Well, I hate to tell you, but you're out of luck, unless you can make some assumptions. First of all, the definition of a triangle is "a convex polygon with three segments joining three non-collinear points. Each of the three segments is called a side, and each of the three non-collinear points is called a vertex." (
GoMath.com)
So in reality, if you have a bunch of points, any 3 points creates a triangle. However, since you're talking about a mesh, it is POSSIBLE that you could do this, but ONLY if its a convex shape (
Convex)
I suppose it'd be POSSIBLE to extract all the INTENDED triangles out of the mesh, however, if its a non convex mesh, there is absolutely no way.
Where are you getting these points? Are you sure you can't get the triangle data too? most model formats (in fact all I can think of) provide triangle indices.
hope that helps
-Dan