Higher-degree super-smooth C 1 splines over a Powell–Sabin refined triangulation

The paper provides a generalization of ▫C¹▫ quadratic splines over a Powell-Sabin refined triangulation to ▫C¹▫ splines of any degree greater than two. The splines are constructed by imposing maximal super-smoothness at Powell-Sabin triangle split points and reproduce polynomials to the highest possible degree. The spline spaces are characterized by functionals that induce a B-spline representation over a triangulation, i.e., a representation of splines in terms of locally supported nonnegative basis functions that form a partition of unity. This makes the considered splines readily applicable in computer aided geometric design, function approximation problems, and finite element methods for solving partial differential equations.