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We present two numerical methods to approximate the shortest path or a geodesic between two points on a three-dimensional parametric surface. The first one consists of minimizing the path length, working in the parameter domain, where the approximation class is composed of Bezier curves. In the second approach, we consider Bezier surfaces and their control net. The numerical implementation is based on finding the shortest path on the successive control net subdivisions. The convergence property of the Bezier net to the surface gives an approximation of the required shortest path. These approximations, also called pseudo-geodesics, are then applied to the creation of pseudo-geodesic meshes. Experimental results are also provided.

International audience; This paper deals with the acquisition and reconstruction of physical surfaces by mean of a ribbon device equipped with micro-sensors, providing geodesic curves running on the surface. The whole process involves the reconstruction of these 3D ribbon curves together with their global treatment so as to produce a consistent network for the geodesic surface interpolation by filling methods based on triangular Coons-like approaches. However, the ribbon curves follow their own way, subdividing thus the surface into arbitrary n-sided patches. We present here a method for the reconstruction of quasi developable surfaces from such n-sided curvilinear boundary curves acquired with the ribbon device.

We present some computational methods in a particular case of mixing and separation theory, as an application of classical results in the field of computational geometry. Our aim is the production of some given mixtures by mixing parts of basic products. In the geometrical approach we use, products or mixtures are characterized by vectors and the mixing process by vector sums, in the vector space of physico-chemical species. The feasibility of a mixture is viewed as a point-inclusion in the convex set of mixtures which is a zonotope associated with basic mixtures. This paper is concerned with binary mixtures characterized by two species. The geometrical approach leads to plane geometry problems and gives complete solutions to the optimal fabrication of a mixture, as well as to the fabrication of a sequence of several mixtures. Using the framework of computational geometry, we present efficient algorithms for solving the main problems related to the management of binary mixtures.

International audience; This paper is concerned with reconstruction of numerical or real surfaces based on the knowledge of some geodesic curves on the surface. So, considering two regular 3D-curves f0(t) and f1(t), our purpose is to construct a surface which interpolates these two curves in such a way that these two curves are geodesics on this surface. This will be accomplished using Hermite interpolation. For a real surface, it will be shown that geodesics can be acquired using a ribbon of micro-sensors.