# Any distance metrics to measure the similarity between 2 sets of 2D points?

I have 2 sets of 2D points, and each of the points P(x,y) satisfies these conditions

1. $x \geq 0$
2. $y \geq 0$
3. $x + y \leq 1$

I am looking for a way to find out the similarity of the 2 sets.

In the "distance" Wikipedia page, the part "Distances between sets.." covers distances between sets of 1D points, such as Hausdorff distance. I would like to know if there are other distances between sets of 2D points.

Note however that a pair $(x,y)$ satisfying your 1. 2. 3. is the same as a point in a closed triangle $T$; so your subsets are subsets of $T,$ and you can consider the associate Hausdorff distance between them (however, as usual, it is a genuine distance on closed sets, while on general subsets it's just a semi-distance). –  Pietro Majer Oct 11 '10 at 12:07