[mkl]

It's common to want some minimum spacing between your random points, so they don't get clumped together, i.e. approximating uniform spacing rather than uniform probability distribution. For that, Poisson-disk sampling is good. See e.g. https://www.jasondavies.com/maps/random-points/, https://www.cs.ubc.ca/~rbridson/docs/bridson-siggraph07-pois..., https://www.jasondavies.com/poisson-disc/.