@article{f0f4b097560a4630970806ef9dadeefb,
title = "A Constructive Algorithm for Disk Conformal Parameterizations",
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.",
keywords = "Conformal parameterization, Double covering, Geodesic algorithm, Laplace–Beltrami operator, Triangular mesh",
author = "Liao, {Wei Hung} and Yueh, {Mei Heng}",
note = "Funding Information: The work of the authors was partially supported by the Ministry of Science and Technology (MoST), the National Center for Theoretical Sciences, and the Ministry of Education. M.-H. Yueh was partially supported by the MoST grants 109-2115-M-003-010-MY2 and 110-2115-M-003-014-. . Funding Information: The work of the authors was partially supported by the Ministry of Science and Technology (MoST), the National Center for Theoretical Sciences, and the Ministry of Education (MoE). M.-H. Yueh was partially supported by the MoST grants 109-2115-M-003-010-MY2 and 110-2115-M-003-014-, and the MoE grant. Publisher Copyright: {\textcopyright} 2022, The Author(s).",
year = "2022",
month = aug,
doi = "10.1007/s10915-022-01898-5",
language = "English",
volume = "92",
journal = "Journal of Scientific Computing",
issn = "0885-7474",
publisher = "Springer New York",
number = "2",
}