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 , AirelaVille, Switzerland, pp. 4351. ISBN 9783905673340 http://resolver.caltech.edu/CaltechAUTHORS:20101005093706360

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Abstract
We present a generalpurpose numerical scheme for time integration of Lagrangian dynamical systems—an important computational tool at the core of most physicsbased 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 highorder 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 PontryaginHamilton principle, expressing time integration in a geometric manner. We demonstrate the applicability of our integrators to the simulation of nonlinear elasticity with implementation details.
Item Type:  Book Section  

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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 (ACI0204932, DMS0453145, CCF0503786 & 0528101, CCR0133983), DOE (W7405ENG48/B341492 & DEFG02 04ER25657), Caltech Center for Mathematics of Information, nVidia, Autodesk, and Pixar.  
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Subject Keywords:  geometric algorithms, languages, systems, animations  
Record Number:  CaltechAUTHORS:20101005093706360  
Persistent URL:  http://resolver.caltech.edu/CaltechAUTHORS:20101005093706360  
Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided.  
ID Code:  20295  
Collection:  CaltechAUTHORS  
Deposited By:  Tony Diaz  
Deposited On:  17 Nov 2010 17:44  
Last Modified:  26 Dec 2012 12:30 
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