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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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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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