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oai:drops-oai.dagstuhl.de:8722 2024-03-06T10:42:30Z ddc:004 open_access

Local Criteria for Triangulation of Manifolds Boissonnat, Jean-Daniel Dyer, Ramsay Ghosh, Arijit Wintraecken, Mathijs manifold simplicial complex homeomorphism triangulation 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Jean-Daniel Boissonnat and Ramsay Dyer and Arijit Ghosh and Mathijs Wintraecken 2018 Is Part Of LIPIcs, Volume 99, 34th International Symposium on Computational Geometry (SoCG 2018) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.SoCG.2018.9 urn:nbn:de:0030-drops-87224 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2018.9 eng https://creativecommons.org/licenses/by/3.0/legalcode