A Novel Stretch Energy Minimization Algorithm for Equiareal Parameterizations

Mei Heng Yueh*, Wen-Wei Lin, Chin-Tien Wu, Shing Tung Yau

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

Surface parameterizations have been widely applied to computer graphics and digital geometry processing. In this paper, we propose a novel stretch energy minimization (SEM) algorithm for the computation of equiareal parameterizations of simply connected open surfaces with very small area distortions and highly improved computational efficiencies. In addition, the existence of nontrivial limit points of the SEM algorithm is guaranteed under some mild assumptions of the mesh quality. Numerical experiments indicate that the accuracy, effectiveness, and robustness of the proposed SEM algorithm outperform the other state-of-the-art algorithms. Applications of the SEM on surface remeshing, registration and morphing for simply connected open surfaces are demonstrated thereafter. Thanks to the SEM algorithm, the computation for these applications can be carried out efficiently and reliably.

Original languageEnglish
Pages (from-to)1353-1386
Number of pages34
JournalJournal of Scientific Computing
Volume78
Issue number3
DOIs
StatePublished - 1 Mar 2019

Keywords

  • Equiareal parameterizations
  • Simply connected open surfaces
  • Surface registration
  • Surface remeshing

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