A normalized representation of super splines of arbitrary degree on Powell-Sabin triangulations
The paper proposes a family of spline spaces of arbitrary degree \(d\) on Powell-Sabin triangulations, which extends the class of super spline spaces of arbitrary smoothness \(r\) and degree \(d=3r-1\) introduced by \textit{H. Speleers} [Constr. Approx. 37, No. 1, 41--72 (2013; Zbl 1264.41014)]. The new types of spline spaces studied in the paper are of degree \(d=3r-2\) and \(d=3r\) with global smoothness \(r-1\) and \(r\), respectively, and possess some additional super smoothness across certain edges of the Powell-Sabin partition. The paper also details the construction of normalized bases for the proposed family of spaces. It is proved that the resulting B-spline functions have local supports, are nonnegative, and form a partition of unity, which may serve as useful properties in future applications.
smooth splines on Powell-Sabin triangulations
scientific article; zbMATH DE number 6667563
scientific article