Symmetrization

Niloy J. Mitra*, Leonidas J. Guibas, Mark Pauly

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

84 Scopus citations

Abstract

We present a symmetrization algorithm for geometric objects. Our algorithm enhances approximate symmetries of a model while minimally altering its shape. Symmetrizing deformations are formulated as an optimization process that couples the spatial domain with a transformation configuration space, where symmetries can be expressed more naturally and compactly as parametrized point-pair mappings. We derive closed-form solution for the optimal symmetry transformations, given a set of corresponding sample pairs. The resulting optimal displacement vectors are used to drive a constrained deformation model that pulls the shape towards symmetry. We show how our algorithm successfully symmetrizes both the geometry and the discretization of complex 2D and 3D shapes and discuss various applications of such symmetrizing deformations.

Original languageEnglish (US)
Article number1276456
JournalACM Transactions on Graphics
Volume26
Issue number3
DOIs
StatePublished - Jul 29 2007

Keywords

  • Correspondence
  • Matching
  • Shape analysis
  • Shape optimization
  • Symmetry

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design

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