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＜電子ブック＞
Bézier and B-Spline Techniques / by Hartmut Prautzsch, Wolfgang Boehm, Marco Paluszny
(Mathematics and Visualization. ISSN:2197666X)

版	1st ed. 2002.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2002
本文言語	英語
大きさ	XIV, 304 p : online resource
著者標目	*Prautzsch, Hartmut author Boehm, Wolfgang author Paluszny, Marco author SpringerLink (Online service)
件　名	LCSH:Computer vision LCSH:Geometry LCSH:Computer-aided engineering LCSH:Computer graphics LCSH:Engineering mathematics LCSH:Engineering -- Data processing  全ての件名で検索 LCSH:Numerical analysis FREE:Computer Vision FREE:Geometry FREE:Computer-Aided Engineering (CAD, CAE) and Design FREE:Computer Graphics FREE:Mathematical and Computational Engineering Applications FREE:Numerical Analysis
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/978-3-662-04919-8

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