*Originally posted by iamatiger*

**How are the random points generated? The answer is dependent on this.**

Does not matter how the points are generated, what matters is what we mean by random. And I believe that was what you meant.

The natural definition of random distribution of points within a circle would be that any two areas within the circle (of same area) has the same probability of containing a point.

The interesting question is then how do we obtain a parametrization of the points that preserves this randomness.

My initial idea was to go for polar coordinates : (x,y) = (r cos(t), r sin(t)) and let r be uniform on [0,R] and t uniform on [-pi,pi] (R=radius)

but that would not preserve the above mentioned randomness. So we have to find an other distribution of r.

It should be fairly simple.