David F. Rogers 
Introduction to NURBS [PDF ebook] 
With Historical Perspective

The latest from a computer graphics pioneer, An Introduction to NURBS is the ideal resource for anyone seeking a theoretical and practical understanding of these very important curves and surfaces. Beginning with Bezier curves, the book develops a lucid explanation of NURBS curves, then does the same for surfaces, consistently stressing important shape design properties and the capabilities of each curve and surface type. Throughout, it relies heavily on illustrations and fully worked examples that will help you grasp key NURBS concepts and deftly apply them in your work. Supplementing the lucid, point-by-point instructions are illuminating accounts of the history of NURBS, written by some of its most prominent figures. Whether you write your own code or simply want deeper insight into how your computer graphics application works, An Introduction to NURBS will enhance and extend your knowledge to a degree unmatched by any other resource. Presents vital information with applications in many different areas: CAD, scientific visualization, animation, computer games, and more. Facilitates accessiblity to anyone with a knowledge of first-year undergraduate mathematics. Details specific NURBS-based techniques, including making cusps with B-spline curves and conic sections with rational B-spline curves. Presents all important algorithms in easy-to-read pseudocode-useful for both implementing them and understanding how they work. Includes complete references to additional NURBS resources.