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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.
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