Convex combination maps over triangulations, tilings, and tetrahedral meshes

: 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. AMS subject classification: Primary: 05C10, 05C85, Secondary: 65D17, 58E20. Key words: triangulation, tiling, tetrahedral mesh, convex combination, discrete maximum principle, parameterization, planar embedding. Short title: Convex combination maps.

• Type: Journal
• Year: 2006
• Where: ADCM
• Authors: Michael S. Floater, Valérie Pham-Trong
• Keywords: ADCM 2006, Barycentric Mappings, Convex Combination, Mappings