Representation Of Uniform B-spline Curve By Eulerian Numbers
Price
Free (open access)
Volume
15
Pages
8
Published
1995
Size
476 kb
Paper DOI
10.2495/VID950071
Copyright
WIT Press
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
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