Fast uniformly distributed random points on the surface of a unit hemisphere

Question

I am trying to generate uniform random points on the surface of a unit sphere for a Monte Carlo ray tracing program. When I say uniform I mean the points are uniformly distr

Answer 1

The second and third methods do in fact produce uniformly distributed random points on the surface of a sphere with the second method (Marsaglia 1972) producing the fastest run times at around twice the speed on an Intel Xeon 2.8 GHz Quad-Core.

As noted by Alexandre C there is an additional method using the normal distribution which expands to n-spheres better than the methods I have presented.

This link will give you further information on selecting uniformly distributed random points on the surface of a sphere.

My initial method as pointed out by TonyK does not produce uniformly distributed points and rather bias's the poles when generating the random points. This is required by the problem I am trying to solve however I simply assumed it would generate uniformly random points. As suggested by Pablo this method can be optimised by removing the asin() call to reduce run time by around 20%.