Isotopic Implicit Surface Meshing

Jean-Daniel Boissonnat, David Cohen-Steiner, Gert Vegter

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    Abstract

    This paper addresses the problem of piecewise linear approximation of implicit surfaces. We first give a criterion ensuring that the zero-set of a smooth function and the one of a piecewise linear approximation of it are isotopic. Then, we deduce from this criterion an implicit surface meshing algorithm certifying that the output mesh is isotopic to the actual implicit surface. This is the first algorithm achieving this goal in a provably correct way.
    Original languageEnglish
    Pages (from-to)138-157
    Number of pages20
    JournalDiscrete & computational geometry
    Volume39
    Issue number1-3
    DOIs
    Publication statusPublished - Mar-2008

    Keywords

    • Algorithms
    • Morse theory
    • Triangulations
    • Topology

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