2026-07-20T14:44:45Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:7217 2024-03-06T10:40:01Z ddc:004 open_access

Implementing Delaunay Triangulations of the Bolza Surface Iordanov, Iordan Teillaud, Monique hyperbolic surface Fuchsian group arithmetic issues Dehn's algorithm CGAL The CGAL library offers software packages to compute Delaunay triangulations of the (flat) torus of genus one in two and three dimensions. To the best of our knowledge, there is no available software for the simplest possible extension, i.e., the Bolza surface, a hyperbolic manifold homeomorphic to a torus of genus two. In this paper, we present an implementation based on the theoretical results and the incremental algorithm proposed last year at SoCG by Bogdanov, Teillaud, and Vegter. We describe the representation of the triangulation, we detail the different steps of the algorithm, we study predicates, and report experimental results. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Iordan Iordanov and Monique Teillaud 2017 Is Part Of LIPIcs, Volume 77, 33rd International Symposium on Computational Geometry (SoCG 2017) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.SoCG.2017.44 urn:nbn:de:0030-drops-72173 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2017.44 eng https://creativecommons.org/licenses/by/3.0/legalcode