The art to keep in touch - The "good use" of Lagrange multipliers

Physically-based modeling for computer animation has become a wide spread framework because it allows to produce more realistic motions in less time without requiring the expertise of skilled animators. But, a computer animation is not only a numerical simulation based on classical mechanics since it follows a precise story-line. One common way to define aims in an animation is to add geometric constraints. There are several methods to manage these constraints within a physically-based framework. In this paper, we present an algorithm for constraints handling based on Lagrange multipliers. After few remarks on the equations of motion that we use, we present a first algorithm proposed by Platt. We show with a simple example that this method is not reliable. Our contribution consists in improving this algorithm to provide an efficient and robust method to handle simultaneous and antagonist constraints.