Sampling points on a disc is a special problem that turns up a lot in practice. One obvious thing to do is just sample points on the square and throw out the ones that aren't in the disc but numericists don't like the throwing away bit because of performance. That Numerical Recipes book [1] has a section on it (has one on disc sampling and those sexy quasirandom numbers), the #1 answer on this StackOverflow page describes an algorithm that I remember from it.

https://stats.stackexchange.com/questions/481543/generating-...

[1] I took a class on numerics taught by one of the authors; great book but it's a shame about the software license