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Journal Articles Discrete and Computational Geometry Year : 2023

Local Criteria for Triangulating General Manifolds


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.
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Dates and versions

hal-03794702 , version 1 (06-10-2022)





Jean-Daniel Boissonnat, Ramsay Dyer, Arijit Ghosh, Mathijs Wintraecken. Local Criteria for Triangulating General Manifolds. Discrete and Computational Geometry, 2023, 69, pp.156-191. ⟨10.1007/s00454-022-00431-7⟩. ⟨hal-03794702⟩
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