TY - JOUR
T1 - Optimized surface parameterizations with applications to Chinese virtual broadcasting
AU - Yueh, Mei Heng
AU - Huang, Hsiao Han
AU - Li, Tiexiang
AU - Lin, Wen Wei
AU - Yau, Shing Tung
N1 - Funding Information:
Acknowledgments. The authors want to thank Prof. Chin-Tien Wu for many valuable discussions. M.-H. Yueh was partially supported by MoST 107-2115-M-003-012-. T. Li was supported in parts by the National Natural Science Foundation of China (NSFC) 11971105. W.-W. Lin was partially supported by MoST 106-2628-M-009-004-. This work was partially supported by the Ministry of Science and Technology, the National Center for Theoretical Sciences, the ST Yau Centers in National Chiao Tung University, the Shing-Tung Yau Center of Southeast University, and the Center of Mathematical Sciences and Applications at Harvard University.
Publisher Copyright:
© 2020 Kent State University. All rights reserved.
PY - 2020
Y1 - 2020
N2 - Surface parameterizations have been widely applied in computer-aided design for the geometric processing tasks of surface registration, remeshing, texture mapping, and so on. In this paper, we present an efficient balanced energy minimization algorithm for the computation of simply connected open surface parameterizations with balanced angle and area distortions. The existence of a nontrivial accumulation function of the proposed algorithm is guaranteed under some mild conditions, and the limiting function is shown to be one-to-one. Comparisons of the proposed algorithm with angle- and area-preserving parameterizations show that the angular distortion is close to that of an angle-preserving parameterization while the area distortion is significantly improved. An application of the proposed algorithm involving surface remeshing, registration, and morphing to the Chinese virtual broadcasting technique is demonstrated.
AB - Surface parameterizations have been widely applied in computer-aided design for the geometric processing tasks of surface registration, remeshing, texture mapping, and so on. In this paper, we present an efficient balanced energy minimization algorithm for the computation of simply connected open surface parameterizations with balanced angle and area distortions. The existence of a nontrivial accumulation function of the proposed algorithm is guaranteed under some mild conditions, and the limiting function is shown to be one-to-one. Comparisons of the proposed algorithm with angle- and area-preserving parameterizations show that the angular distortion is close to that of an angle-preserving parameterization while the area distortion is significantly improved. An application of the proposed algorithm involving surface remeshing, registration, and morphing to the Chinese virtual broadcasting technique is demonstrated.
KW - Balanced energy minimization
KW - Simply connected open surface
KW - Surface parameterization
KW - Virtual broadcasting
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U2 - 10.1553/etna_vol53s383
DO - 10.1553/etna_vol53s383
M3 - Article
AN - SCOPUS:85085261903
SN - 1068-9613
VL - 53
SP - 383
EP - 405
JO - Electronic Transactions on Numerical Analysis
JF - Electronic Transactions on Numerical Analysis
ER -