TY - JOUR
T1 - A Novel Stretch Energy Minimization Algorithm for Equiareal Parameterizations
AU - Yueh, Mei Heng
AU - Lin, Wen Wei
AU - Wu, Chin Tien
AU - Yau, Shing Tung
N1 - Funding Information:
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.
Funding Information:
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.
Publisher Copyright:
© 2018, Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2019/3/1
Y1 - 2019/3/1
N2 - 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.
AB - 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.
KW - Equiareal parameterizations
KW - Simply connected open surfaces
KW - Surface registration
KW - Surface remeshing
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U2 - 10.1007/s10915-018-0822-7
DO - 10.1007/s10915-018-0822-7
M3 - Article
AN - SCOPUS:85053390455
SN - 0885-7474
VL - 78
SP - 1353
EP - 1386
JO - Journal of Scientific Computing
JF - Journal of Scientific Computing
IS - 3
ER -