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 suppose no. 16 on http://mathworld.wolfram.com/SpherePointPicking.html hints
at the solution: You "just" need a space defined by a vector that meets the
above criteria. The "distortion" of the space at the selected point will then
allow computation of a scalar that should have some relation to the sample
density. Basically, with the shape of the unit hull you can also shape the
sample density by projecting it back on a unit sphere.

However, I am not sure if the "incorrect" example on that page won't
already solve most of your problem.

Post a reply to this message