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Geometric, Variational Integrators for Computer Animation

Kharevych, L. and Wei, W. and Tong, Y. and Kanso, E. and Marsden, J. E. and Schröder, P. and Desbrun, M. (2006) Geometric, Variational Integrators for Computer Animation. In: Computer animation 2006 : ACM SIGGRAPH / Eurographics Symposium Proceedings : Vienna, Austria September 2 - 4, 2006. Eurographics Association , Aire-la-Ville, Switzerland, pp. 43-51. ISBN 9783905673340.

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We present a general-purpose numerical scheme for time integration of Lagrangian dynamical systems—an important computational tool at the core of most physics-based animation techniques. Several features make this particular time integrator highly desirable for computer animation: it numerically preserves important invariants, such as linear and angular momenta; the symplectic nature of the integrator also guarantees a correct energy behavior, even when dissipation and external forces are added; holonomic constraints can also be enforced quite simply; finally, our simple methodology allows for the design of high-order accurate schemes if needed. Two key properties set the method apart from earlier approaches. First, the nonlinear equations that must be solved during an update step are replaced by a minimization of a novel functional, speeding up time stepping by more than a factor of two in practice. Second, the formulation introduces additional variables that provide key flexibility in the implementation of the method. These properties are achieved using a discrete form of a general variational principle called the Pontryagin-Hamilton principle, expressing time integration in a geometric manner. We demonstrate the applicability of our integrators to the simulation of non-linear elasticity with implementation details.

Item Type:Book Section
Related URLs:
URLURL TypeDescription
Schröder, P.0000-0002-0323-7674
Desbrun, M.0000-0003-3424-6079
Additional Information:© 2006 The Eurographics Association. We thank Rasmus Tamstorf, Eitan Grinspun, Matt West, Hiroaki Yoshimura, and Michael Ortiz for helpful comments. This research was partially supported by NSF (ACI-0204932, DMS-0453145, CCF-0503786 & 0528101, CCR-0133983), DOE (W-7405-ENG-48/B341492 & DE-FG02- 04ER25657), Caltech Center for Mathematics of Information, nVidia, Autodesk, and Pixar.
Funding AgencyGrant Number
Department of Energy (DOE)W-7405-ENG-48/B341492
Department of Energy (DOE)DE-FG02-04ER25657
Caltech Center for Mathematics of InformationUNSPECIFIED
Subject Keywords:geometric algorithms, languages, systems, animations
Record Number:CaltechAUTHORS:20101005-093706360
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:20295
Deposited By: Tony Diaz
Deposited On:17 Nov 2010 17:44
Last Modified:09 Mar 2020 13:19

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