research-article

Maximum entropy coordinates for arbitrary polytopes

Authors:

N. SukumarAuthors Info & Claims

SGP '08: Proceedings of the Symposium on Geometry Processing

Pages 1513 - 1520

Published: 02 July 2008 Publication History

Abstract

Barycentric coordinates can be used to express any point inside a triangle as a unique convex combination of the triangle's vertices, and they provide a convenient way to linearly interpolate data that is given at the vertices of a triangle. In recent years, the ideas of barycentric coordinates and barycentric interpolation have been extended to arbitrary polygons in the plane and general polytopes in higher dimensions, which in turn has led to novel solutions in applications like mesh parameterization, image warping, and mesh deformation. In this paper we introduce a new generalization of barycentric coordinates that stems from the maximum entropy principle. The coordinates are guaranteed to be positive inside any planar polygon, can be evaluated efficiently by solving a convex optimization problem with Newton's method, and experimental evidence indicates that they are smooth inside the domain. Moreover, the construction of these coordinates can be extended to arbitrary polyhedra and higher-dimensional polytopes.

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Maximum entropy coordinates for arbitrary polytopes

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Published In

cover image Guide Proceedings

SGP '08: Proceedings of the Symposium on Geometry Processing

July 2008

215 pages

Program Chairs:
Pierre Alliez
INRIA Sophia Antipolis - Méditerranée
,
Szymon Rusinkiewicz
Princeton University

Publisher

Eurographics Association

Goslar, Germany

Publication History

Published: 02 July 2008

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Bunge AAlexa MBotsch MKim J(2023)Discrete Laplacians for General Polygonal and Polyhedral MeshesSIGGRAPH Asia 2023 Courses10.1145/3610538.3614620(1-49)Online publication date: 6-Dec-2023
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Bunge AHerholz PSorkine-Hornung OBotsch MKazhdan M(2022)Variational quadratic shape functions for polygons and polyhedraACM Transactions on Graphics10.1145/3528223.353013741:4(1-14)Online publication date: 22-Jul-2022
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