Convex combination maps over triangulations, tilings, and tetrahedral meshes |
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| Authors: | Michael S Floater Valérie Pham-Trong |
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| Institution: | (1) Centre of Mathematics for Applications, University of Oslo, P.O. Box 1053, Blindern, 0316 Oslo, Norway;(2) Masters EPITA, 14–16 rue Voltaire, 94276, Le Kremlin-Bicetre, France |
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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.
Mathematics subject classifications (2000) 05C10, 05C85, 65D17, 58E20 |
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| Keywords: | triangulation tiling tetrahedral mesh convex combination discrete maximum principle parameterization planar embedding |
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