Higher-degree super-smooth $C^1$ splines over a Powell-Sabin refined triangulationGrošelj, Jan (Avtor) $C^1$ splines over triangulationsPowell–Sabin splinesB-spline representationThe paper provides a generalization of $C^1$ quadratic splines over a Powell-Sabin refined triangulation to $C^1$ 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.20262026-03-18 08:05:19Članek v reviji180837sl