TABLE OF CONTENTS 
Compared with composite B zier curves, a more complete theory of splines is found in B-spline curves. These days, B-spline curves are often referred to as NURBS (NonUniform Rational B-Splines), which are treated in some length in Chapter 13.
A B zier curve is defined by
The properties of a B zier curve are determined by its basis functions B n i. Each Bernstein basis function is a polynomial function. B-spline curves are defined by more flexible, piecewise polynomial basis functions called B-splines, and give rise to a more general curve method. A B-spline curve is expressed as
The N n i are the degree n B-splines. The precise definition of these piecewise polynomial functions is given in Section 10.5. The d i are called de Boor points or simply control points.
Let's start with a practical introduction. Figure 10.2 illustrates a variety of cubic B-spline curves. The squares are de Boor points, and the ends of each polynomial curve segment are marked with solid circles. As you can see, the B-spline polygon, formed by the de Boor points, allows for a construction of several polynomial segments. The continuity between pieces can be varied. All of the B-spline polygons are identical; the discussion below will clarify how we get differently shaped curves.
A degree n B-spline curve is defined by a control polygon
similar to a B zier curve. Because a B-spline curve...
