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DOI: 10.4230/LIPIcs.SoCG.2018.9
URN: urn:nbn:de:0030-drops-87224
URL: https://drops.dagstuhl.de/opus/volltexte/2018/8722/
Boissonnat, Jean-Daniel ; Dyer, Ramsay ; Ghosh, Arijit ; Wintraecken, Mathijs
Local Criteria for Triangulation of Manifolds
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Abstract
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
@InProceedings{boissonnat_et_al:LIPIcs:2018:8722,
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 = {http://drops.dagstuhl.de/opus/volltexte/2018/8722},
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 | |
| Seminar: | 34th International Symposium on Computational Geometry (SoCG 2018) | |
| Issue date: | 2018 | |
| Date of publication: | 08.06.2018 |
