A package for representing C^1 interpolating surfaces: Application to the lagoon of Venice's bed

The paper deals with the description of a method and the accompanying software, the package LABSUP, for representing C 1 interpolating surfaces. The application to the lagoon of Venice's bed is also proposed. The surfaces are built over the Delaunay triangulation and the polynomial patches used for the representation can be chosen among the Q 18 element, the Clough-Tocher or the Powell–Sabin finite elements or simply using global Bézier methods. The first three patches require the knowledge of the gradients at the nodes, or at least a suitable estimation of them. Therefore, interesting in itself is the derivative estimation process based on the minimization of the energy functional associated with the interpolant. For the representation of the lagoon of Venice's bed we only used the reduced Clough-Tocher finite element, due to the high number of points involved for which one needs to compute the Delaunay triangulation, and simply the partial derivatives of first order. A brief description of the software modules together with some graphical results of parts of the lagoon of Venice's bed are also presented.