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Titlebook: Bézier and B-Spline Techniques; Hartmut Prautzsch,Wolfgang Boehm,Marco Paluszny Textbook 2002 Springer-Verlag Berlin Heidelberg 2002 B-spl

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期刊全称Bézier and B-Spline Techniques
影响因子2023Hartmut Prautzsch,Wolfgang Boehm,Marco Paluszny
视频video
发行地址Modern, graduate-level book on computer aided geometric design.Includes supplementary material:
学科分类Mathematics and Visualization
图书封面Titlebook: Bézier and B-Spline Techniques;  Hartmut Prautzsch,Wolfgang Boehm,Marco Paluszny Textbook 2002 Springer-Verlag Berlin Heidelberg 2002 B-spl
影响因子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.
Pindex Textbook 2002
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Smooth curvesenerally, a curve is said to be .. if it has an r times continuously differentiate parametrization. An even more general smoothness concept is based on the continuity of higher order geometric invariants. Piecewise polynomial curves with this general smoothness can be nicely studied using a geometri
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Tensor product surfacescontrol curves control the surface. The surface representation by these control points has properties analogous to those of a univariate curve (e.g., Bézier or B-spline) representation. This is due to the fact that one can deal with these surfaces by applying just curve algorithms. Similarly, one ca
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Bézier representation of triangular patchesrty, basically all properties of the Bézier representation of curves have a surface equivalent. The Bézier representation over triangles can be generalized further to Bézier representations over multi-dimensional simplices, see Chapter 19.
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Stationary subdivision for arbitrary netsk presented a similar generalization for bicubic splines. Their algorithms can be applied to arbitrary quadrilateral control nets and yield sequences of control nets that converge to piecewise biquadratic or bicubic surfaces with finitely many so-called extraordinary points.
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