How to Represent the Shape of a Deformable Object and Ease the Control of the Deformation?

The research on the reconstruction and the representation of the shape of objects in motion is nowadays particularly active, both on the theoretical ground and on the field of applications. It is particularly active the discussion present in the scientific community on how to make the mathematical formalism of shape representation compatible with the intuitiveness and perception of physical phenomena. In this paper we pose the problem of how to describe the shape of an object through the definition of a framework that allows not only the analysis but also the control of the shape of objects under continuous deformation.