NURBS (Non-Uniform Rational B-Splines) have become the de facto standard for geometric definitions in CAD/CAM and computer graphics. This well-known book covers NURBS from their geometric beginnings to their industrial applications. The second edition incorporates new research results and a chapter on Pythagorean curves, a development that shows promise in applications such as NC machining or robot motion control. More than fifty new figures have been added.