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DOI: 10.4230/LIPIcs.SoCG.2017.44
Implementing Delaunay Triangulations of the Bolza Surface

Authors: Iordan Iordanov and Monique Teillaud

Published in: LIPIcs, Volume 77, 33rd International Symposium on Computational Geometry (SoCG 2017)

Abstract
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.
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Iordan Iordanov and Monique Teillaud. Implementing Delaunay Triangulations of the Bolza Surface. In 33rd International Symposium on Computational Geometry (SoCG 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 77, pp. 44:1-44:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{iordanov_et_al:LIPIcs.SoCG.2017.44,
  author =	{Iordanov, Iordan and Teillaud, Monique},
  title =	{{Implementing Delaunay Triangulations of the Bolza Surface}},
  booktitle =	{33rd International Symposium on Computational Geometry (SoCG 2017)},
  pages =	{44:1--44:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-038-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{77},
  editor =	{Aronov, Boris and Katz, Matthew J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2017.44},
  URN =		{urn:nbn:de:0030-drops-72173},
  doi =		{10.4230/LIPIcs.SoCG.2017.44},
  annote =	{Keywords: hyperbolic surface, Fuchsian group, arithmetic issues, Dehn's algorithm, CGAL}
}
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