Mémoire sur la théorie des coordonnées curvilignes, et des systèmes orthogonaux
Let us consider two closed surfaces , of class and two functions , of class , called measuring functions. The natural pseudodistance between the pairs , is defined as the infimum of as varies in the set of all homeomorphisms from onto . In this paper we prove that the natural pseudodistance equals either , , or , where and are two suitable critical values of the measuring functions. This shows that a previous relation between the natural pseudodistance and critical values...
In this article, we present a mathematical model and numerical method for surface reconstruction from 3D point cloud data, using the level-set method. The presented method solves surface reconstruction by the computation of the distance function to the shape, represented by the point cloud, using the so called Fast Sweeping Method, and the solution of advection equation with curvature term, which creates the evolution of an initial condition to the final state. A crucial point for efficiency is...
We study quadric surfaces in Euclidean 3-space with non-degenerate second fundamental form, and classify them in terms of the Gaussian curvature, the mean curvature, the second Gaussian curvature and the second mean curvature.