The triangulation problem is one that crops up pretty frequently in Computer Graphics. Given a set of points, a triangulation of the discrete point set is obtained by decomposing the point-set into a triangle mesh.
While there are many ways to measure the quality of a triangulation, one provable method is the Delaunay triangulation, that leads to a "good" triangulation - maximizing the minimum angles. There are a number of delaunay triangulation methods, and I've implemented a couple of them here.
Mesh subdivision is another frequently encountered for mesh deformations, etc. Basically, you want to split up the triangles in a triangulation taking into account some constraint.
Below is an applet that I worked on in class, in a team of 3. We implement the Delaunay triangulation of a point set.
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