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Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable
Buch von Rida T Farouki
Sprache: Englisch

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Beschreibung
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.
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.
Zusammenfassung

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.

Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 2007
Fachbereich: Wahrscheinlichkeitstheorie
Genre: Mathematik, Medizin, Naturwissenschaften, Technik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Inhalt: xvi
728 S.
204 s/w Illustr.
728 p. 204 illus.
ISBN-13: 9783540733973
ISBN-10: 3540733973
Sprache: Englisch
Herstellernummer: 12081448
Einband: Gebunden
Autor: Farouki, Rida T
Hersteller: Springer-Verlag GmbH
Springer Berlin Heidelberg
Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße: 241 x 160 x 45 mm
Von/Mit: Rida T Farouki
Erscheinungsdatum: 11.10.2007
Gewicht: 1,273 kg
Artikel-ID: 101980543
Zusammenfassung

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.

Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 2007
Fachbereich: Wahrscheinlichkeitstheorie
Genre: Mathematik, Medizin, Naturwissenschaften, Technik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Inhalt: xvi
728 S.
204 s/w Illustr.
728 p. 204 illus.
ISBN-13: 9783540733973
ISBN-10: 3540733973
Sprache: Englisch
Herstellernummer: 12081448
Einband: Gebunden
Autor: Farouki, Rida T
Hersteller: Springer-Verlag GmbH
Springer Berlin Heidelberg
Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße: 241 x 160 x 45 mm
Von/Mit: Rida T Farouki
Erscheinungsdatum: 11.10.2007
Gewicht: 1,273 kg
Artikel-ID: 101980543
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