CSR Point Distribution for an Arbitrary Shape

I have a series of xyz coordinates distributed on the surface of an arbitrary shape (receptors on the surface of a cell).

I have the CDF of the nearest-neighbor distances for each point but I need a CSR distribution to compare this to. How can I generate a set of points with complete spatial randomness when the surface the occupy is a totally random shape? I have the surface area value but surely I cant just generate the points across a square of the same area?