On the Theorem of Curry Schoenberg and the Relation between B-Spline and Box-Spline Functions

摘要

The work has three sections. Section 1 deals with one theorem of Curry and Schoenberg, defines the B-Spline function and gives the formula of computing the coefficients in B-Spline written as a sum of truncated powers of degree m. Section 2 contains the B-Spline for equidistant knots and an algorithm based on the truncated powers. Section 3 shows a relation between B-Spline and Box-Spline [1].