Blossoming begets 𝐵-spline bases built better by 𝐵-patches

Abstract

The concept of symmetric recursive algorithm leads to new, s -dimensional spline spaces. We present a general scheme for constructing a collection of multivariate B -splines with k − 1 k - 1 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 B -spline. The new spline space introduced here seems to offer possibilities for economizing the computation for evaluating linear combinations of B -splines.