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Journal of Scientific Computing
Published in: Journal of Scientific Computing 1/2017

14-03-2017

An Efficient Energy Minimization for Conformal Parameterizations

Authors: Mei-Heng Yueh, Wen-Wei Lin, Chin-Tien Wu, Shing-Tung Yau

Published in: Journal of Scientific Computing | Issue 1/2017

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Abstract

Surface parameterizations have been widely applied to digital geometry processing. In this paper, we propose an efficient conformal energy minimization (CEM) algorithm for computing conformal parameterizations of simply-connected open surfaces with a very small angular distortion and a highly improved computational efficiency. In addition, we generalize the proposed CEM algorithm to computing conformal parameterizations of multiply-connected surfaces. Furthermore, we prove the existence of a nontrivial accumulation point of the proposed CEM algorithm under some mild conditions. Several numerical results show the efficiency and robustness of the CEM algorithm comparing to the existing state-of-the-art algorithms. An application of the CEM on the surface morphing between simply-connected open surfaces is demonstrated thereafter. Thanks to the CEM algorithm, the whole computations for the surface morphing can be performed efficiently and robustly.
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Metadata
Title
An Efficient Energy Minimization for Conformal Parameterizations
Authors
Mei-Heng Yueh
Wen-Wei Lin
Chin-Tien Wu
Shing-Tung Yau
Publication date
14-03-2017
Publisher
Springer US
Published in
Journal of Scientific Computing / Issue 1/2017
Print ISSN: 0885-7474
Electronic ISSN: 1573-7691
DOI
https://doi.org/10.1007/s10915-017-0414-y

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