Generate a uniformly random point within an annulus (ring) [duplicate]

Answer 1

Its very easy. Use polar coordinates, i.e. you generate one random value for the angular value theta, and one for the distance from the origin. As your circles are both at the same origin this gets very easy.

BUT ATTENTION: you can generate the theta value by a uniform random function, that is fine, but for the distance you cant do that, as then the points will cluster around the origin. You have to take into consideration that the perimeter of a circle grows in ^2 (you have to use the inverse which is the square root).

Using a uniform distributed random function rnd (0..1) it would be like this:

theta = 360 * rnd();
dist = sqrt(rnd()*(R1^2-R2^2)+R2^2);

EDIT: For conversion into cartesion coordinates, you just compute:

x =  dist * cos(theta);
y =  dist * sin(theta);