> I use this:
>
> y = sqrt(rand(0..1))
> theta = acos(y)
> phi = 2*PI*rand(0..1)
>
> x = sin(theta)*cos(phi)
> z = sin(theta)*sin(phi)
>
> What I don't get is the sqrt(rand()). Why sqrt? Why not just rnd()? Does
> the sqrt give us the cosine distribution and should remove the need to
> later scale by taking cosine of the angle between normal and the light 
> ray?

No, you are simply choosing a fixed Y position, which then defines a ring 
around the sphere of possible points.  Then phi is used to choose a point at 
random on this ring which gives you the final point.

The reason for using sqrt for y is because you want points equally 
distributed over the surface of the sphere, not between y=0 to 1.  You can 
visualise this by drawing a straight line alongside a circle.  If you 
distribute points evenly on the line, then trace them across to the circle, 
they won't be distributed evenly on the circle.  The sqrt fixes that.

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