For some computational project, I'm interested in the pairwise distance matrix between random points on a unit square of $\mathbb{R}^2$.
I now want to extend this case to non-zero curvature 2D spaces, but I don't see what is the proper way to spread random points on such spaces. Does one define the random distribution on $[0,1]^2$ and maps it to the space through an appropriate coordinate transform, or is there a way to do it directly ?
How would you expect the distance matrix to change with curvature ?
Thank you for your answers !