Anisotropic quadrangulation

Denis Kovacs, Ashish Myles, Denis Zorin

Research output: Contribution to journalArticle

Abstract

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 complementary 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)
Pages (from-to)449-462
Number of pages14
JournalComputer Aided Geometric Design
Volume28
Issue number8
DOIs
StatePublished - Nov 2011

Fingerprint

Quadrangulation
Parameterization
Harmonic
Shape Operator
Semiregular
Principal curvature
Remeshing
Approximation Error
Parametrization
Anisotropy
Curvature
Mesh
Gradient
Metric
Dependent
Approximation

Keywords

  • Conformal parameterization
  • Parameterization
  • Quadrangulation
  • Remeshing

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design
  • Aerospace Engineering
  • Automotive Engineering
  • Modeling and Simulation

Cite this

Anisotropic quadrangulation. / Kovacs, Denis; Myles, Ashish; Zorin, Denis.

In: Computer Aided Geometric Design, Vol. 28, No. 8, 11.2011, p. 449-462.

Research output: Contribution to journalArticle

Kovacs, Denis ; Myles, Ashish ; Zorin, Denis. / Anisotropic quadrangulation. In: Computer Aided Geometric Design. 2011 ; Vol. 28, No. 8. pp. 449-462.
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