Discrete and continuous reenement equations have been widely studied in the literature for the last few years, due to their applications to the areas of wavelet analysis and geometric modeling. However, there is nòuniversal' theorem that deals with the problem about the existence of compactly supported distributional solutions for both discrete and continuous reenement equations simultaneously....

In model-based computer vision it is necessary to have a geometric model of the object the pose of which is being estimated. In this paper a very compact model of the shoulder complex and arm is presented. First an investigation of the anatomy of the arm and the shoulder is conducted to identify the primary joints and degrees of freedom. To model the primary joints we apply image features and c...

We study a simple geometric model of transportation facility that consists of two points between which the travel speed is high. This elementary definition can model shuttle services, tunnels, bridges, teleportation devices, escalators or moving walkways. The travel time between a pair of points is defined as a time distance, in such a way that a customer uses the transportation facility only i...

ii To my new daughter Mia, my wife Anne, my son Philippe, and my daughter Sylvie.

In this paper we discuss the variety of planar spiral segments and their applications in objects in both the real and artificial world. The discussed curves with monotonic curvature function are well-known in geometric modelling and computer aided geometric design as fair curves, and they are very significant in aesthetic shape modelling. Fair curve segments are used for two-point G1 and G2 Her...

In this paper we present a novel, interactive shape modeling technique: Dynamic Implicit Solid Modeling, which unifies volumetric implicit functions and powerful physics-based modeling. Although implicit functions are extremely powerful in graphics, geometric design, and shape modeling, the full potential of implicit functions is yet to be fully realized due to the lack of flexible and interact...

Geometric-modeling systems with trimmed-surface patches typically store multiple representations of the same geometric information, and these representations may be inconsistent. This is true in particular for approximations of the intersection curve between two trimmed-surface patches. The Grandine-Klein intersector provides an error bound in parameter space for each computed approximation of ...

Discrete Laplace operators are ubiquitous in applications spanning geometric modeling to simulation. For robustness and efficiency, many applications require discrete operators that retain key structural properties inherent to the continuous setting. Building on the smooth setting, we present a set of natural properties for discrete Laplace operators for triangular surface meshes. We prove an i...

This paper describes a method for the determination of the four grasping points that are necessary to get a force closure grasp for a planar object considering frictionless contacts. The geometric model of the object is assumed to be unknown. The proposed approach starts from the object boundary obtained from the binary digitalization of an object image, and then uses the dual representation of...