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Re^3: computational efficiencyby Lotus1 (Chaplain) 
on Oct 12, 2011 at 18:53 UTC ( #931065=note: print w/ replies, xml )  Need Help?? 
The approach I like for this problem is what Perlbotics suggested. Make a table. I suggest a hash of arrays where the keys are angles and each value is an array of sin and cos values. Then you choose a random angle (0360) and get both sin and cos from a fast hash with the negative signs included. This takes care of all four quadrands. Do this for each axis of rotation as you proposed. The article I posted was about picking uniformly distributed points on the surface of a sphere which I believe is more difficult than your problem. The only point I was making with my previous post is that if you pick random sine values the corresponding angles are not uniformly distributed. I'm not sure about proving this approach of three rotations but it seems good to me. I'll think about it more and maybe I'll come up with a proof.
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