Polygon Triangle Count Optimization

Question

Recently I wrote myself an Ear Clipping Triangulator as personal research. After visualizing some of the results, I can't help but feel that the object could be reproduced with fewer than n-2 triangles. Unfortunately, my small graphics book library could not lead me to any possible algorithms or methods to achieve this goal.

I know of simplification of course, but that affects the actual shape and appearance of the model. I wish to just remove extraneous triangles. Is this at all possible? Or is a more efficient triangulation method required?

For example, the top diamond shaped object is composed of 34 triangles. On paper I was able to triangulate it using just 18.

Answer 1

This is a common problem in FEM and CFD. There are some open-source packages available that you could look to see how they do this problem. Two that come to mind are OOF and OpenFOAM.