Algorithm to generate rectangle coordinates given a set of points

Question

I have a set of points on 2D plane, each has its screen coordinates X and Y. They are placed this way:

You see they are placed in horizontal lines, but X coordinate is quite random. A number of points in each line is not necessarily the same.

Given these coordinates, I need to generate triangles so that each edge of the triangle connects a pair of points which are close to each other, if possible:

Is there any known algorithm or library for this?

Answer 1

You need point set triangulation .

In described case Delaunay triangulation should give desired result.

Library by JRShewchuk (and it's not hard to find triangulation implementation for any popular language)