SHAPE DEFORMATION AND OPTIMAL CONTROL

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.