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＜電子ブック＞
Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable / by Rida T Farouki
(Geometry and Computing. ISSN:18666809 ; 1)

版	1st ed. 2008.
出版者	Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
出版年	2008
本文言語	英語
大きさ	XVI, 728 p. 204 illus : online resource
著者標目	*Farouki, Rida T author SpringerLink (Online service)
件　名	LCSH:Geometry LCSH:Computer-aided engineering LCSH:Mathematics -- Data processing  全ての件名で検索 LCSH:Algebra LCSH:Image processing -- Digital techniques  全ての件名で検索 LCSH:Computer vision LCSH:Computational intelligence FREE:Geometry FREE:Computer-Aided Engineering (CAD, CAE) and Design FREE:Computational Mathematics and Numerical Analysis FREE:Algebra FREE:Computer Imaging, Vision, Pattern Recognition and Graphics FREE:Computational Intelligence
一般注記	Algebra -- Preamble -- Polynomials -- Complex Numbers -- Quaternions -- Clifford Algebra -- Geometry -- Coordinate Systems -- Differential Geometry -- Algebraic Geometry -- Non—Euclidean Geometry -- Computer Aided Geometric Design -- The Bernstein Basis -- Numerical Stability -- Bézier Curves and Surfaces -- C2 Cubic Spline Curves -- Spline Basis Functions -- Planar Pythagorean-hodograph Curves -- Arc—length Parameterization -- Pythagorean—hodograph Curves -- Tschirnhausen's Cubic -- Complex Representation -- Rational Pythagorean-hodograph Curves -- Spatial Pythagorean-hodograph Curves -- Pythagorean Hodographs in ?3 -- Quaternion Representation -- Helical Polynomial Curves -- Minkowski Pythagorean Hodographs -- Algorithms -- Planar Hermite Interpolants -- Elastic Bending Energy -- Planar C2 PH Quintic Splines -- Spatial Hermite Interpolants -- Applications -- Real—time CNC Interpolators -- Rotation—minimizing Frames -- Closure By virtue of their special algebraic structures, Pythagorean-hodograph (PH) curves offer unique advantages for computer-aided design and manufacturing, robotics, motion control, path planning, computer graphics, animation, and related fields. This book offers a comprehensive and self-contained treatment of the mathematical theory of PH curves, including algorithms for their construction and examples of their practical applications. Special features include an emphasis on the interplay of ideas from algebra and geometry and their historical origins, detailed algorithm descriptions, and many figures and worked examples. The book may appeal, in whole or in part, to mathematicians, computer scientists, and engineers HTTP:URL=https://doi.org/10.1007/978-3-540-73398-0

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