Rotating in 3d space - random values of x,y,z rotation so end result = beginning

Can anyone tell me the formula for determining what combinatio开发者_如何转开发n of x,y,z rotation values will give the same result as a normalized object(no rotation) in 3d space?

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If you know both the end result and the initial state, then it's just basic matrix multiplication. You'd have to find the angles used to rotate the object (one for the x-axis, y-axis and z-axis) and left-multiply your coordinate vectors by this guy:

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Choosing uniformly distributed random angles [-pi, pi] will not lead to a uniformly random rotation axis on the sphere! Wikipedia has a nice explanation about this phenomenon, which is called the "gimbal lock". See "Fast Random Rotation Matrices" by James Arvo for one algorithm that produces uniformly random rotations.