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

1st try (wrong)

point=[rand(-1,1),rand(-1,1),rand(-1,1)];
len = length_of_vector(point);

EDITED:

What about?

while(1)
 point=[rand(-1,1),rand(-1,1),rand(-1,1)];
 len = length_of_vector(point);
 if( len > 1 )
     continue;
 point = point / len
     break

Acception is here approx 0.4. Than mean that you will reject 60% of solutions.