Maximum Likelihood Coordinates

Author:

Chang Q.1ORCID,Deng C.2ORCID,Hormann K.1ORCID

Affiliation:

1. Università della Svizzera italiana Lugano Switzerland

2. Hangzhou Dianzi University Hangzhou Zhejiang China

Abstract

AbstractAny point inside a d‐dimensional simplex can be expressed in a unique way as a convex combination of the simplex's vertices, and the coefficients of this combination are called the barycentric coordinates of the point. The idea of barycentric coordinates extends to general polytopes with n vertices, but they are no longer unique if n > d+1. Several constructions of such generalized barycentric coordinates have been proposed, in particular for polygons and polyhedra, but most approaches cannot guarantee the non‐negativity of the coordinates, which is important for applications like image warping and mesh deformation. We present a novel construction of non‐negative and smooth generalized barycentric coordinates for arbitrary simple polygons, which extends to higher dimensions and can include isolated interior points. Our approach is inspired by maximum entropy coordinates, as it also uses a statistical model to define coordinates for convex polygons, but our generalization to non‐convex shapes is different and based instead on the project‐and‐smooth idea of iterative coordinates. We show that our coordinates and their gradients can be evaluated efficiently and provide several examples that illustrate their advantages over previous constructions.

Funder

Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung

National Natural Science Foundation of China

Publisher

Wiley

Subject

Computer Graphics and Computer-Aided Design

Cited by 5 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Optimized Dual‐Volumes for Tetrahedral Meshes;Computer Graphics Forum;2024-07-31

2. Stochastic Computation of Barycentric Coordinates;ACM Transactions on Graphics;2024-07-19

3. Generalized Bézier volumes over simple convex polyhedra;Computer Aided Geometric Design;2024-06

4. Genuine multi-sided parametric surface patches – A survey;Computer Aided Geometric Design;2024-05

5. A Survey on Cage‐based Deformation of 3D Models;Computer Graphics Forum;2024-04-30

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