TITLE: How to get a part of a quaternion? e.g. get half of the rotation of a quaternion?
QUESTION [7 upvotes]: if I have a quaternion which describes an arbitrary rotation, how can I get for example only the half rotation or something like 30% of this rotation?
Thanks in advance!

REPLY [3 votes]: I believe what you're looking for are exponent and logarithm formulas for quaternions, which can be found on the Wikipedia page on quaternions. The Wikipedia page even gives a formula for raising a quaternion to an arbitrary power, which is exactly what you want. If your original rotation is given by $q$, and you want to take 30% of this rotation, you simply take $q^{0.3}$.