clipka <ano### [at] anonymousorg> wrote:
> Folks, I could need a bit of help with a maths problem.
>
> I need an algorithm to generate random points on the surface of a
> sphere, conforming to the following criteria:
>
> - The distribution must be radially symmetric around the Y axis.
> - The sample density should be roughly uniform, except for a pronounced
> peak centered at +Y (but not -Y!)
> - For each random point generated, the algorithm also needs to compute
> the theoretical sample density at that location.
> - The algorithm must be reasonably fast.
>
> Ideally, the algorithm should also have the following properties:
>
> - The density should fall off smoothly from the peak.
> - The algorithm should have a parameter to govern the "tightness" of the
> peak.
> - The sample density away from the peak should approach (but not reach!)
> zero.

I see a certain contradiction because a uniform distribution cannot fall off
smoothly to zero. My first idea is to use a 2D-normal distribution and project
it onto the sphere. One can play with the sigma(s) to sharpen the peak and/or
use weighted averages of such distributions.

Best regards,
Michael

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