A Novel Stretch Energy Minimization Algorithm for Equiareal Parameterizations

Mei-Heng Yueh National Taiwan Normal University Wen-Wei Lin National Chiao Tung University Chin-Tien Wu National Chiao Tung University Shing-Tung Yau Harvard University

Computational Geometry mathscidoc:1708.09001

Distinguished Paper Award in 2018

Journal of Scientific Computing, 78, (3), 1353–1386, 2019
Surface parameterizations have been widely applied to computer graphics and digital geometry processing. In this paper, we propose a novel stretch energy minimization (SEM) algorithm for the computation of equiareal parameterizations of simply connected open surfaces with very small area distortions and highly improved computational efficiencies. In addition, the existence of nontrivial limit points of the SEM algorithm is guaranteed under some mild assumptions of the mesh quality. Numerical experiments indicate that the accuracy, effectiveness, and robustness of the proposed SEM algorithm outperform the other state-of-the-art algorithms. Applications of the SEM on surface remeshing, registration and morphing for simply connected open surfaces are demonstrated thereafter. Thanks to the SEM algorithm, the computation for these applications can be carried out efficiently and reliably.
Equiareal parameterizations, Simply connected open surfaces, Surface remeshing, Surface registration
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  • https://doi.org/10.1007/s10915-018-0822-7
  title={A Novel Stretch Energy Minimization Algorithm for Equiareal Parameterizations},
  author={Mei-Heng Yueh, Wen-Wei Lin, Chin-Tien Wu, and Shing-Tung Yau},
  booktitle={Journal of Scientific Computing},
Mei-Heng Yueh, Wen-Wei Lin, Chin-Tien Wu, and Shing-Tung Yau. A Novel Stretch Energy Minimization Algorithm for Equiareal Parameterizations. 2019. Vol. 78. In Journal of Scientific Computing. pp.1353–1386. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170803175252330127805.
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