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Implementation of the ε-net algorithm

Authors: Vincent Despré, Camille Lanuel, Marc Pouget, and Monique Teillaud

Abstract

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Vincent Despré, Camille Lanuel, Marc Pouget, Monique Teillaud. Implementation of the ε-net algorithm (Software). Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@misc{dagstuhl-artifact-24672,
   title = {{Implementation of the \epsilon-net algorithm}}, 
   author = {Despr\'{e}, Vincent and Lanuel, Camille and Pouget, Marc and Teillaud, Monique},
   note = {Software, ANR Abysm, swhId: \href{https://archive.softwareheritage.org/swh:1:dir:2fab64276f7d193b0b712c135fa9eebba62f0509;origin=https://github.com/camille-lanuel/ESA_2025_implementation_epsilon_net;visit=swh:1:snp:746a88c723aa2bdc5fda86b1aab596931229dcb5;anchor=swh:1:rev:a97883aef3bfd9ee69ee5dbb8ec117ddc72f7686}{\texttt{swh:1:dir:2fab64276f7d193b0b712c135fa9eebba62f0509}} (visited on 2025-10-01)},
   url = {https://github.com/camille-lanuel/ESA_2025_implementation_epsilon_net},
   doi = {10.4230/artifacts.24672},
}

Document

DOI: 10.4230/LIPIcs.ESA.2025.61

ε-Net Algorithm Implementation on Hyperbolic Surfaces

Authors: Vincent Despré, Camille Lanuel, Marc Pouget, and Monique Teillaud

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract

We propose an implementation, using the CGAL library, of an algorithm to compute ε-nets on hyperbolic surfaces proposed by Despré, Lanuel and Teillaud [Despré et al., 2024]. We describe the data structure, detail the implemented algorithm and report experimental results on hyperbolic surfaces of genus 2. The implementation differs from the cited algorithm on several aspects. In particular, we use a different data structure, based on combinatorial maps, to represent a triangulation of a surface. We explain how to generate fundamental polygons to represent our input hyperbolic surfaces and the arithmetic issues related to the number type of the coordinates of their vertices.

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Vincent Despré, Camille Lanuel, Marc Pouget, and Monique Teillaud. ε-Net Algorithm Implementation on Hyperbolic Surfaces. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 61:1-61:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{despre_et_al:LIPIcs.ESA.2025.61,
  author =	{Despr\'{e}, Vincent and Lanuel, Camille and Pouget, Marc and Teillaud, Monique},
  title =	{{\epsilon-Net Algorithm Implementation on Hyperbolic Surfaces}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{61:1--61:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.61},
  URN =		{urn:nbn:de:0030-drops-245296},
  doi =		{10.4230/LIPIcs.ESA.2025.61},
  annote =	{Keywords: Hyperbolic surface, Delaunay triangulation, Data structure, Combinatorial map, Implementation, CGAL}
}

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Documents authored by Pouget, Marc

Implementation of the ε-net algorithm

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ε-Net Algorithm Implementation on Hyperbolic Surfaces

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