Close-to-conformal deformations of volumes
- Creators
- Chern, Albert
- Pinkall, Ulrich
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Schröder, Peter
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.
Additional Information
© 2015 Copyright is held by the owner/author(s). Publication rights licensed to ACM. The work reported here was supported in part by ONR Award N00014-11-1002, the DFG Collaborative Research Center TRR 109, "Discretization in Geometry and Dynamics," and a software donation from Side Effects Software. We are grateful to Houman Owhadi and Chiu-Yen Kao for generously sharing their knowledge; Kovalsky and Lipman for providing code from [Kovalsky et al. 2014]; and Paillé for the models used in [Paillé and Poulin 2012]. Last but not least the detailed reviewer feedback helped us greatly improve the paper.Additional details
- Eprint ID
- 59563
- DOI
- 10.1145/2766916
- Resolver ID
- CaltechAUTHORS:20150814-145256783
- Office of Naval Research (ONR)
- N00014-11-1002
- Deutsche Forschungsgemeinschaft (DFG)
- Created
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2015-08-14Created from EPrint's datestamp field
- Updated
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2021-11-10Created from EPrint's last_modified field