Minimal energy surfaces on Powell–Sabin type triangulations

In this paper we present a method to obtain an explicit surface on a polygonal domain D which approximates a Lagrangian data set and minimizes a certain “energy functional”. The minimization space is the C1-quadratic spline space constructed from an α-triangulation over D and its Powell–Sabin subtriangulation, i.e., we obtain a C1-polynomial with the minimal possible degree. A convergence result is established and some numerical and graphical examples are analyzed.