TABLE OF CONTENTS NURBS is short for " Non- Uniform Rational B-splines. This is a somewhat unlucky naming convention, since B-splines are non-uniform to begin with. We give an outline of B-spline curves in 
there, nothing is rational but rather piecewise polynomial. The "rational" part, as usual, comes when we project into affine space.
A B-spline curve is a curve consisting of several polynomial pieces (the segments, much like the conic splines in 
from Chapter 6). The main difference is that now we do not restrict the degree the only stipulation is that all segments be of the same degree. We will develop an algorithm for these curves the de Boor algorithm that is the analogue to the de Casteljau algorithm for B zier curves.
A B-spline curve is defined by the degree n of each of its polynomial pieces (the segments), and by the number L of segments. Also needed is the domain of the curve, which is a partition of part of the real line into L intervals. This partition is a nondecreasing sequence of knots u i As a parameter u traces out the domain, the corresponding point d( u) on the B-spline curve traces out a piecewise polynomial curve, defined by a set of control points d i. The smoothness of this curve depends on the precise makeup of the knot sequence.
The most basic operation...
