Etat de l’art des méthodes d’interpolation locale de maillages triangulaires par des facettes non-planes C^0-continues

Since the end of the 1980's, parametric interpolation of points and normals over triangular meshes has been investigated to answer the problem of modelling two-manifold surfaces of arbitrary topological type. In particular, local parametric curved shape interpolation is a problem of ongoing research, since it is difficult to obtain surfaces with fair and smooth shapes. Locality of data is extremely important in some applications, for instance in computer graphics used for gaming and real time rendering. Continuous interpolant curved shape schemes recently emerged to address specific requirements of resource-limited hardware environments and to offer smooth surfaces by visually enhancing the resulting C^0 surface using only local information. In this paper we present a survey on the recently developed continuous surface schemes discussing their original construction and then comparing them from a geometric point of view in Bézier patch form. We compare the different surfaces constructed by the schemes for low triangle count meshes that actually correspond to their real-world utilization.