How Many Potatoes Are in a Mesh?

摘要

We consider the combinatorial question of how many convex polygons can be made at most by using the edges taken from a fixed triangulation of n vertices. For general triangulations, there can be exponentially many: Ω(1.5028 n) and O(1.62 n) in the worst case. If the triangulation is fat (every triangle has its angles lower-bounded by a constant δ?