Computer Graphics Through OpenGL, 2nd Edition

Chapter 16

B-Spline

Our aim in this chapter is to master the theory underpinning B-spline primitives, the dominant class of primitives used in freeform design nowadays. As in the preceding chapter on Bézier theory, we’ll restrict ourselves here to the polynomial version, reserving the more general rational class of NURBS (Non-Uniform Rational B-Spline) primitives for Chapter 18, as an application of projective spaces, which are the natural setting for these primitives.

Almost all 3D modelers support NURBS primitives – and so, of course, their polynomial subclass as well – in a WYSIWYG design environment. In such a setting, the user can get by merely pushing control points around, with little understanding of theory. OpenGL, on the other ...