A normalized representation of super splines of arbitrary degree on Powell-Sabin triangulations

In the paper, a family of bivariate super spline spaces of arbitrary degree defined on a triangulation with Powell-Sabin refinement is introduced. It includes known spaces of arbitrary smoothness r and degree but provides also other choices of spline degree for the same r which, in particular, generalize a known space of cubic super splines. Minimal determining sets of the proposed super spline spaces of arbitrary degree are presented, and the interpolation problems that uniquely specify their elements are provided. Furthermore, a normalized representation of the discussed splines is considered. It is based on the definition of basis functions that have local supports, are nonnegative, and form a partition of unity. The basis functions share numerous similarities with classical univariate B-splines.