A truly unique book that focuses on the essence of geometric modeling and treats it as a discipline in its own right, this new edition is a comprehensive, up-to-date presentation of the core concepts of geometric modeling, with new material added to its coverage of the mathematics of curves, surfaces, and solids. As with the two previous editions, it emphasizes clarity and thoroughness in the mathematical development of the subject and is written in a style that is free of the jargon of special applications. Its emphasis on fundamentals prepares the reader for more advanced mathematical topics, such as 3D modeling, CAD/CAM, animation, and scientific visualization. References are incorporated throughout the text to direct the reader to more specialized treatments of the subject.