One-to-one piecewise linear mappings over triangulations

Floater, Michael

doi:10.1090/S0025-5718-02-01466-7

One-to-one piecewise linear mappings over triangulations
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by Michael S. Floater;

Math. Comp. 72 (2003), 685-696

DOI: https://doi.org/10.1090/S0025-5718-02-01466-7

Published electronically: October 17, 2002

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Abstract:

We call a piecewise linear mapping from a planar triangulation to the plane a convex combination mapping if the image of every interior vertex is a convex combination of the images of its neighbouring vertices. Such mappings satisfy a discrete maximum principle and we show that they are one-to-one if they map the boundary of the triangulation homeomorphically to a convex polygon. This result can be viewed as a discrete version of the Radó-Kneser-Choquet theorem for harmonic mappings, but is also closely related to Tutte’s theorem on barycentric mappings of planar graphs.

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