2 Search Results for "Parlier, Hugo"

Document
DOI: 10.4230/LIPIcs.SoCG.2023.27
Computing a Dirichlet Domain for a Hyperbolic Surface

Authors: Vincent Despré, Benedikt Kolbe, Hugo Parlier, and Monique Teillaud

Published in: LIPIcs, Volume 258, 39th International Symposium on Computational Geometry (SoCG 2023)

Abstract
This paper exhibits and analyzes an algorithm that takes a given closed orientable hyperbolic surface and outputs an explicit Dirichlet domain. The input is a fundamental polygon with side pairings. While grounded in topological considerations, the algorithm makes key use of the geometry of the surface. We introduce data structures that reflect this interplay between geometry and topology and show that the algorithm runs in polynomial time, in terms of the initial perimeter and the genus of the surface.
Cite as

Vincent Despré, Benedikt Kolbe, Hugo Parlier, and Monique Teillaud. Computing a Dirichlet Domain for a Hyperbolic Surface. In 39th International Symposium on Computational Geometry (SoCG 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 258, pp. 27:1-27:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{despre_et_al:LIPIcs.SoCG.2023.27,
  author =	{Despr\'{e}, Vincent and Kolbe, Benedikt and Parlier, Hugo and Teillaud, Monique},
  title =	{{Computing a Dirichlet Domain for a Hyperbolic Surface}},
  booktitle =	{39th International Symposium on Computational Geometry (SoCG 2023)},
  pages =	{27:1--27:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-273-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{258},
  editor =	{Chambers, Erin W. and Gudmundsson, Joachim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2023.27},
  URN =		{urn:nbn:de:0030-drops-178771},
  doi =		{10.4230/LIPIcs.SoCG.2023.27},
  annote =	{Keywords: Hyperbolic geometry, Topology, Voronoi diagram, Algorithm}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2021.31
Minimal Delaunay Triangulations of Hyperbolic Surfaces

Authors: Matthijs Ebbens, Hugo Parlier, and Gert Vegter

Published in: LIPIcs, Volume 189, 37th International Symposium on Computational Geometry (SoCG 2021)

Abstract
Motivated by recent work on Delaunay triangulations of hyperbolic surfaces, we consider the minimal number of vertices of such triangulations. First, we 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 construct a class of hyperbolic surfaces for which the order of this bound is optimal. Finally, to give a general lower bound, we 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.
Cite as

Matthijs Ebbens, Hugo Parlier, and Gert Vegter. Minimal Delaunay Triangulations of Hyperbolic Surfaces. In 37th International Symposium on Computational Geometry (SoCG 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 189, pp. 31:1-31:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

Copy BibTex To Clipboard

@InProceedings{ebbens_et_al:LIPIcs.SoCG.2021.31,
  author =	{Ebbens, Matthijs and Parlier, Hugo and Vegter, Gert},
  title =	{{Minimal Delaunay Triangulations of Hyperbolic Surfaces}},
  booktitle =	{37th International Symposium on Computational Geometry (SoCG 2021)},
  pages =	{31:1--31:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-184-9},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{189},
  editor =	{Buchin, Kevin and Colin de Verdi\`{e}re, \'{E}ric},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2021.31},
  URN =		{urn:nbn:de:0030-drops-138305},
  doi =		{10.4230/LIPIcs.SoCG.2021.31},
  annote =	{Keywords: Delaunay triangulations, hyperbolic surfaces, metric graph embeddings, moduli spaces}
}
  • Refine by Author
  • 2 Parlier, Hugo
  • 1 Despré, Vincent
  • 1 Ebbens, Matthijs
  • 1 Kolbe, Benedikt
  • 1 Teillaud, Monique
  • Show More...

  • Refine by Classification
  • 2 Mathematics of computing → Geometric topology
  • 2 Theory of computation → Computational geometry
  • 1 Mathematics of computing → Graphs and surfaces

  • Refine by Keyword
  • 1 Algorithm
  • 1 Delaunay triangulations
  • 1 Hyperbolic geometry
  • 1 Topology
  • 1 Voronoi diagram
  • Show More...

  • Refine by Type
  • 2 document

  • Refine by Publication Year
  • 1 2021
  • 1 2023

Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH Imprint Privacy Contact