An Efficient Energy Minimization for Conformal Parameterizations

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

Computational Geometry mathscidoc:1608.09013

Journal of Scientific Computing, 73, (1), 203--227, 2017
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.
Conformal Energy Minimization, Conformal Parameterizations, Simply-Connected Open Surfaces, Surface Morphing
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@inproceedings{mei-heng2017an,
  title={An Efficient Energy Minimization for Conformal Parameterizations},
  author={Mei-Heng Yueh, Wen-Wei Lin, Chin-Tien Wu, and Shing-Tung Yau},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160823204832117243415},
  booktitle={Journal of Scientific Computing},
  volume={73},
  number={1},
  pages={203--227},
  year={2017},
}
Mei-Heng Yueh, Wen-Wei Lin, Chin-Tien Wu, and Shing-Tung Yau. An Efficient Energy Minimization for Conformal Parameterizations. 2017. Vol. 73. In Journal of Scientific Computing. pp.203--227. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160823204832117243415.
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