Conformal mesh deformations with Möbius transformations

Amir Vaxman, Christian Müller, Ofir Weber

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

We establish a framework to design triangular and circular polygonal meshes by using face-based compatible Möbius transformations. Embracing the viewpoint of surfaces from circles, we characterize discrete conformality for such meshes, in which the invariants are circles, cross-ratios, and mutual intersection angles. Such transformations are important in practice for editing meshes without distortions or loss of details. In addition, they are of substantial theoretical interest in discrete differential geometry. Our framework allows for handle-based deformations, and interpolation between given meshes with controlled conformal error.

Original languageEnglish
Article number55
Pages (from-to)1-11
Number of pages11
JournalACM Transactions on Graphics
Volume34
Issue number4
DOIs
Publication statusPublished - 27 Jul 2015
Externally publishedYes

Keywords

  • Circular meshes
  • Discrete conformal transformations
  • Handle-based editing
  • Interpolation
  • Möbius transformations

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