Random Points on a Sphere

Re:Random Points on a Sphere by carlob on Monday April 27, 2015 @07:39AM (#9445563)

Not necessarily the most efficient though: the Box-Muller transform that is probably used in the call to randn is related to the transform you'd need to start from uniformly distributed reals.

So your solution ends up pretty much using the same math (while probably calling cos a few more times) and throwing away at least one random number and possibly half of them (depending on the implementation of randn).

http://en.wikipedia.org/wiki/Box–Muller_transform

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Re:Random Points on a Sphere by davmre on Monday April 27, 2015 @03:03PM (#9448449)

Yeah, the Gaussian trick is like programming in a high-level language: using existing abstractions lets you write clean and concise code, at the price of some efficiency versus the optimal engineered-from-scratch solution.

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Re:Random Points on a Sphere by carlob on Tuesday April 28, 2015 @07:19AM (#9451440)

I'm not sure I agree, I think the really high-level option is to use a library and not roll your own.

For example:

https://www.gnu.org/software/gsl/manual/html_node/Spherical-...

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Re:Random Points on a Sphere by davmre on Tuesday April 28, 2015 @03:51PM (#9454712)

Fair enough. Though it looks like gsl_ran_dir_nd is implemented using normalized Gaussians, so in this case we're back where we started. :-)

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