Flipping Geometric Triangulations on Hyperbolic Surfaces
Computational Geometry
2019-12-11 v1 Geometric Topology
Abstract
We consider geometric triangulations of surfaces, i.e., triangulations whose edges can be realized by disjoint locally geodesic segments. We prove that the flip graph of geometric triangulations with fixed vertices of a flat torus or a closed hyperbolic surface is connected. We give upper bounds on the number of edge flips that are necessary to transform any geometric triangulation on such a surface into a Delaunay triangulation.
Cite
@article{arxiv.1912.04640,
title = {Flipping Geometric Triangulations on Hyperbolic Surfaces},
author = {Vincent Despré and Jean-Marc Schlenker and Monique Teillaud},
journal= {arXiv preprint arXiv:1912.04640},
year = {2019}
}