>>    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);
> 
> Or:
>
>>    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));
>>
> 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).

Ok, that makes me wonder, because:

1. The 2 methods above produce 100% identical images. It was a scene of
one light emitting sphere, ground and 3 diffusing spheres of different
colors. (I did use the cosine ratio relative to the angle of light
falling on surface.) I can post the images if needed. The only
difference is that the second method is faster - with a great margin.

2. If the distribution is not identical by the 2 methods, why are the
images still 100% identical?

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