Stable Constrained Dynamics

摘要

We present a unification of the two main approaches to simulatedeformable solids, namely elasticity and constraints.Elasticity accurately handles soft to moderately stiff objects,but becomes numerically hard as stiffness increases. Constraintsefficiently handle high stiffness, but when integratedin time they can suffer from instabilities in the nullspacedirections, generating spurious transverse vibrations whenpulling hard on thin inextensible objects or articulated rigidbodies. We show that geometric stiffness, the tensor encodingthe change of force directions (as opposed to intensities) in responseto a change of positions, is the missing piece betweenthe two approaches. This previously neglected stiffness termis easy to implement and dramatically improves the stabilityof inextensible objects and articulated chains, without addingartificial bending forces. This allows time step increases up toseveral orders of magnitude using standard linear solvers.