On Computing Derivatives for C~1 Interpolating Schemes: an Optimization

摘要

The application of Powell-Sabin's or Clough-Tocher's schemes to scattered data problems, as known requires the knowledge of the partial derivatives of first order at the vertices of an underlying triangulation. We study a local method for generating partial derivatives based on the minimization of the energy functional on the star of triangles sharing a node that we called a cell. The functional is associated to some piecewise polynomial function interpolating the points.