Hermite spline interpolation on a three direction mesh from Powell-Sabin and Hsieh-Clough-Tocher finite elements

In this paper we develop a general local method to define Hermite interpolants of prescribed order r≥1 and global class Cs on the three direction mesh of the real plane. They are defined from Powell-Sabin and Hsieh-Clough-Tocher finite elements in such a way that the interpolation operators have fundamental functions with compact support and reproduce a given space Pm of polynomials included in the spline space.