Stable and effective enforcement of hard constraints is one of the crucial components in controlling physics-based dynamic simulation systems. The conventional explicit Baumgarte constraint stabilization confines the time step to be within a stability limit and requires users to pick problem-dependent coefficients to achieve fast convergence or to prevent oscillations. The recently proposed post-stabilization method has shown a successful constraint drift reduction but it does not guarantee the physically correct behavior of motion and requires additional computational cost to decrease the constraint errors. This paper presents our new implicit constraint enforcement technique that is stable over large time steps and does not require problem dependent stabilization parameters. This new implicit constraint enforcement method uses the future time step to estimate the correct magnitude of the constraint forces, resulting in better stability over bigger time steps. More importantly, the proposed method generates physically conforming constraint forces while minimizing the constraint drifts, resulting in physically correct motion. Its asymptotic computational complexity is same as the explicit Baumgarte method. It can be easily integrated into various constrained dynamic systems including rigid body or deformable structure applications. This paper describes a formulation of implicit constraint enforcement and an accumulated constraint error and dynamic behavior analysis for comparison with existing methods.

This paper presents a multi-resolutional surface deformable model with physical property adjustment scheme and shape-preserving springs to represent surface-deformable objects efficiently and robustly. In order to reduce the computational complexity while ensuring the same global volumetric behaviour for the deformable object, we introduce a multi-resolutional mass-spring model that is locally refined using the modified-butterfly subdivision scheme. For robust deformation, a shape-preserving spring, which helps to restore the model to the original shape, is proposed to reduce the animation instability. Volume and shape preservation is indirectly achieved by restoring the model to the original shape without computing the actual volume and associated forces at every iteration. Most existing methods concentrate on visual realism of multi-resolutional deformation and often neglect to maintain the dynamic behavioural integrity between detail levels. In order to preserve overall physical behaviour, we present a new scheme for adjusting physical properties between different levels of details. During the animation of deformable objects, the part of the object under external forces beyond a threshold or with large surface curvature variations is refined with a higher level of detail. The physical properties of nodes and springs in the locally refined area are adjusted in order to preserve the total mass and global behaviour of the object. The adequacy of the proposed scheme was analysed with tests using practical mesh examples. Experimental results demonstrate improved efficiency in object deformation and preservation of overall behaviour between different levels. Copyright © 2005 John Wiley & Sons, Ltd.