Anisotropic quadrangulation

Denis Kovacs, Ashish Myles, Denis Zorin

Research output: Chapter in Book/Report/Conference proceedingConference contribution


Quadrangulation methods aim to approximate surfaces by semiregular meshes with as few extraordinary vertices as possible. A number of techniques use the harmonic parameterization to keep quads close to squares, or fit parametrization gradients to align quads to features. Both types of techniques create near-isotropic quads; feature-aligned quadrangulation algorithms reduce the remeshing error by aligning isotropic quads with principal curvature directions. A complimentary approach is to allow for anisotropic elements, which are well-known to have significantly better approximation quality. In this work we present a simple and efficient technique to add curvature-dependent anisotropy to harmonic and feature-aligned parameterization and improve the approximation error of the quadrangulations. We use a metric derived from the shape operator which results in a more uniform error distribution, decreasing the error near features.

Original languageEnglish (US)
Title of host publicationProceedings - 14th ACM Symposium on Solid and Physical Modeling, SPM'10
Number of pages10
StatePublished - 2010
Event14th ACM Symposium on Solid and Physical Modeling, SPM'10 - Haifa, Israel
Duration: Sep 1 2010Sep 3 2010

Publication series

NameProceedings - 14th ACM Symposium on Solid and Physical Modeling, SPM'10


Other14th ACM Symposium on Solid and Physical Modeling, SPM'10


  • Conformal parameterization
  • Parameterization
  • Quadrangulation
  • Remeshing

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design
  • Algebra and Number Theory
  • Geometry and Topology


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