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

Wolfgang Dahmen, Charles A. Micchelli, Hans-Peter Seidel
1992 Mathematics of Computation  
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
more » ... uced here seems to offer possibilities for economizing the computation for evaluating linear combinations of B-splines.
doi:10.1090/s0025-5718-1992-1134724-1 fatcat:pqlgmcaokjetrh7f3xtlf6pkty