Stable Constrained Dynamics

Maxime Tournier 1, 2, 3 Matthieu Nesme 4 Benjamin Gilles 5, 2 François Faure 4
3 DEMAR - Artificial movement and gait restoration
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier, CRISAM - Inria Sophia Antipolis - Méditerranée
4 IMAGINE - Intuitive Modeling and Animation for Interactive Graphics & Narrative Environments
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
5 ICAR - Image & Interaction
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : We present a unification of the two main approaches to simulate deformable solids, namely elasticity and constraints. Elasticity accurately handles soft to moderately stiff objects, but becomes numerically hard as stiffness increases. Constraints efficiently handle high stiffness, but when integrated in time they can suffer from instabilities in the nullspace directions, generating spurious transverse vibrations when pulling hard on thin inextensible objects or articulated rigid bodies. We show that geometric stiffness, the tensor encoding the change of force directions (as opposed to intensities) in response to a change of positions, is the missing piece between the two approaches. This previously neglected stiffness term is easy to implement and dramatically improves the stability of inextensible objects and articulated chains, without adding artificial bending forces. This allows time step increases up to several orders of magnitude using standard linear solvers.
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Maxime Tournier, Matthieu Nesme, Benjamin Gilles, François Faure. Stable Constrained Dynamics. ACM Transactions on Graphics, Association for Computing Machinery, 2015, Proceedings of SIGGRAPH, 34 (4), pp.132:1--132:10. ⟨10.1145/2766969⟩. ⟨hal-01157835v2⟩

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