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DOI: 10.4230/LIPIcs.SoCG.2020.35

Flipping Geometric Triangulations on Hyperbolic Surfaces

Authors: Vincent Despré, Jean-Marc Schlenker, and Monique Teillaud

Published in: LIPIcs, Volume 164, 36th International Symposium on Computational Geometry (SoCG 2020)

Abstract

We consider geometric triangulations of surfaces, i.e., triangulations whose edges can be realized by disjoint 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.

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Vincent Despré, Jean-Marc Schlenker, and Monique Teillaud. Flipping Geometric Triangulations on Hyperbolic Surfaces. In 36th International Symposium on Computational Geometry (SoCG 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 164, pp. 35:1-35:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{despre_et_al:LIPIcs.SoCG.2020.35,
  author =	{Despr\'{e}, Vincent and Schlenker, Jean-Marc and Teillaud, Monique},
  title =	{{Flipping Geometric Triangulations on Hyperbolic Surfaces}},
  booktitle =	{36th International Symposium on Computational Geometry (SoCG 2020)},
  pages =	{35:1--35:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-143-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{164},
  editor =	{Cabello, Sergio and Chen, Danny Z.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2020.35},
  URN =		{urn:nbn:de:0030-drops-121939},
  doi =		{10.4230/LIPIcs.SoCG.2020.35},
  annote =	{Keywords: Hyperbolic surface, Topology, Delaunay triangulation, Algorithm, Flip graph}
}

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Flipping Geometric Triangulations on Hyperbolic Surfaces

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