Bézier and B-Spline Techniques [book]

Hartmut Prautzsch, Wolfgang Boehm, Marco Paluszny
2002 Mathematics and Visualization  
Preface Computer-aided modeling techniques have been developed since the advent of NC milling machines in the late 40's. Since the early 60's Bézier and Bspline representations evolved as the major tool to handle curves and surfaces. These representations are geometrically intuitive and meaningful and they lead to constructive numerically robust algorithms. It is the purpose of this book to provide a solid and unified derivation of the various properties of Bézier and B-spline representations
more » ... d to show the beauty of the underlying rich mathematical structure. The book focuses on the core concepts of Computer-aided Geometric Design (CAGD) with the intent to provide a clear and illustrative presentation of the basic principles as well as a treatment of advanced material, including multivariate splines, some subdivision techniques and constructions of arbitrarily smooth free-form surfaces. In order to keep the book focused, many further CAGD methods are excluded. In particular, rational Bézier and B-spline techniques are not addressed since a rigorous treatment within the appropriate context of projective geometry would have been beyond the scope of this book. The book grew out of several courses taught repeatedly at the graduate and intermediate under-graduate levels by the authors at the Rensselaer Polytechnic Institute, USA, the Universities of Braunschweig and Karlsruhe, Germany, and the Universidad Central de Venezuela. These courses were taught as part of the curricula in mathematics and computer sciences, and they were regularly attended also by students from electrical and mechanical engineering, geophysics and other sciences. For the careful proofreading of parts of the manuscript, we like to thank
doi:10.1007/978-3-662-04919-8 fatcat:lqdxh5ga2vdmrjls67tfhr5gza