Werne" + }, + "point_b": { + "lat": 33.7515, + "lon": -84.74771, + "name": "Douglasville" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 52.817598, + "lon": -47.180076 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (51.66446°, 7.63421°)", + " Point B: (33.7515°, -84.74771°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 52.817598°", + " Longitude: -47.180076°", + "FINAL ANSWER: 52.817598, -47.180076" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 55.1904, + "lon": 30.2049, + "name": "Vitebsk" + }, + "point_b": { + "lat": 47.8638, + "lon": 12.01055, + "name": "Bad Aibling" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 49.945688, + "lon": 16.015554 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (55.1904°, 30.2049°)", + " Point B: (47.8638°, 12.01055°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 49.945688°", + " Longitude: 16.015554°", + "FINAL ANSWER: 49.945688, 16.015554" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -21.93472, + "lon": -50.51361, + "name": "Tupã" + }, + "point_b": { + "lat": -29.99569, + "lon": 30.80724, + "name": "Folweni" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -33.148075, + "lon": 9.950496 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-21.93472°, -50.51361°)", + " Point B: (-29.99569°, 30.80724°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -33.148075°", + " Longitude: 9.950496°", + "FINAL ANSWER: -33.148075, 9.950496" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 40.73583, + "lon": 31.60611, + "name": "Bolu" + }, + "point_b": { + "lat": 6.81944, + "lon": 3.91731, + "name": "Ijebu Ode" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 15.688231, + "lon": 9.63241 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (40.73583°, 31.60611°)", + " Point B: (6.81944°, 3.91731°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 15.688231°", + " Longitude: 9.632410°", + "FINAL ANSWER: 15.688231, 9.632410" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 40.72316, + "lon": -73.91264, + "name": "Maspeth" + }, + "point_b": { + "lat": 43.27083, + "lon": 5.3821, + "name": "Marseille 08" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 49.457513, + "lon": -35.21569 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (40.72316°, -73.91264°)", + " Point B: (43.27083°, 5.3821°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 49.457513°", + " Longitude: -35.215690°", + "FINAL ANSWER: 49.457513, -35.215690" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 53.32498, + "lon": -3.83148, + "name": "Llandudno" + }, + "point_b": { + "lat": -8.4504, + "lon": 115.5925, + "name": "Bedugul" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 53.037655, + "lon": 44.707505 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (53.32498°, -3.83148°)", + " Point B: (-8.4504°, 115.5925°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 53.037655°", + " Longitude: 44.707505°", + "FINAL ANSWER: 53.037655, 44.707505" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -5.7, + "lon": 34.48333, + "name": "Itigi" + }, + "point_b": { + "lat": 45.93778, + "lon": 8.57088, + "name": "Pallanza-Intra-Suna" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 7.474265, + "lon": 29.335151 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-5.7°, 34.48333°)", + " Point B: (45.93778°, 8.57088°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 7.474265°", + " Longitude: 29.335151°", + "FINAL ANSWER: 7.474265, 29.335151" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 35.3242, + "lon": 51.6457, + "name": "Varāmīn" + }, + "point_b": { + "lat": -3.54964, + "lon": 143.63229, + "name": "Wewak" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 9.896936, + "lon": 124.385404 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (35.3242°, 51.6457°)", + " Point B: (-3.54964°, 143.63229°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 9.896936°", + " Longitude: 124.385404°", + "FINAL ANSWER: 9.896936, 124.385404" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -37.91928, + "lon": 145.05301, + "name": "Bentleigh East" + }, + "point_b": { + "lat": -14.91694, + "lon": 40.30222, + "name": "Monapo" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -42.451988, + "lon": 115.353119 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-37.91928°, 145.05301°)", + " Point B: (-14.91694°, 40.30222°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -42.451988°", + " Longitude: 115.353119°", + "FINAL ANSWER: -42.451988, 115.353119" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 48.71419, + "lon": 8.74031, + "name": "Calw" + }, + "point_b": { + "lat": 12.234, + "lon": 79.65551, + "name": "Tindivanam" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 24.533299, + "lon": 67.147429 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (48.71419°, 8.74031°)", + " Point B: (12.234°, 79.65551°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 24.533299°", + " Longitude: 67.147429°", + "FINAL ANSWER: 24.533299, 67.147429" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -22.40293, + "lon": 46.12576, + "name": "Ihosy" + }, + "point_b": { + "lat": 56.33871, + "lon": -2.79902, + "name": "Saint Andrews" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 18.4206, + "lon": 28.161368 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-22.40293°, 46.12576°)", + " Point B: (56.33871°, -2.79902°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 18.420600°", + " Longitude: 28.161368°", + "FINAL ANSWER: 18.420600, 28.161368" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 31.01547, + "lon": 47.43362, + "name": "Al Qurnah" + }, + "point_b": { + "lat": 18.82154, + "lon": 78.71186, + "name": "Koratla" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 25.752247, + "lon": 63.868632 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (31.01547°, 47.43362°)", + " Point B: (18.82154°, 78.71186°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 25.752247°", + " Longitude: 63.868632°", + "FINAL ANSWER: 25.752247, 63.868632" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 51.7604, + "lon": -0.56528, + "name": "Berkhamsted" + }, + "point_b": { + "lat": 43.29194, + "lon": 126.00944, + "name": "Yantongshan" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 64.317729, + "lon": 25.947759 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (51.7604°, -0.56528°)", + " Point B: (43.29194°, 126.00944°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 64.317729°", + " Longitude: 25.947759°", + "FINAL ANSWER: 64.317729, 25.947759" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 27.86614, + "lon": -82.32648, + "name": "Riverview" + }, + "point_b": { + "lat": 36.8427, + "lon": 54.44391, + "name": "Gorgān" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 59.628272, + "lon": -21.094646 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (27.86614°, -82.32648°)", + " Point B: (36.8427°, 54.44391°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 59.628272°", + " Longitude: -21.094646°", + "FINAL ANSWER: 59.628272, -21.094646" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -4.21861, + "lon": 13.76167, + "name": "Bouansa" + }, + "point_b": { + "lat": 38.86101, + "lon": -9.06453, + "name": "Póvoa de Santa Iria" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 6.738043, + "lon": 8.880718 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-4.21861°, 13.76167°)", + " Point B: (38.86101°, -9.06453°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 6.738043°", + " Longitude: 8.880718°", + "FINAL ANSWER: 6.738043, 8.880718" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -16.36314, + "lon": -72.1921, + "name": "El Pedregal" + }, + "point_b": { + "lat": 12.25162, + "lon": -0.42565, + "name": "Pouytenga" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -9.933845, + "lon": -53.682139 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-16.36314°, -72.1921°)", + " Point B: (12.25162°, -0.42565°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -9.933845°", + " Longitude: -53.682139°", + "FINAL ANSWER: -9.933845, -53.682139" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -6.14755, + "lon": 143.65633, + "name": "Mendi" + }, + "point_b": { + "lat": 35.69006, + "lon": 10.67598, + "name": "Ouerdanine" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 32.779002, + "lon": 90.210581 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-6.14755°, 143.65633°)", + " Point B: (35.69006°, 10.67598°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 32.779002°", + " Longitude: 90.210581°", + "FINAL ANSWER: 32.779002, 90.210581" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 11.54444, + "lon": -72.90722, + "name": "Riohacha" + }, + "point_b": { + "lat": 31.34038, + "lon": -110.93425, + "name": "Nogales" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 22.55303, + "lon": -90.567926 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (11.54444°, -72.90722°)", + " Point B: (31.34038°, -110.93425°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 22.553030°", + " Longitude: -90.567926°", + "FINAL ANSWER: 22.553030, -90.567926" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 5.92801, + "lon": -4.21319, + "name": "Agboville" + }, + "point_b": { + "lat": -10.97833, + "lon": -39.62639, + "name": "Queimadas" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -2.650554, + "lon": -21.799898 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (5.92801°, -4.21319°)", + " Point B: (-10.97833°, -39.62639°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -2.650554°", + " Longitude: -21.799898°", + "FINAL ANSWER: -2.650554, -21.799898" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 30.65, + "lon": 113.1, + "name": "Jingling" + }, + "point_b": { + "lat": 40.05, + "lon": 0.06667, + "name": "Benicàssim" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 52.018601, + "lon": 61.621871 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (30.65°, 113.1°)", + " Point B: (40.05°, 0.06667°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 52.018601°", + " Longitude: 61.621871°", + "FINAL ANSWER: 52.018601, 61.621871" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 50.80904, + "lon": 8.77069, + "name": "Marburg an der Lahn" + }, + "point_b": { + "lat": 31.91102, + "lon": 120.26302, + "name": "Jiangyin" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 58.717848, + "lon": 39.951005 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (50.80904°, 8.77069°)", + " Point B: (31.91102°, 120.26302°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 58.717848°", + " Longitude: 39.951005°", + "FINAL ANSWER: 58.717848, 39.951005" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -0.50974, + "lon": 34.73067, + "name": "Oyugis" + }, + "point_b": { + "lat": -30.08389, + "lon": -51.61611, + "name": "Eldorado do Sul" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -27.268952, + "lon": -27.105198 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-0.50974°, 34.73067°)", + " Point B: (-30.08389°, -51.61611°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -27.268952°", + " Longitude: -27.105198°", + "FINAL ANSWER: -27.268952, -27.105198" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 22.78498, + "lon": 88.32586, + "name": "Baidyabāti" + }, + "point_b": { + "lat": 34.3665, + "lon": -89.51925, + "name": "Oxford" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 65.020746, + "lon": -86.660594 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (22.78498°, 88.32586°)", + " Point B: (34.3665°, -89.51925°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 65.020746°", + " Longitude: -86.660594°", + "FINAL ANSWER: 65.020746, -86.660594" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 31.16611, + "lon": 112.58306, + "name": "Zhongxiang" + }, + "point_b": { + "lat": 47.92038, + "lon": 123.50046, + "name": "Gannan" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 35.441299, + "lon": 114.852821 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (31.16611°, 112.58306°)", + " Point B: (47.92038°, 123.50046°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 35.441299°", + " Longitude: 114.852821°", + "FINAL ANSWER: 35.441299, 114.852821" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 28.56456, + "lon": 77.15126, + "name": "Murādābād Pahāri" + }, + "point_b": { + "lat": 52.80521, + "lon": -2.11636, + "name": "Stafford" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 47.815315, + "lon": 46.211357 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (28.56456°, 77.15126°)", + " Point B: (52.80521°, -2.11636°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 47.815315°", + " Longitude: 46.211357°", + "FINAL ANSWER: 47.815315, 46.211357" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 20.70137, + "lon": -103.97461, + "name": "Ahualulco de Mercado" + }, + "point_b": { + "lat": 45.64997, + "lon": 0.15345, + "name": "Angoulême" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 35.240356, + "lon": -86.458972 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (20.70137°, -103.97461°)", + " Point B: (45.64997°, 0.15345°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 35.240356°", + " Longitude: -86.458972°", + "FINAL ANSWER: 35.240356, -86.458972" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -9.01667, + "lon": 34.8, + "name": "Mtwango" + }, + "point_b": { + "lat": 14.90598, + "lon": 105.07836, + "name": "Det Udom" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -2.837631, + "lon": 52.243481 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-9.01667°, 34.8°)", + " Point B: (14.90598°, 105.07836°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -2.837631°", + " Longitude: 52.243481°", + "FINAL ANSWER: -2.837631, 52.243481" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 16.96036, + "lon": 82.23809, + "name": "Kākināda" + }, + "point_b": { + "lat": 39.40371, + "lon": -76.95026, + "name": "Eldersburg" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 68.718528, + "lon": 32.708453 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (16.96036°, 82.23809°)", + " Point B: (39.40371°, -76.95026°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 68.718528°", + " Longitude: 32.708453°", + "FINAL ANSWER: 68.718528, 32.708453" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -20.17944, + "lon": -48.03194, + "name": "Miguelópolis" + }, + "point_b": { + "lat": 31.1933, + "lon": 120.71758, + "name": "Songling" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 12.282437, + "lon": -22.141333 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-20.17944°, -48.03194°)", + " Point B: (31.1933°, 120.71758°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 12.282437°", + " Longitude: -22.141333°", + "FINAL ANSWER: 12.282437, -22.141333" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 43.42107, + "lon": 11.12739, + "name": "Colle di Val d'Elsa" + }, + "point_b": { + "lat": 33.97612, + "lon": -117.90534, + "name": "Rowland Heights" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 61.532415, + "lon": -61.293987 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (43.42107°, 11.12739°)", + " Point B: (33.97612°, -117.90534°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 61.532415°", + " Longitude: -61.293987°", + "FINAL ANSWER: 61.532415, -61.293987" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 60.98267, + "lon": 25.66151, + "name": "Lahti" + }, + "point_b": { + "lat": 29.3375, + "lon": 47.65806, + "name": "Al Jahrā’" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 45.647227, + "lon": 39.829966 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (60.98267°, 25.66151°)", + " Point B: (29.3375°, 47.65806°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 45.647227°", + " Longitude: 39.829966°", + "FINAL ANSWER: 45.647227, 39.829966" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 12.2, + "lon": -10.7, + "name": "Sagalo" + }, + "point_b": { + "lat": 52.0488, + "lon": 20.44599, + "name": "Żyrardów" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 42.939908, + "lon": 9.356141 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (12.2°, -10.7°)", + " Point B: (52.0488°, 20.44599°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 42.939908°", + " Longitude: 9.356141°", + "FINAL ANSWER: 42.939908, 9.356141" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -5.25837, + "lon": 14.85838, + "name": "Mbanza-Ngungu" + }, + "point_b": { + "lat": 12.8939, + "lon": -14.94125, + "name": "Kolda" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 3.950167, + "lon": 0.121078 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-5.25837°, 14.85838°)", + " Point B: (12.8939°, -14.94125°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 3.950167°", + " Longitude: 0.121078°", + "FINAL ANSWER: 3.950167, 0.121078" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 15.65841, + "lon": -91.42994, + "name": "Soloma" + }, + "point_b": { + "lat": 37.85944, + "lon": 126.785, + "name": "Munsan" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 55.97536, + "lon": -146.384279 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (15.65841°, -91.42994°)", + " Point B: (37.85944°, 126.785°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 55.975360°", + " Longitude: -146.384279°", + "FINAL ANSWER: 55.975360, -146.384279" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -6.75472, + "lon": -51.08389, + "name": "Ourilândia do Norte" + }, + "point_b": { + "lat": 38.91872, + "lon": -77.23109, + "name": "Tysons" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 27.892327, + "lon": -69.117873 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-6.75472°, -51.08389°)", + " Point B: (38.91872°, -77.23109°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 27.892327°", + " Longitude: -69.117873°", + "FINAL ANSWER: 27.892327, -69.117873" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 40.79968, + "lon": 16.92298, + "name": "Gioia del Colle" + }, + "point_b": { + "lat": 11.97634, + "lon": 75.41675, + "name": "Kolaccheri" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 29.561368, + "lon": 50.253393 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (40.79968°, 16.92298°)", + " Point B: (11.97634°, 75.41675°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 29.561368°", + " Longitude: 50.253393°", + "FINAL ANSWER: 29.561368, 50.253393" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 24.56427, + "lon": 120.82367, + "name": "Miaoli" + }, + "point_b": { + "lat": -34.65187, + "lon": -71.19724, + "name": "Nancagua" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -51.475955, + "lon": -124.584706 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (24.56427°, 120.82367°)", + " Point B: (-34.65187°, -71.19724°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -51.475955°", + " Longitude: -124.584706°", + "FINAL ANSWER: -51.475955, -124.584706" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 14.24362, + "lon": -16.27231, + "name": "Gandiaye" + }, + "point_b": { + "lat": 17.699, + "lon": 103.25957, + "name": "Ban Dung" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 26.893735, + "lon": 74.482382 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (14.24362°, -16.27231°)", + " Point B: (17.699°, 103.25957°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 26.893735°", + " Longitude: 74.482382°", + "FINAL ANSWER: 26.893735, 74.482382" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 40.76496, + "lon": -73.9909, + "name": "Hell's Kitchen" + }, + "point_b": { + "lat": 32.21667, + "lon": 130.4, + "name": "Minamata" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 63.65254, + "lon": -94.715394 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (40.76496°, -73.9909°)", + " Point B: (32.21667°, 130.4°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 63.652540°", + " Longitude: -94.715394°", + "FINAL ANSWER: 63.652540, -94.715394" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 8.55666, + "lon": -74.26355, + "name": "Tiquisio" + }, + "point_b": { + "lat": -9.39667, + "lon": -36.15361, + "name": "Cajueiro" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -0.444352, + "lon": -55.231497 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (8.55666°, -74.26355°)", + " Point B: (-9.39667°, -36.15361°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -0.444352°", + " Longitude: -55.231497°", + "FINAL ANSWER: -0.444352, -55.231497" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -15.47949, + "lon": -44.3652, + "name": "Januária" + }, + "point_b": { + "lat": 34.61581, + "lon": 43.67861, + "name": "Tikrīt" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 13.156346, + "lon": -4.696804 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-15.47949°, -44.3652°)", + " Point B: (34.61581°, 43.67861°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 13.156346°", + " Longitude: -4.696804°", + "FINAL ANSWER: 13.156346, -4.696804" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 47.90248, + "lon": 1.90407, + "name": "Orléans" + }, + "point_b": { + "lat": 25.75089, + "lon": 32.6776, + "name": "Az Zaynīyah Qiblī" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 43.197344, + "lon": 11.483049 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (47.90248°, 1.90407°)", + " Point B: (25.75089°, 32.6776°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 43.197344°", + " Longitude: 11.483049°", + "FINAL ANSWER: 43.197344, 11.483049" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 6.5225, + "lon": 124.65917, + "name": "Norala" + }, + "point_b": { + "lat": -6.12085, + "lon": 14.62086, + "name": "Cuímba" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 3.873762, + "lon": 97.037027 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (6.5225°, 124.65917°)", + " Point B: (-6.12085°, 14.62086°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 3.873762°", + " Longitude: 97.037027°", + "FINAL ANSWER: 3.873762, 97.037027" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 36.83528, + "lon": 7.45333, + "name": "Berrahal" + }, + "point_b": { + "lat": -23.88384, + "lon": 29.70557, + "name": "Mankweng" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 21.82162, + "lon": 14.03214 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (36.83528°, 7.45333°)", + " Point B: (-23.88384°, 29.70557°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 21.821620°", + " Longitude: 14.032140°", + "FINAL ANSWER: 21.821620, 14.032140" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 1.3504, + "lon": 103.84875, + "name": "Bishan New Town" + }, + "point_b": { + "lat": -16.39899, + "lon": -71.53747, + "name": "Arequipa" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -37.72182, + "lon": 90.164946 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (1.3504°, 103.84875°)", + " Point B: (-16.39899°, -71.53747°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -37.721820°", + " Longitude: 90.164946°", + "FINAL ANSWER: -37.721820, 90.164946" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 25.03889, + "lon": 102.71833, + "name": "Kunming" + }, + "point_b": { + "lat": -13.71029, + "lon": -76.20538, + "name": "Pisco" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 28.287873, + "lon": -72.434125 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (25.03889°, 102.71833°)", + " Point B: (-13.71029°, -76.20538°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 28.287873°", + " Longitude: -72.434125°", + "FINAL ANSWER: 28.287873, -72.434125" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 30.15522, + "lon": -95.21132, + "name": "New Caney" + }, + "point_b": { + "lat": -38.8805, + "lon": -62.07503, + "name": "Punta Alta" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -4.550288, + "lon": -79.537462 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (30.15522°, -95.21132°)", + " Point B: (-38.8805°, -62.07503°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -4.550288°", + " Longitude: -79.537462°", + "FINAL ANSWER: -4.550288, -79.537462" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 35.29483, + "lon": 139.57812, + "name": "Zushi" + }, + "point_b": { + "lat": -5.74306, + "lon": -39.6275, + "name": "Mombaça" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 72.866703, + "lon": 136.257475 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (35.29483°, 139.57812°)", + " Point B: (-5.74306°, -39.6275°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 72.866703°", + " Longitude: 136.257475°", + "FINAL ANSWER: 72.866703, 136.257475" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -21.03306, + "lon": -44.75806, + "name": "Bom Sucesso" + }, + "point_b": { + "lat": 25.14257, + "lon": 86.97967, + "name": "Purāini" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 17.975699, + "lon": 51.226308 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-21.03306°, -44.75806°)", + " Point B: (25.14257°, 86.97967°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 17.975699°", + " Longitude: 51.226308°", + "FINAL ANSWER: 17.975699, 51.226308" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 36.73944, + "lon": 7.10528, + "name": "Azzaba" + }, + "point_b": { + "lat": -9.07786, + "lon": 143.20893, + "name": "Daru" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 32.528397, + "lon": 89.633608 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (36.73944°, 7.10528°)", + " Point B: (-9.07786°, 143.20893°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 32.528397°", + " Longitude: 89.633608°", + "FINAL ANSWER: 32.528397, 89.633608" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 36.45028, + "lon": 6.26444, + "name": "Mila" + }, + "point_b": { + "lat": 26.66167, + "lon": 119.52278, + "name": "Ningde" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 46.503014, + "lon": 33.735282 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (36.45028°, 6.26444°)", + " Point B: (26.66167°, 119.52278°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 46.503014°", + " Longitude: 33.735282°", + "FINAL ANSWER: 46.503014, 33.735282" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 41.83844, + "lon": 15.56535, + "name": "Sannicandro Garganico" + }, + "point_b": { + "lat": 45.81667, + "lon": 4.9, + "name": "Rillieux-la-Pape" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 44.91726, + "lon": 7.700189 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (41.83844°, 15.56535°)", + " Point B: (45.81667°, 4.9°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 44.917260°", + " Longitude: 7.700189°", + "FINAL ANSWER: 44.917260, 7.700189" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 53.65917, + "lon": 10.08472, + "name": "Poppenbüttel" + }, + "point_b": { + "lat": 20.43189, + "lon": 96.13875, + "name": "Yamethin" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 52.792046, + "lon": 40.077623 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (53.65917°, 10.08472°)", + " Point B: (20.43189°, 96.13875°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 52.792046°", + " Longitude: 40.077623°", + "FINAL ANSWER: 52.792046, 40.077623" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 25.47509, + "lon": 85.96813, + "name": "Bāruni" + }, + "point_b": { + "lat": -22.27528, + "lon": -51.5, + "name": "Pirapozinho" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 4.401375, + "lon": 15.414693 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (25.47509°, 85.96813°)", + " Point B: (-22.27528°, -51.5°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 4.401375°", + " Longitude: 15.414693°", + "FINAL ANSWER: 4.401375, 15.414693" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -25.8725, + "lon": -49.49778, + "name": "Quitandinha" + }, + "point_b": { + "lat": 24.0692, + "lon": 120.5512, + "name": "Changhua" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 8.999029, + "lon": 78.639821 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-25.8725°, -49.49778°)", + " Point B: (24.0692°, 120.5512°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 8.999029°", + " Longitude: 78.639821°", + "FINAL ANSWER: 8.999029, 78.639821" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -23.27583, + "lon": -51.27833, + "name": "Cambé" + }, + "point_b": { + "lat": -37.74496, + "lon": 144.80049, + "name": "St Albans" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -74.967478, + "lon": -105.332011 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-23.27583°, -51.27833°)", + " Point B: (-37.74496°, 144.80049°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -74.967478°", + " Longitude: -105.332011°", + "FINAL ANSWER: -74.967478, -105.332011" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 34.70882, + "lon": 11.2147, + "name": "Kellabine" + }, + "point_b": { + "lat": -37.74124, + "lon": 144.73631, + "name": "Caroline Springs" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 18.022063, + "lon": 46.766692 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (34.70882°, 11.2147°)", + " Point B: (-37.74124°, 144.73631°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 18.022063°", + " Longitude: 46.766692°", + "FINAL ANSWER: 18.022063, 46.766692" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 40.78343, + "lon": -73.96625, + "name": "Manhattan" + }, + "point_b": { + "lat": 22.81567, + "lon": 70.86653, + "name": "Trajpar" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 60.159503, + "lon": -43.106106 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (40.78343°, -73.96625°)", + " Point B: (22.81567°, 70.86653°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 60.159503°", + " Longitude: -43.106106°", + "FINAL ANSWER: 60.159503, -43.106106" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 5.31667, + "lon": 39.58333, + "name": "Negēlē" + }, + "point_b": { + "lat": 42.24115, + "lon": -83.61299, + "name": "Ypsilanti" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 25.331057, + "lon": 19.914905 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (5.31667°, 39.58333°)", + " Point B: (42.24115°, -83.61299°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 25.331057°", + " Longitude: 19.914905°", + "FINAL ANSWER: 25.331057, 19.914905" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -6.23169, + "lon": -77.86903, + "name": "Chachapoyas" + }, + "point_b": { + "lat": -23.65055, + "lon": -46.64591, + "name": "Jabaquara" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -19.751388, + "lon": -54.986636 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-6.23169°, -77.86903°)", + " Point B: (-23.65055°, -46.64591°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -19.751388°", + " Longitude: -54.986636°", + "FINAL ANSWER: -19.751388, -54.986636" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 50.90634, + "lon": 4.00093, + "name": "Haaltert" + }, + "point_b": { + "lat": 9.43, + "lon": -82.52, + "name": "Changuinola" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 47.836198, + "lon": -26.781171 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (50.90634°, 4.00093°)", + " Point B: (9.43°, -82.52°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 47.836198°", + " Longitude: -26.781171°", + "FINAL ANSWER: 47.836198, -26.781171" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 9.18485, + "lon": 76.56076, + "name": "Bharanikāvu Tekku" + }, + "point_b": { + "lat": 54.52021, + "lon": 9.56829, + "name": "Schleswig" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 23.177598, + "lon": 65.901564 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (9.18485°, 76.56076°)", + " Point B: (54.52021°, 9.56829°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 23.177598°", + " Longitude: 65.901564°", + "FINAL ANSWER: 23.177598, 65.901564" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 40.85843, + "lon": -74.16376, + "name": "Clifton" + }, + "point_b": { + "lat": -25.85, + "lon": 25.63333, + "name": "Mmabatho" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 29.026041, + "lon": -42.376237 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (40.85843°, -74.16376°)", + " Point B: (-25.85°, 25.63333°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 29.026041°", + " Longitude: -42.376237°", + "FINAL ANSWER: 29.026041, -42.376237" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 42.97096, + "lon": 132.41035, + "name": "Fokino" + }, + "point_b": { + "lat": 8.40207, + "lon": 48.48284, + "name": "Garoowe" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 32.662752, + "lon": 82.781371 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (42.97096°, 132.41035°)", + " Point B: (8.40207°, 48.48284°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 32.662752°", + " Longitude: 82.781371°", + "FINAL ANSWER: 32.662752, 82.781371" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -10.37812, + "lon": 24.54516, + "name": "Malemba" + }, + "point_b": { + "lat": 25.39689, + "lon": 68.37718, + "name": "Hyderabad" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 17.060897, + "lon": 56.39757 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-10.37812°, 24.54516°)", + " Point B: (25.39689°, 68.37718°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 17.060897°", + " Longitude: 56.397570°", + "FINAL ANSWER: 17.060897, 56.397570" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -3.57972, + "lon": -59.13056, + "name": "Autazes" + }, + "point_b": { + "lat": 23.64824, + "lon": -100.64334, + "name": "Matehuala" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 3.62092, + "lon": -68.965264 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-3.57972°, -59.13056°)", + " Point B: (23.64824°, -100.64334°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 3.620920°", + " Longitude: -68.965264°", + "FINAL ANSWER: 3.620920, -68.965264" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -3.10056, + "lon": -45.03361, + "name": "Matinha" + }, + "point_b": { + "lat": -0.33379, + "lon": 31.73409, + "name": "Masaka" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -1.336117, + "lon": 12.565706 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-3.10056°, -45.03361°)", + " Point B: (-0.33379°, 31.73409°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -1.336117°", + " Longitude: 12.565706°", + "FINAL ANSWER: -1.336117, 12.565706" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 29.39306, + "lon": 106.81917, + "name": "Jiangjia" + }, + "point_b": { + "lat": 29.87522, + "lon": -98.26251, + "name": "Canyon Lake" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 54.571921, + "lon": 126.850839 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (29.39306°, 106.81917°)", + " Point B: (29.87522°, -98.26251°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 54.571921°", + " Longitude: 126.850839°", + "FINAL ANSWER: 54.571921, 126.850839" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 33.6103, + "lon": -117.72533, + "name": "Laguna Woods" + }, + "point_b": { + "lat": 4.43139, + "lon": -61.14639, + "name": "Pacaraima" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 13.209294, + "lon": -73.466675 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (33.6103°, -117.72533°)", + " Point B: (4.43139°, -61.14639°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 13.209294°", + " Longitude: -73.466675°", + "FINAL ANSWER: 13.209294, -73.466675" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 5.71681, + "lon": 100.65819, + "name": "Teloi Kanan" + }, + "point_b": { + "lat": 28.61052, + "lon": -13.92912, + "name": "La Oliva" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 29.636089, + "lon": 48.927105 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (5.71681°, 100.65819°)", + " Point B: (28.61052°, -13.92912°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 29.636089°", + " Longitude: 48.927105°", + "FINAL ANSWER: 29.636089, 48.927105" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 43.07704, + "lon": -70.75766, + "name": "Portsmouth" + }, + "point_b": { + "lat": 59.80083, + "lon": 30.54778, + "name": "Metallostroy" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 62.613587, + "lon": -32.779635 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (43.07704°, -70.75766°)", + " Point B: (59.80083°, 30.54778°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 62.613587°", + " Longitude: -32.779635°", + "FINAL ANSWER: 62.613587, -32.779635" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 3.4537, + "lon": 101.6413, + "name": "Hulu Yam Lama" + }, + "point_b": { + "lat": 12.04888, + "lon": 24.88069, + "name": "Nyala" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 7.029768, + "lon": 82.811497 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (3.4537°, 101.6413°)", + " Point B: (12.04888°, 24.88069°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 7.029768°", + " Longitude: 82.811497°", + "FINAL ANSWER: 7.029768, 82.811497" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 44.11806, + "lon": 43.40278, + "name": "Nezlobnaya" + }, + "point_b": { + "lat": 39.36923, + "lon": 22.94769, + "name": "Volos" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 40.888962, + "lon": 27.765056 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (44.11806°, 43.40278°)", + " Point B: (39.36923°, 22.94769°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 40.888962°", + " Longitude: 27.765056°", + "FINAL ANSWER: 40.888962, 27.765056" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 6.55504, + "lon": 3.34363, + "name": "Oshodi" + }, + "point_b": { + "lat": -3.55097, + "lon": -40.65724, + "name": "Coreaú" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 4.164109, + "lon": -7.717808 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (6.55504°, 3.34363°)", + " Point B: (-3.55097°, -40.65724°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 4.164109°", + " Longitude: -7.717808°", + "FINAL ANSWER: 4.164109, -7.717808" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 58.753, + "lon": 17.00788, + "name": "Nyköping" + }, + "point_b": { + "lat": 40.78343, + "lon": -73.96625, + "name": "Manhattan" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 58.878997, + "lon": -39.242403 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (58.753°, 17.00788°)", + " Point B: (40.78343°, -73.96625°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 58.878997°", + " Longitude: -39.242403°", + "FINAL ANSWER: 58.878997, -39.242403" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 40.78338, + "lon": 72.35067, + "name": "Andijon" + }, + "point_b": { + "lat": -33.88096, + "lon": 151.07986, + "name": "Strathfield" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -15.477902, + "lon": 130.718405 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (40.78338°, 72.35067°)", + " Point B: (-33.88096°, 151.07986°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -15.477902°", + " Longitude: 130.718405°", + "FINAL ANSWER: -15.477902, 130.718405" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 39.84753, + "lon": -75.35785, + "name": "Chester" + }, + "point_b": { + "lat": 45.9902, + "lon": 18.68621, + "name": "Mohács" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 53.714592, + "lon": -31.400821 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (39.84753°, -75.35785°)", + " Point B: (45.9902°, 18.68621°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 53.714592°", + " Longitude: -31.400821°", + "FINAL ANSWER: 53.714592, -31.400821" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -2.06719, + "lon": 105.16228, + "name": "Muntok" + }, + "point_b": { + "lat": 41.54566, + "lon": -71.29144, + "name": "Middletown" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 67.750461, + "lon": 94.767112 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-2.06719°, 105.16228°)", + " Point B: (41.54566°, -71.29144°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 67.750461°", + " Longitude: 94.767112°", + "FINAL ANSWER: 67.750461, 94.767112" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 8.33702, + "lon": 77.86776, + "name": "Tisaiyanvilai" + }, + "point_b": { + "lat": 34.01223, + "lon": -117.68894, + "name": "Chino" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 63.124992, + "lon": -145.265009 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (8.33702°, 77.86776°)", + " Point B: (34.01223°, -117.68894°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 63.124992°", + " Longitude: -145.265009°", + "FINAL ANSWER: 63.124992, -145.265009" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -23.37278, + "lon": -48.18417, + "name": "Guareí" + }, + "point_b": { + "lat": 34.11279, + "lon": 2.10228, + "name": "Aflou" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 20.518831, + "lon": -12.397739 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-23.37278°, -48.18417°)", + " Point B: (34.11279°, 2.10228°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 20.518831°", + " Longitude: -12.397739°", + "FINAL ANSWER: 20.518831, -12.397739" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -21.00944, + "lon": -48.22167, + "name": "Pitangueiras" + }, + "point_b": { + "lat": -21.69785, + "lon": 21.64581, + "name": "Ghanzi" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -24.610375, + "lon": 4.39382 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-21.00944°, -48.22167°)", + " Point B: (-21.69785°, 21.64581°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -24.610375°", + " Longitude: 4.393820°", + "FINAL ANSWER: -24.610375, 4.393820" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 36.56041, + "lon": 4.85454, + "name": "Feraoun" + }, + "point_b": { + "lat": 48.80078, + "lon": 2.16181, + "name": "Viroflay" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 42.688402, + "lon": 3.641325 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (36.56041°, 4.85454°)", + " Point B: (48.80078°, 2.16181°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 42.688402°", + " Longitude: 3.641325°", + "FINAL ANSWER: 42.688402, 3.641325" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 51.17343, + "lon": 7.0845, + "name": "Solingen" + }, + "point_b": { + "lat": 47.50369, + "lon": 19.06583, + "name": "Budapest VI. kerület" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 49.49336, + "lon": 13.299406 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (51.17343°, 7.0845°)", + " Point B: (47.50369°, 19.06583°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 49.493360°", + " Longitude: 13.299406°", + "FINAL ANSWER: 49.493360, 13.299406" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -34.18551, + "lon": 142.16251, + "name": "Mildura" + }, + "point_b": { + "lat": -32.83369, + "lon": -70.59827, + "name": "Los Andes" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -55.931108, + "lon": 164.376626 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-34.18551°, 142.16251°)", + " Point B: (-32.83369°, -70.59827°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -55.931108°", + " Longitude: 164.376626°", + "FINAL ANSWER: -55.931108, 164.376626" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 48.75955, + "lon": -122.48822, + "name": "Bellingham" + }, + "point_b": { + "lat": 45.19275, + "lon": 5.68821, + "name": "Fontaine" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 67.765381, + "lon": -54.471685 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (48.75955°, -122.48822°)", + " Point B: (45.19275°, 5.68821°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 67.765381°", + " Longitude: -54.471685°", + "FINAL ANSWER: 67.765381, -54.471685" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 40.71598, + "lon": 22.72841, + "name": "Ágios Athanásios" + }, + "point_b": { + "lat": -33.79798, + "lon": 151.28826, + "name": "Manly" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -14.772639, + "lon": 119.047635 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (40.71598°, 22.72841°)", + " Point B: (-33.79798°, 151.28826°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -14.772639°", + " Longitude: 119.047635°", + "FINAL ANSWER: -14.772639, 119.047635" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 18.61472, + "lon": -99.31806, + "name": "Puente de Ixtla" + }, + "point_b": { + "lat": -32.93324, + "lon": 27.77656, + "name": "Mdantsane" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -28.89229, + "lon": -10.248605 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (18.61472°, -99.31806°)", + " Point B: (-32.93324°, 27.77656°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -28.892290°", + " Longitude: -10.248605°", + "FINAL ANSWER: -28.892290, -10.248605" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 53.44852, + "lon": -2.35419, + "name": "Urmston" + }, + "point_b": { + "lat": -0.97357, + "lon": -62.9269, + "name": "Barcelos" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 14.489306, + "lon": -52.756916 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (53.44852°, -2.35419°)", + " Point B: (-0.97357°, -62.9269°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 14.489306°", + " Longitude: -52.756916°", + "FINAL ANSWER: 14.489306, -52.756916" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 3.76667, + "lon": 9.98333, + "name": "Dizangué" + }, + "point_b": { + "lat": 44.95914, + "lon": -89.63012, + "name": "Wausau" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 43.977772, + "lon": -56.461554 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (3.76667°, 9.98333°)", + " Point B: (44.95914°, -89.63012°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 43.977772°", + " Longitude: -56.461554°", + "FINAL ANSWER: 43.977772, -56.461554" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -32.88076, + "lon": 27.39377, + "name": "Qonce" + }, + "point_b": { + "lat": 9.99207, + "lon": 77.35657, + "name": "Chokkanāthapuram" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -1.320753, + "lon": 65.97854 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-32.88076°, 27.39377°)", + " Point B: (9.99207°, 77.35657°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -1.320753°", + " Longitude: 65.978540°", + "FINAL ANSWER: -1.320753, 65.978540" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 11.73748, + "lon": 1.77718, + "name": "Namponkoré" + }, + "point_b": { + "lat": 38.77144, + "lon": -90.37095, + "name": "Hazelwood" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 39.455114, + "lon": -63.109051 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (11.73748°, 1.77718°)", + " Point B: (38.77144°, -90.37095°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 39.455114°", + " Longitude: -63.109051°", + "FINAL ANSWER: 39.455114, -63.109051" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 32.6852, + "lon": -4.74512, + "name": "Midelt" + }, + "point_b": { + "lat": -20.7725, + "lon": -49.71417, + "name": "Monte Aprazível" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 19.953978, + "lon": -17.607364 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (32.6852°, -4.74512°)", + " Point B: (-20.7725°, -49.71417°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 19.953978°", + " Longitude: -17.607364°", + "FINAL ANSWER: 19.953978, -17.607364" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 40.37444, + "lon": 50.08528, + "name": "Hövsan" + }, + "point_b": { + "lat": 50.43109, + "lon": 7.40425, + "name": "Andernach" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 49.515432, + "lon": 19.429969 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (40.37444°, 50.08528°)", + " Point B: (50.43109°, 7.40425°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 49.515432°", + " Longitude: 19.429969°", + "FINAL ANSWER: 49.515432, 19.429969" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -36.61756, + "lon": -72.95593, + "name": "Tomé" + }, + "point_b": { + "lat": 49.68866, + "lon": 21.77058, + "name": "Krosno" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -14.395945, + "lon": -50.421108 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-36.61756°, -72.95593°)", + " Point B: (49.68866°, 21.77058°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -14.395945°", + " Longitude: -50.421108°", + "FINAL ANSWER: -14.395945, -50.421108" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -27.46784, + "lon": -58.8344, + "name": "Corrientes" + }, + "point_b": { + "lat": -6.76667, + "lon": 38.91667, + "name": "Kibaha" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -28.817679, + "lon": -32.258574 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-27.46784°, -58.8344°)", + " Point B: (-6.76667°, 38.91667°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -28.817679°", + " Longitude: -32.258574°", + "FINAL ANSWER: -28.817679, -32.258574" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 6.64678, + "lon": -4.70519, + "name": "Dimbokro" + }, + "point_b": { + "lat": 31.01887, + "lon": 33.0098, + "name": "Bi’r al ‘Abd" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 13.379057, + "lon": 3.764899 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (6.64678°, -4.70519°)", + " Point B: (31.01887°, 33.0098°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 13.379057°", + " Longitude: 3.764899°", + "FINAL ANSWER: 13.379057, 3.764899" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 24.62166, + "lon": 74.67999, + "name": "Nīmbāhera" + }, + "point_b": { + "lat": 5.89674, + "lon": -5.15792, + "name": "Ogoudou" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 23.505552, + "lon": 53.248107 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (24.62166°, 74.67999°)", + " Point B: (5.89674°, -5.15792°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 23.505552°", + " Longitude: 53.248107°", + "FINAL ANSWER: 23.505552, 53.248107" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -14.27806, + "lon": -170.7025, + "name": "Pago Pago" + }, + "point_b": { + "lat": 14.99433, + "lon": 103.10392, + "name": "Buri Ram" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": -7.403934, + "lon": 167.439146 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-14.27806°, -170.7025°)", + " Point B: (14.99433°, 103.10392°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -7.403934°", + " Longitude: 167.439146°", + "FINAL ANSWER: -7.403934, 167.439146" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 10.63333, + "lon": 107.06667, + "name": "Phú Mỹ" + }, + "point_b": { + "lat": 49.35994, + "lon": 6.16044, + "name": "Thionville" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 27.168541, + "lon": 91.283366 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (10.63333°, 107.06667°)", + " Point B: (49.35994°, 6.16044°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 27.168541°", + " Longitude: 91.283366°", + "FINAL ANSWER: 27.168541, 91.283366" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 45.67207, + "lon": -118.7886, + "name": "Pendleton" + }, + "point_b": { + "lat": 30.15293, + "lon": 31.31501, + "name": "Al Khuşūş" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 70.383739, + "lon": -22.058638 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (45.67207°, -118.7886°)", + " Point B: (30.15293°, 31.31501°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 70.383739°", + " Longitude: -22.058638°", + "FINAL ANSWER: 70.383739, -22.058638" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -17.32694, + "lon": 35.58417, + "name": "Morrumbala" + }, + "point_b": { + "lat": 11.8904, + "lon": 120.0222, + "name": "Culion" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": -3.667959, + "lon": 78.446494 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-17.32694°, 35.58417°)", + " Point B: (11.8904°, 120.0222°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -3.667959°", + " Longitude: 78.446494°", + "FINAL ANSWER: -3.667959, 78.446494" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -5.9988, + "lon": 23.25386, + "name": "Kabeya-Kamwanga" + }, + "point_b": { + "lat": 64.59417, + "lon": 39.81028, + "name": "Yagry" + }, + "fraction": 0.25, + "ground_truth": { + "interpolated_point": { + "lat": 11.768067, + "lon": 25.573296 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-5.9988°, 23.25386°)", + " Point B: (64.59417°, 39.81028°)", + " Fraction f = 0.25", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 11.768067°", + " Longitude: 25.573296°", + "FINAL ANSWER: 11.768067, 25.573296" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 10.02798, + "lon": 39.8528, + "name": "Kobo" + }, + "point_b": { + "lat": -22.73083, + "lon": -45.12472, + "name": "Lorena" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": -16.827753, + "lon": -22.21276 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (10.02798°, 39.8528°)", + " Point B: (-22.73083°, -45.12472°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: -16.827753°", + " Longitude: -22.212760°", + "FINAL ANSWER: -16.827753, -22.212760" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 26.4835, + "lon": 89.52286, + "name": "Alīpur Duār" + }, + "point_b": { + "lat": 36.54828, + "lon": 3.11006, + "name": "Ouled Slama Fouaga" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 40.036058, + "lon": 49.219831 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (26.4835°, 89.52286°)", + " Point B: (36.54828°, 3.11006°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 40.036058°", + " Longitude: 49.219831°", + "FINAL ANSWER: 40.036058, 49.219831" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 53.63793, + "lon": 55.9533, + "name": "Sterlitamak" + }, + "point_b": { + "lat": 34.35833, + "lon": 117.05278, + "name": "Liuji" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 48.139225, + "lon": 92.032224 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (53.63793°, 55.9533°)", + " Point B: (34.35833°, 117.05278°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 48.139225°", + " Longitude: 92.032224°", + "FINAL ANSWER: 48.139225, 92.032224" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -19.53944, + "lon": -40.63056, + "name": "Colatina" + }, + "point_b": { + "lat": 51.33795, + "lon": 26.60191, + "name": "Sarny" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 18.72569, + "lon": -14.689712 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-19.53944°, -40.63056°)", + " Point B: (51.33795°, 26.60191°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 18.725690°", + " Longitude: -14.689712°", + "FINAL ANSWER: 18.725690, -14.689712" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 25.19413, + "lon": 32.6771, + "name": "As Sibā‘īyah" + }, + "point_b": { + "lat": 36.87744, + "lon": 10.2468, + "name": "Sukrah" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 34.345001, + "lon": 16.394008 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (25.19413°, 32.6771°)", + " Point B: (36.87744°, 10.2468°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 34.345001°", + " Longitude: 16.394008°", + "FINAL ANSWER: 34.345001, 16.394008" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": 49.84527, + "lon": 18.43011, + "name": "Orlová" + }, + "point_b": { + "lat": 20.2113, + "lon": -75.99362, + "name": "Palma Soriano" + }, + "fraction": 0.5, + "ground_truth": { + "interpolated_point": { + "lat": 45.335417, + "lon": -40.109212 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (49.84527°, 18.43011°)", + " Point B: (20.2113°, -75.99362°)", + " Fraction f = 0.5", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 45.335417°", + " Longitude: -40.109212°", + "FINAL ANSWER: 45.335417, -40.109212" + ] + }, + { + "task": "interpolation", + "point_a": { + "lat": -5.50361, + "lon": -41.32333, + "name": "São Miguel do Tapuio" + }, + "point_b": { + "lat": 50.54322, + "lon": 7.1113, + "name": "Bad Neuenahr-Ahrweiler" + }, + "fraction": 0.75, + "ground_truth": { + "interpolated_point": { + "lat": 38.366752, + "lon": -10.554347 + }, + "tolerance_deg": 0.01 + }, + "reasoning_steps": [ + "Step 1: Identify the endpoints", + " Point A: (-5.50361°, -41.32333°)", + " Point B: (50.54322°, 7.1113°)", + " Fraction f = 0.75", + "Step 2: Convert to radians and 3D Cartesian", + " Convert lat/lon to unit sphere coordinates (x, y, z)", + "Step 3: Calculate angular distance d between points", + " d = arccos(sin(lat₁)sin(lat₂) + cos(lat₁)cos(lat₂)cos(Δlon))", + "Step 4: Apply spherical linear interpolation (slerp)", + " a = sin((1-f)×d) / sin(d)", + " b = sin(f×d) / sin(d)", + " P = a×A + b×B", + "Step 5: Convert back to lat/lon", + " Latitude: 38.366752°", + " Longitude: -10.554347°", + "FINAL ANSWER: 38.366752, -10.554347" + ] + } +] \ No newline at end of file