License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SoCG.2018.9
URN: urn:nbn:de:0030-drops-87224
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Boissonnat, Jean-Daniel ; Dyer, Ramsay ; Ghosh, Arijit ; Wintraecken, Mathijs

Local Criteria for Triangulation of Manifolds

LIPIcs-SoCG-2018-9.pdf (0.5 MB)


We present criteria for establishing a triangulation of a manifold. Given a manifold M, a simplicial complex A, and a map H from the underlying space of A to M, our criteria are presented in local coordinate charts for M, and ensure that H is a homeomorphism. These criteria do not require a differentiable structure, or even an explicit metric on M. No Delaunay property of A is assumed. The result provides a triangulation guarantee for algorithms that construct a simplicial complex by working in local coordinate patches. Because the criteria are easily verified in such a setting, they are expected to be of general use.

BibTeX - Entry

  author =	{Jean-Daniel Boissonnat and Ramsay Dyer and Arijit Ghosh and Mathijs Wintraecken},
  title =	{{Local Criteria for Triangulation of Manifolds}},
  booktitle =	{34th International Symposium on Computational Geometry (SoCG 2018)},
  pages =	{9:1--9:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-066-8},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{99},
  editor =	{Bettina Speckmann and Csaba D. T{\'o}th},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-87224},
  doi =		{10.4230/LIPIcs.SoCG.2018.9},
  annote =	{Keywords: manifold, simplicial complex, homeomorphism, triangulation}

Keywords: manifold, simplicial complex, homeomorphism, triangulation
Collection: 34th International Symposium on Computational Geometry (SoCG 2018)
Issue Date: 2018
Date of publication: 08.06.2018

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