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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. ACM Transactions on Graphics, 29 (4). Art. No. 38. ISSN 0730-0301. doi:10.1145/1778765.1778775.

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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:Article
Related URLs:
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
Rose Hill FoundationUNSPECIFIED
Subject Keywords:Digital Geometry Processing; Discrete Differential Geometry; elasticity; geometric modeling; shape space interpolation; morphing; parameterization
Issue or Number:4
Record Number:CaltechAUTHORS:20100803-090608485
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Official Citation:Chao, I., Pinkall, U., Sanan, P., Schröder, P. 2010. A Simple Geometric Model for Elastic Deformations. ACM Trans. Graph. 29, 4, Article 38 (July 2010), 6 pages. DOI = 10.1145/1778765.1778775
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:19251
Deposited By: Tony Diaz
Deposited On:03 Aug 2010 18:11
Last Modified:08 Nov 2021 23:50

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