Bézier and B-Spline Techniques

1. Auflage. Softcover version of original hardcover Auflage 2002
ISBN: 978-3-642-07842-2
Verlag: Springer

Buch, Englisch, 304 Seiten, Paperback, Format (B × H): 155 mm x 235 mm, Gewicht: 487 g

Reihe: Mathematics and Visualization

Computer-aided modeling techniques have been developed since the advent of NC milling machines in the late 40's. Since the early 60's Bezier and B­ spline 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 Bezier and B-spline representations and 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 ex­ cluded. In particular, rational Bezier and B-spline techniques are not ad­ dressed since a rigorous treatment within the appropriate context of projec­ tive geometry would have been beyond the scope of this book.

Zielgruppe

Professional/practitioner

Autoren/Hrsg.

Prautzsch, Hartmut

Paluszny, Marco

Boehm, Wolfgang

Fachgebiete

• Mathematik | Informatik EDV | Informatik Professionelle Anwendung Computer-Aided Design (CAD)
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen
• Mathematik | Informatik EDV | Informatik Angewandte Informatik Computeranwendungen in Wissenschaft & Technologie
• Technische Wissenschaften Sonstige Technologien | Angewandte Technik Signalverarbeitung, Bildverarbeitung, Scanning
• Mathematik | Informatik EDV | Informatik Programmierung | Softwareentwicklung Grafikprogrammierung
• Mathematik | Informatik EDV | Informatik Informatik Bildsignalverarbeitung

Inhaltsverzeichnis

1 Geometric fundamentals.- 2 Bézier representation.- 3 Bézier techniques.- 4 Interpolation and approximation.- 5 B-spline representation.- 6 B-spline techniques.- 7 Smooth curves.- 8 Uniform subdivision.- 9 Tensor product surfaces.- 10 Bézier representation of triangular patches.- 11 Bézier techniques for triangular patches.- 12 Interpolation.- 13 Constructing smooth surfaces.- 14 Gk-constructions.- 15 Stationary subdivision for regular nets.- 16 Stationary subdivision for arbitrary nets.- 17 Box splines.- 18 Simplex splines.- 19 Multivariate splines.- References.