Generate a random point within a circle (uniformly)

Question

I need to generate a uniformly random point within a circle of radius R.

I realize that by just picking a uniformly random angle in the interval [0 ... 2π),

Answer 1

Note the point density in proportional to inverse square of the radius, hence instead of picking r from [0, r_max], pick from [0, r_max^2], then compute your coordinates as:

x = sqrt(r) * cos(angle)
y = sqrt(r) * sin(angle)

This will give you uniform point distribution on a disk.

http://mathworld.wolfram.com/DiskPointPicking.html