A Constructive Algorithm for Disk Conformal Parameterizations

Wei Hung Liao, Mei Heng Yueh*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

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.

Original languageEnglish
Article number40
JournalJournal of Scientific Computing
Volume92
Issue number2
DOIs
Publication statusPublished - 2022 Aug

Keywords

  • Conformal parameterization
  • Double covering
  • Geodesic algorithm
  • Laplace–Beltrami operator
  • Triangular mesh

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Software
  • Numerical Analysis
  • General Engineering
  • Computational Mathematics
  • Computational Theory and Mathematics
  • Applied Mathematics

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