In this paper, we present the first steps of a 4-D oriented study of object deformation based on both local geometric deformations and global topological constraints of regularization, and shape preservation. The model described handles the shape of the objects to simulate the manipulation of elastic objects that always return to their original shape when no constraints are applied. Many kinds of forces can be applied on the objects in a scene, e.g., some user forces, object interactions or attraction/repulsion fields. Following the placement of objects into a scene, the deformation process consists in three stages, a free deformation stage under the effect of all the forces of the scene, a stage of regularization to constrain the previous deformation with respect to the original shape of the object, and finally a stage of re-positioning the object in the scene using the theory of material systems.

Keywords: regularization, material systems, free form deformation, differential geometry.