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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Bibliographic Details
Published in:Journal of scientific computing Vol. 92; no. 2; p. 40
Main Authors: Liao, Wei-Hung, Yueh, Mei-Heng
Format: Journal Article
Language:English
Published: New York Springer US 01.08.2022
Springer Nature B.V
Subjects:
Algorithms
Computational Mathematics and Numerical Analysis
Mapping
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Methods
Original Research
Parameterization
Spherical harmonics
Surface layers
Texture mapping
Theoretical
Conformal parameterization
Geodesic algorithm
Laplace–Beltrami operator
Triangular mesh
52C26
15B48
Double covering
68U05
65F05
65D18
ISSN:0885-7474, 1573-7691
Online Access:Get full text
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Summary: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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ISSN:0885-7474
1573-7691
DOI:10.1007/s10915-022-01898-5