Random sampling in a polygon I would like to sample a uniformly random point in a polygon...

If sample a large number they'd be equally likely to fall into two regions if they have the same area.

This would be quite simple if it were a square since I would take two random numbers in [0,1] as my coordinates.

The shape I have is a regular polygon, but I'd like it to work for any polygon.

https://stackoverflow.com/questions/3058150/how-to-find-a-random-point-in-a-quadrangle
Triangulate the polygon
Determine in which of the triangles the point should lie (weights triangle areas)
Sample the point in the triangle as explained in this post