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

This should be quick if you have a fast RNG:

// RNG::draw() returns a uniformly distributed number between -1 and 1.

void drawSphereSurface(RNG& rng, double& x1, double& x2, double& x3)
{
    while (true) {
        x1 = rng.draw();
        x2 = rng.draw();
        x3 = rng.draw();
        const double radius = sqrt(x1*x1 + x2*x2 + x3*x3);
        if (radius > 0 && radius < 1) {
            x1 /= radius;
            x2 /= radius;
            x3 /= radius;
            return;
        }
    }   
}

To speed it up, you can move the sqrt call inside the if block.