Intrinsic Parameterizations of Surface Meshes
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Date
2002
Journal Title
Journal ISSN
Volume Title
Publisher
Blackwell Publishers, Inc and the Eurographics Association
Abstract
Parameterization of discrete surfaces is a fundamental and widely-used operation in graphics, required, for instance, for texture mapping or remeshing. As 3D data becomes more and more detailed, there is an increased need for fast and robust techniques to automatically compute least-distorted parameterizations of large meshes. In this paper, we present new theoretical and practical results on the parameterization of triangulated surface patches. Given a few desirable properties such as rotation and translation invariance, we show that the only admissible parameterizations form a two-dimensional set and each parameterization in this set can be computed using a simple, sparse, linear system. Since these parameterizations minimize the distortion of different intrinsic measures of the original mesh, we call them Intrinsic Parameterizations. In addition to this partial theoretical analysis, we propose robust, efficient and tunable tools to obtain least-distorted parameterizations automatically. In particular, we give details on a novel, fast technique to provide an optimal mapping without fixing the boundary positions, thus providing a unique Natural Intrinsic Parameterization. Other techniques based on this parameterization family, designed to ease the rapid design of parameterizations, are also proposed.
Description
@article{10.1111:1467-8659.00580,
journal = {Computer Graphics Forum},
title = {{Intrinsic Parameterizations of Surface Meshes}},
author = {Desbrun, Mathieu and Meyer, Mark and Alliez, Pierre},
year = {2002},
publisher = {Blackwell Publishers, Inc and the Eurographics Association},
ISSN = {1467-8659},
DOI = {10.1111/1467-8659.00580}
}