Fast and exact evaluation of box splines via the PP-form

Abstract: For the class of non-degenerate box splines, we prove that these box splines are piecewise polynomial. This is not a new result, it is in fact a well known and useful property of box splines. However, our proof is constructive, and the main result of this work is a corollary that follows from this proof, namely one that gives an explicit construction scheme for the polynomial pieces in the interior regions of any non-degenerate box spline.