Blossoming Begets ß-spline Bases Built Better by ß-patches

The concept of symmetric recursive algorithm leads to new, sdimensional spline spaces. We present a general scheme for constructing a collection of multivariate S-splines with k-l continuous derivatives whose linear span contains all polynomials of degree at most k . This scheme is different from the one developed earlier by Dahmen and Micchelli and, independently, by Höllig, which was based on combinatorial principles and the geometric interpretation of the ß-spline. The new spline space introduced here seems to offer possibilities for economizing the computation for evaluating linear combinations of B-splines.