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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 !

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    Absolutely; that's sort of the point of curvature. Overall, pairs of points will on average be further away from each other in negatively-curved spaces and closer together in positively-curved spaces. For example, on a sphere no two points can ever be further than $\pi r$ apart. (@ whoever cares: I get the notification "Please avoid extended discussions in comments. Would you like to automatically move this discussion to chat?", but apparently I can't do this because AlexPof doesn't have high enough reputation.)2011-07-11

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