The Location of the Control Points in the Case of Box Splines

In this paper a theorem of Greville (1967) for univariate splinesis carried over to multivariate box splines; namely, it is shownhow the vector-valued function s(x)=x can expressed in termsof some translates of a box spline. The result means that thegraph of a spline function s(x), which is given as a linearcombination of box splines, can be viewed as a parametric splinesurface. The control points of the graph are explicitly given.