Calculating with box splines (Q1083172)

Box splines are multivariate splines over regular grids. Two recursion formulas for box splines are developed: (1) a Mansfield-de Boor-like expression of box splines as linear combinations of box splines of lower degree and (2) a de Boor-like reduction of the net of box spline control points. The ideas follow those from C. \textit{de Boor} [J. Approximation Theory 6, 50-62 (1972; Zbl 0239.41006)]. The proofs are geometrical and simple.