I'm a computer science student working on a paper regarding constrained delaunay triangulations. I have been searching for a proof regarding the upper bound for the number of triangles in a constrained delaunay triangulation with $n$ vertices and I managed to find this paper:
http://www.cs.ucdavis.edu/~amenta/pubs/HiDeeDel.pdf
It provides an upper bound on the number of triangles in a delaunay triangulation (I was looking for constrained) using McMullen's Upper Bound Theorem (http://www.ifor.math.ethz.ch/teaching/lectures/poly_comp_ss11/lecture7). The paper doesn't describe their technique for finding the upper bound from McMullen's theorem in depth, so I'm forced to figure it out for myself.
Here's the problem. I have almost no math and geometry background past vector calculus and probability (my strengths lie in discrete math and graph theory), so I can't understand what McMullen's theorem means. I have a hunch that it can be applied to arbitrary triangulations (not just DTs), but I'm not sure how I would go about showing this.
Additionally, I really only care about the 2-dimensional case.