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

I think the problem you are having with non-uniform results is because in polar coordinates, a random point on the circle is not uniformly distributed on the radial axis. If you look at the area on [theta, theta+dtheta]x[r,r+dr], for fixed theta and dtheta, the area will be different of different values of r. Intuitivly, there is "more area" further out from the center. Thus, you need to scale your random radius to account for this. I haven't got the proof lying around, but the scaling is r=R*sqrt(rand), with R being the radius of the circle and rand begin the random number.