Shape Deformation and Optimal Control
نویسندگان
چکیده
Shape deformation analysis is concerned with determining a deformation of a given shape into another one, which is optimal for a certain cost. We provide the main ideas for a new general approach to shape deformation analysis, using the framework of optimal control theory. This point of view can be made independent from the parametrization of the shape, and allows to model general constrained shape analysis problems. The use of a infinite dimensional variant of the constrained Pontryagin Maximum Principle characterizes the optimal solutions of the shape deformation problem in a very general way. Résumé. L’analyse des déformations consiste à déterminer une transformation d’une forme donnée en une autre, optimale pour un certain coût. Nous donnons ici les idées principales pour une nouvelle approche générale pour cette analyse à l’aide de la théorie du contrôle optimal. Ce point de vue peut être pris de manière à ne pas dépendre de la paramétrisation de la forme, et permet également de modéliser des contraintes dans les problèmes d’analyse de déformations. Nous utilisons une variante en dimension infinie (cadre naturel de l’analyse des déformations) du principe du maximum de Pontryagin avec contraintes permettant de caractériser de façon très générale les déformations optimales recherchées.
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