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Close-to-conformal deformations of volumes

Published: 27 July 2015 Publication History

Abstract

Conformal deformations are infinitesimal scale-rotations, which can be parameterized by quaternions. The condition that such a quaternion field gives rise to a conformal deformation is nonlinear and in any case only admits Möbius transformations as solutions. We propose a particular decoupling of scaling and rotation which allows us to find near to conformal deformations as minimizers of a quadratic, convex Dirichlet energy. Applied to tetrahedral meshes we find deformations with low quasiconformal distortion as the principal eigenvector of a (quaternionic) Laplace matrix. The resulting algorithms can be implemented with highly optimized standard linear algebra libraries and yield deformations comparable in quality to far more expensive approaches.

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cover image ACM Transactions on Graphics
ACM Transactions on Graphics  Volume 34, Issue 4
August 2015
1307 pages
ISSN:0730-0301
EISSN:1557-7368
DOI:10.1145/2809654
Issue’s Table of Contents
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].

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Publication History

Published: 27 July 2015
Published in TOG Volume 34, Issue 4

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Author Tags

  1. conformal metric
  2. deformations
  3. digital geometry processing
  4. discrete differential geometry
  5. geometric modeling

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