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AuthorPrautzsch, Hartmut. author
TitleBรฉzier and B-Spline Techniques [electronic resource] / by Hartmut Prautzsch, Wolfgang Boehm, Marco Paluszny
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2002
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Descript XIV, 304 p. online resource


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 Bยญ 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 exยญ cluded. In particular, rational Bezier and B-spline techniques are not adยญ dressed since a rigorous treatment within the appropriate context of projecยญ tive geometry would have been beyond the scope of this book


1 Geometric fundamentals -- 2 Bรฉzier representation -- 3 Bรฉzier techniques -- 4 Interpolation and approximation -- 5 B-spline representation -- 6 B-spline techniques -- 7 Smooth curves -- 8 Uniform subdivision -- 9 Tensor product surfaces -- 10 Bรฉzier representation of triangular patches -- 11 Bรฉzier 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

Computer science Computer graphics Image processing Computer-aided engineering Numerical analysis Geometry Applied mathematics Engineering mathematics Computer Science Image Processing and Computer Vision Geometry Computer-Aided Engineering (CAD CAE) and Design Computer Graphics Appl.Mathematics/Computational Methods of Engineering Numerical Analysis


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