> 1. Is this equally good as the above - at least it looks to be. And a
> bit faster.
>
>    double y = sqrt((double) rand()/RAND_MAX);
>    double phi = 2*M_PI* (double)rand()/RAND_MAX;
>    double x = sqrt(1-y*y)*cos(phi);
>    double z = sqrt(1-y*y)*sin(phi);

Looks ok to me.

> What is the proper way to actually test the uniformity?

Either mathematically proving it, or write a test program that measures the 
density of points over the surface.

> I also tried that:
>
>
>    do{
>        x = (double) 2.0*rand()/RAND_MAX -1.0;
>        z = (double) 2.0*rand()/RAND_MAX-1.0;
>    }
>    while(x*x+z*z > 1.0);
>
>    y = sqrt(1.0-(x*x+z*z));
>
> And the results are very close to the 2 other methods.

This result is different to the above and not spread uniformly over the 
surface of the sphere (it is uniform only in the xz plane).

Post a reply to this message