TITLE: Find whether two triangles intersect or not in 3D
QUESTION [12 upvotes]: Given 2 set of points
((x1,y1,z1),(x2,y2,z2),(x3,y3,z3)) and
((p1,q1,r1),(p2,q2,r2),(p3,q3,r3)) each forming a triangle in 3D space.
How will you find out whether these triangles intersect or not?
One obvious solution to this problem is to find the equation of the plane formed by each triangle. If the planes are parallel, then they don't intersect.
Else, find out the equation of line formed by the intersection of these planes using the normal vectors of these planes.
Now, if this line lies in both of the triangular regions, then these two triangles intersect, otherwise not.
Is there any other solution?

REPLY [4 votes]: I haven't had time to check the other answers in detail, so this may be equivalent... but the standard method of doing this is by the "separating axis theorem", which basically says that two convex objects are separated if there exists an axis so that the projections of the objects onto the axis do not overlap.
In the case of two triangles this amounts to just a couple of cross products, dot products and interval checks, which can be done very efficiently. A quick Google search turned up this:
http://www.geometrictools.com/Documentation/MethodOfSeparatingAxes.pdf