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Simulating flexible models can create aesthetic motion for computer animation. Animators can control these motions through the use of constraints on the physical behavior of the models. This paper shows how to use mathematical constraint methods based on physics and on optimization theory to create controlled, realistic animation of physically-based flexible models. Two types of constraints are presented in this paper: reaction constraints (RCs) and augrmented Lagrangian constraints (ALCs). RCs allow the fast computation of collisions of flexible models with polygonal models. In addition, RCs allow flexible models to be pushed and pulled under the control of an animator. ALCs create animation effects such as volume-preserving squashing and the molding of taffy-like substances. ALCs are compatible with RCs. In this paper, we describe how to apply these constraint methods to a flexible model that uses finite elements.
Platt et al. (1988) studied this question.