Closed Free-Form Surface Geometrical Modeling A New Approach With Global And Local Characterization

In this paper, we present a new approach to geometrical modeling which allows the user to easily characterize and control the shape defined to a closed surface. We will focus on dealing with the shape’s topological, morphological and geometrical properties separately. To do this, we have based our work on the following observations concerning surfaces defined by control-points, and implicit surfaces with skeleton. They both provide complementary approaches to the surface’s deformation, and both have specific advantages and limits. We thus attempted to conceive a model which integrates the local and geometrical characterization induced by the control points, as well as the representation of the morphology given by the skeleton. Knowing that the lattice of control points is close to the surface and that the skeleton is centered in the related shape, we thought of a 3-layer model. The transition layer separates the local geometrical considerations from those linked to the global morphology. We apply our model to shape design in order to modify an object in an interactive and ergonomic way, as well as to reconstruction which allows better shape understanding. To do so, we present the algorithms related to these processes.