B-Splines without Divided Differences. Page 1 A-13762 9-SPLINES WITHOUT DIVIDED DIF;ERENCES(U)
WISCONSIN v/1 UNIV-MRDISON MATHEMATICS RESEARCH CENTER C DE BOOR ET …

This essay reviews those basic facts about (univariate) B-splines which are of interest in
CAGD. The intent is to give a self-contained and complete development of the material in as …

The concept of symmetric recursive algorithm leads to new, s-dimensional spline spaces.
We present a general scheme for constructing a collection of multivariate B-splines with $ k …

Multi-degree splines are smooth piecewise-polynomial functions where the pieces can have
different degrees. We describe a simple algorithmic construction of a set of basis functions …

In this paper it is shown how the algebraic product of two spline functions, each represented
in terms of B-splines, can again be represented as a linear combination of suitable B …

B-splines are constructed from Bézier curves solely using de Casteljau's construction.
Divided differences are not being used, nor is Mansfield's recurrence formula presupposed …

Direct and recursive algorithms are proposed for constructing generalized cubic B-splines.
Explicit formulae are obtained for generalized B-splines. Properties of series consisting of B …

A recurrence relation for chebyshevian <Emphasis Type="Italic">B </Emphasis>-splines Page
1 Constr. Approx. (1985) 1 : 155-173 CONSTRUCTIVE APPROXIMATION 9 1985 …

This paper outlines several ways to evaluate the integral of the product of two B-spline
functions, followed by a detailed description of an algorithm that is based on integration by …

In this first chapter, we consider the following fundamental problem: Given a set of points in
the plane, determine a smooth curve that approximates the points. The algorithm for …