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 http://resolver.caltech.edu/CaltechAUTHORS:20101005-093706360
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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|
|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.|
|Subject Keywords:||geometric algorithms, languages, systems, animations|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Tony Diaz|
|Deposited On:||17 Nov 2010 17:44|
|Last Modified:||26 Dec 2012 12:30|
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