Area-preserving piecewise affine mappings

Authors:
Alan Saalfeld
Affiliations:
The Ohio State University, Department of Civil & Environmental Engineering and Geodetic Science, Columbus, Ohio
Venue:
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Year:
2001

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Abstract

For any two polygons that have the same area, we show how to construct isomorphic triangulations that have additional area-correspondence properties. We use those isomorphic triangulations to prove that there always exist everywhere-area-preserving piecewise-affine homeomorphisms between any two simple polygons of the same area. We prove that, moreover, every piecewise-affine homeomorphism between the boundaries of the two same-area simple polygons extends to a piecewise-affine area-preserving homeomorphism of the interiors as well.