2026-07-23T22:07:00Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:24529 2025-12-16T14:00:25Z ddc:004 open_access

ε-Net Algorithm Implementation on Hyperbolic Surfaces Despré, Vincent Lanuel, Camille Pouget, Marc Teillaud, Monique Hyperbolic surface Delaunay triangulation Data structure Combinatorial map Implementation CGAL 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Vincent Despré and Camille Lanuel and Marc Pouget and Monique Teillaud 2025 Is Part Of LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ESA.2025.61 urn:nbn:de:0030-drops-245296 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.61 eng https://creativecommons.org/licenses/by/4.0/legalcode