A Constructive Algorithm for Disk Conformal Parameterizations
Surface parameterization is a fundamental issue widely studied and applied in various image and geometry processing tasks, such as surface registration, remeshing, and texture mapping. In this paper, we propose an efficient constructive algorithm for the computation of disk conformal parameterizatio...
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| Vydané v: | Journal of scientific computing Ročník 92; číslo 2; s. 40 |
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| Hlavní autori: | , |
| Médium: | Journal Article |
| Jazyk: | English |
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Springer US
01.08.2022
Springer Nature B.V |
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| ISSN: | 0885-7474, 1573-7691 |
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| Abstract | Surface parameterization is a fundamental issue widely studied and applied in various image and geometry processing tasks, such as surface registration, remeshing, and texture mapping. In this paper, we propose an efficient constructive algorithm for the computation of disk conformal parameterizations of simply connected open surfaces by combining the spherical harmonic mapping of the doubly covered surface and the geodesic algorithm. In addition, we prove the number of unknowns involved in the computation of the spherical harmonic mapping of the doubly covered surface can be reduced by roughly half. Numerical experiments indicate that the efficiency of the proposed algorithm is improved while the accuracy remains similar or even slightly better compared to the other state-of-the-art algorithms. |
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| AbstractList | Surface parameterization is a fundamental issue widely studied and applied in various image and geometry processing tasks, such as surface registration, remeshing, and texture mapping. In this paper, we propose an efficient constructive algorithm for the computation of disk conformal parameterizations of simply connected open surfaces by combining the spherical harmonic mapping of the doubly covered surface and the geodesic algorithm. In addition, we prove the number of unknowns involved in the computation of the spherical harmonic mapping of the doubly covered surface can be reduced by roughly half. Numerical experiments indicate that the efficiency of the proposed algorithm is improved while the accuracy remains similar or even slightly better compared to the other state-of-the-art algorithms. |
| ArticleNumber | 40 |
| Author | Liao, Wei-Hung Yueh, Mei-Heng |
| Author_xml | – sequence: 1 givenname: Wei-Hung surname: Liao fullname: Liao, Wei-Hung organization: Department of Applied Mathematics, National Yang Ming Chiao Tung University – sequence: 2 givenname: Mei-Heng orcidid: 0000-0002-6873-5818 surname: Yueh fullname: Yueh, Mei-Heng email: yue@ntnu.edu.tw organization: Department of Mathematics, National Taiwan Normal University |
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| Keywords | Conformal parameterization Geodesic algorithm Laplace–Beltrami operator Triangular mesh 52C26 15B48 Double covering 68U05 65F05 65D18 |
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