Random spherical coordinates
SMRTR summary
Generating random points on a sphere typically involves creating Cartesian coordinates then converting to spherical form, but a more direct approach generates spherical coordinates immediately. While the radius equals 1 and longitude can be chosen uniformly, the polar angle requires special handling to avoid clustering points near the poles, accomplished by making the cosine of the polar angle uniformly distributed rather than the angle itself.
SMRTR provides this summary for quick context. The original article belongs to John D. Cook.
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