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A Simple Geometric Model for Elastic Deformations

Chao, Isaac and Pinkall, Ulrich and Sanan, Patrick and Schröder, Peter (2010) A Simple Geometric Model for Elastic Deformations. In: SIGGRAPH '10 ACM SIGGRAPH 2010 papers. ACM , New York, NY, Art. No. 38. ISBN 978-1-4503-0210-4.

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We advocate a simple geometric model for elasticity: distance between the differential of a deformation and the rotation group. It comes with rigorous differential geometric underpinnings, both smooth and discrete, and is computationally almost as simple and efficient as linear elasticity. Owing to its geometric non-linearity, though, it does not suffer from the usual linearization artifacts. A material model with standard elastic moduli (Lamé parameters) falls out naturally, and a minimizer for static problems is easily augmented to construct a fully variational 2nd order time integrator. It has excellent conservation properties even for very coarse simulations, making it very robust. Our analysis was motivated by a number of heuristic, physics-like algorithms from geometry processing (editing, morphing, parameterization, and simulation). Starting with a continuous energy formulation and taking the underlying geometry into account, we simplify and accelerate these algorithms while avoiding common pitfalls. Through the connection with the Biot strain of mechanics, the intuition of previous work that these ideas are “like” elasticity is shown to be spot on.

Item Type:Book Section
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Schröder, Peter0000-0002-0323-7674
Additional Information:© 2010 ACM. This work was supported in part by NSF (CCF-0635112), Caltech’s Center for the Mathematics of Information, and the DFG Research Center Matheon. Additional support was provided by the Rose Hill Foundation and the IAS at TU München.
Funding AgencyGrant Number
Caltech Center for the Mathematics of InformationUNSPECIFIED
Deutsche Forschungsgemeinschaft (DFG)UNSPECIFIED
Rose Hill FoundationUNSPECIFIED
Technical University of MunichUNSPECIFIED
Subject Keywords:Digital Geometry Processing, Discrete Differential Geometry, elasticity, geometric modeling, shape space interpolation, morphing, parameterization
Record Number:CaltechAUTHORS:20160819-110910323
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Official Citation:Isaac Chao, Ulrich Pinkall, Patrick Sanan, and Peter Schröder. 2010. A simple geometric model for elastic deformations. In ACM SIGGRAPH 2010 papers (SIGGRAPH '10), Hugues Hoppe (Ed.). ACM, New York, NY, USA, , Article 38 , 6 pages. DOI=
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:69787
Deposited On:22 Aug 2016 19:54
Last Modified:11 Nov 2021 04:19

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