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Convex combination maps over triangulations, tilings, and tetrahedral meshes

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Abstract

In a recent paper by the first author, a simple proof was given of a result by Tutte on the validity of barycentric mappings, recast in terms of the injectivity of piecewise linear mappings over triangulations. In this note, we make a short extension to the proof to deal with arbitrary tilings. We also give a simple counterexample to show that convex combination mappings over tetrahedral meshes are not necessarily one-to-one.

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Authors and Affiliations

  1. Centre of Mathematics for Applications, University of Oslo, P.O. Box 1053, Blindern, 0316, Oslo, Norway

    Michael S. Floater

  2. Masters EPITA, 14–16 rue Voltaire, 94276, Le Kremlin-Bicetre, France

    Valérie Pham-Trong

Authors
  1. Michael S. Floater
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  2. Valérie Pham-Trong
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Mathematics subject classifications (2000)

05C10, 05C85, 65D17, 58E20

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Floater, M.S., Pham-Trong, V. Convex combination maps over triangulations, tilings, and tetrahedral meshes. Adv Comput Math 25, 347–356 (2006). https://doi.org/10.1007/s10444-004-7620-5

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  • DOI: https://doi.org/10.1007/s10444-004-7620-5

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