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Journal of Scientific Computing

, Volume 78, Issue 3, pp 1353–1386 | Cite as

A Novel Stretch Energy Minimization Algorithm for Equiareal Parameterizations

  • Mei-Heng YuehEmail author
  • Wen-Wei Lin
  • Chin-Tien Wu
  • Shing-Tung Yau
Article
  • 173 Downloads

Abstract

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.

Keywords

Equiareal parameterizations Simply connected open surfaces Surface remeshing Surface registration 

Mathematics Subject Classification

15B48 52C26 65F05 65F30 

Notes

Acknowledgements

The authors want to thank Prof. Xianfeng David Gu for the useful discussion and the executable program files of the OMT algorithm. This work is partially supported by the Ministry of Science and Technology, the National Center for Theoretical Sciences, the Taida Institute for Mathematical Sciences, the ST Yau Center at NCTU, and the Center of Mathematical Sciences and Applications at Harvard University.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsNational Taiwan Normal UniversityTeipeiTaiwan
  2. 2.Department of Applied MathematicsNational Chiao Tung UniversityHsinchuTaiwan
  3. 3.Department of MathematicsHarvard UniversityCambridgeUSA

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