TABLE OF CONTENTS 
We shall now describe the main geometric features of this curve and surface representation. Much of the discussion of B-spline curves in Chapter 10 and B-spline surfaces in Chapter 12 applies to NURBS. This chapter focuses on the special features of NURBS. Surprisingly, most of these features are already exhibited by conics, which are a special case of NURBS.
Conic sections, the oldest known curve form, are still essential to many CAD systems. In fact, conics were used as the basis for the first "CAD" system: This was done by R. Liming [18] in 1944 he based the design of airplane fuselages upon calculating with conics, as opposed to the traditional drafting with conics.
A number of equivalent ways exist to define a conic section; for our purposes the following one is very useful: A conic section in IE 2 is the perspective projection of a parabola in IE 3.
When it comes to the formulation of conics as rational curves, one typically chooses the center of the projection to be the origin 0 of a 3D Cartesian coordinate system. The plane into which one projects is taken to be the plane z = 1. Since we will study planar curves in this section, we may think of this plane as a copy of IE 2. Our special projection is characterized by
Note that a point x is the projection of...
