Chapter 1: Polynomial Curves

Advantages of NURBS Surfaces over B-Spline Surfaces

To make a long story short, the advantages of NURBS surfaces over B-spline surfaces are essentially the same as the advantages described in the curve chapters. A NURBS representation gives you more control over the surface in the form of weights for the control points. NURBS surfaces are also better formulated for creating shapes from conic sections. In this chapter, I concentrate more on sheets in order to introduce the material, but Chapter 10, "More NURBS Surfaces," will provide examples of where the ability to model conic sections provides the basis for simple models of some fundamental shapes.

Of course, one other advantage is simply that NURBS represent a superset of B-spline surfaces. Therefore, if you are going to implement B-spline surfaces, you might as well implement them in the form of NURBS. A NURBS system may require more computational overhead, but that might not be an issue if your geometry is fairly static.

This chapter and the next will demonstrate some of the types of shapes that are possible with NURBS surfaces. The samples in Chapter 10 are heavily dependent on conic sections, which are only possible with NURBS. In some ways, the advantages of NURBS are implicit in the examples in Chapter 10. However, before I can talk about those examples, I need to explain some of the basics.