Minimal energy CrCr-surfaces on uniform Powell-Sabin type meshes: Estimation of the smoothing parameters

In this paper we present a method to obtain a CrCr-surface (r≥1r≥1) on a polygonal domain which approximates a Lagrange data set and minimizes an “energy functional”. The minimization space is formed by bivariate spline functions constructed on a uniform Powell-Sabin type triangulation of the domain. We prove a convergence result and we present a method for the estimation of the smoothing parameters involved in the functional. We finish with some numerical and graphical examples.