Fast Disk Conformal Parameterization of Simply-Connected Open Surfaces
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AbstractSurface parameterizations have been widely used in computer graphics and geometry processing. In particular, as simply-connected open surfaces are conformally equivalent to the unit disk, it is desirable to compute the disk conformal parameterizations of the surfaces. In this paper, we propose a novel algorithm for the conformal parameterization of a simply-connected open surface onto the unit disk, which significantly speeds up the computation, enhances the conformality and stability, and guarantees the bijectivity. The conformality distortions at the inner region and on the boundary are corrected by two steps, with the aid of an iterative scheme using quasi-conformal theories. Experimental results demonstrate the effectiveness of our proposed method.
All Author(s) ListChoi PT, Lui LM
Journal nameJournal of Scientific Computing
Volume Number65
Issue Number3
Pages1065 - 1090
LanguagesEnglish-United Kingdom
KeywordsBeltrami differential; Conformal Geometry; Disk conformal parameterization; Quasi-conformal theory; Simply-connected open surface
Web of Science Subject CategoriesMathematics; Mathematics, Applied

Last updated on 2021-20-01 at 01:32