Author(s)

E. Santoro

Abstract

Investigating the Eulerian numbers and uniform B-spline recurrence relations, a connection between Eulerian numbers and B-spline values at knot points is proved, and a relation to inner products of uniform B-splines is shown. This connection allows, with few operations, to evaluate the B-spline curve at domain knots and could be utilized to obtain an easy approximation and representation of B-spline curves. 1 Introduction The mathematical properties of B-spline functions and their applications have beeen be the subject of increasing interest in recent years[2]. They appear not only in CAGD (Computer Aided Geometric Design) but also in certain application areas such as probability [8] and approximation theories. Schoenberg [9] was the first to introduce the B-spline for approximating equidistant d

Keywords