A New Approach to Minimisations for Shape Control During Free-Form Surface Deformation

Even if researches on free-form surface deformation have produced a lot of various methods, very few of them are able to really control the shape in an adequately interactive way and most of them propose a unique solution to the underconstrained system of equations coming out of their deformation models. In our approach, where the deformation is performed through the static equilibrium modification of a bar network coupled to the surface control polyhedron, different minimizations have been proposed to overcome these limits and form a set of representative parameters that can be used to give access to the desired shape. In this paper, a reformulation of the optimization problem is presented thus enabling the generation of new shapes based on a common set of minimization criteria. Such a modification widens the variety of shapes still verifying the same set of constraints. When generalizing some of these minimizations the user has access to a continuous set of shapes while acting on a single parameter. Taking advantage of the reformulation, anisotropic surface behaviors are considered too and briefly illustrated. In addition, the possibility of defining several minimizations on different areas of a surface is sketched and aims at giving the user more freedom in local shape definition. The whole minimizations proposed are illustrated through examples resulting from our surface deformation software.