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.