Geometric, Variational Integrators for Computer Animation
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Date
2006
Journal Title
Journal ISSN
Volume Title
Publisher
The Eurographics Association
Abstract
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.
Description
@inproceedings{:10.2312/SCA/SCA06/043-051,
booktitle = {ACM SIGGRAPH / Eurographics Symposium on Computer Animation},
editor = {Marie-Paule Cani and James O'Brien},
title = {{Geometric, Variational Integrators for Computer Animation}},
author = {Kharevych, Liliya and Yang, Weiwei and Tong, Yiying and Kanso, Eva and Marsden, Jerrold E. and Schröder, Peter and Desbrun, Matthieu},
year = {2006},
publisher = {The Eurographics Association},
ISSN = {1727-5288},
ISBN = {3-905673-34-7},
DOI = {/10.2312/SCA/SCA06/043-051}
}