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ε-Net Algorithm Implementation on Hyperbolic Surfaces

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

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LIPIcs.ESA.2025.61.pdf
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ACM Subject Classification
  • Theory of computation → Computational geometry
  • Mathematics of computing → Geometric topology
Keywords
  • Hyperbolic surface
  • Delaunay triangulation
  • Data structure
  • Combinatorial map
  • Implementation
  • CGAL

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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) https://doi.org/10.4230/LIPIcs.ESA.2025.61

Author Details

Vincent Despré
  • Université de Lorraine, CNRS, Inria, LORIA, F-54000 Nancy, France
Camille Lanuel
  • Université de Lorraine, CNRS, Inria, LORIA, F-54000 Nancy, France
Marc Pouget
  • Université de Lorraine, CNRS, Inria, LORIA, F-54000 Nancy, France
Monique Teillaud
  • Université de Lorraine, CNRS, Inria, LORIA, F-54000 Nancy, France

Funding

This work was partially supported by grant ANR-23-CE48-0017 of the French National Research Agency ANR (project Abysm).

Acknowledgements

Experiments presented in this paper were carried out using the Grid'5000 testbed, supported by a scientific interest group hosted by Inria and including CNRS, RENATER and several Universities as well as other organizations (see https://www.grid5000.fr).

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References

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