Minimal Delaunay triangulations of hyperbolic surfaces

11/19/2020
by   Matthijs Ebbens, et al.
0

Motivated by recent work on Delaunay triangulations of hyperbolic surfaces, we consider the minimal number of vertices of such triangulations. First, we will show that every hyperbolic surface of genus g has a simplicial Delaunay triangulation with O(g) vertices, where edges are given by distance paths. Then, we will construct a class of hyperbolic surfaces for which the order of this bound is optimal. Finally, to give a general lower bound, we will show that the Ω(√(g)) lower bound for the number of vertices of a simplicial triangulation of a topological surface of genus g is tight for hyperbolic surfaces as well.

READ FULL TEXT

Please sign up or login with your details

Forgot password? Click here to reset