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Cover: 9783642092435 | Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable | Buch
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Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable
Taschenbuch 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
Preface Chapter 1: Introduction PART I: ALGEBRA Chapter 2: Preamble
Chapter 3: Polynomials
Chapter 4: Complex numbers
Chapter 5: Quaternions
Chapter 6: Clifford algebra PART II: GEOMETRY Chapter 7: Coordinate systems
Chapter 8: Differential geometry
Chapter 9: Algebraic geometry
Chapter 10: Non-Euclidean geometry PART III: COMPUTER-AIDED GEOMETRIC DESIGN Chapter 11: The Bernstein basis
Chapter 12: Numerical stability
Chapter 13: Bezier curves and surfaces
Chapter 14: C^2 cubic spline curves
Chapter 15: Spline basis functions PART IV: PLANAR PYTHAGOREAN-HODOGRAPH CURVES Chapter 16: Arc-length parameterization
Chapter 17: Pythagorean-hodograph curves
Chapter 18: Tschirnhausen's cubic
Chapter 19: Complex representation
Chapter 20: Rational Pythagorean-hodograph curves PART V: SPATIAL PYTHAGOREAN-HODOGRAPH CURVES Chapter 21: Pythagorean hodographs in R^3
Chapter 22: Quaternion representation
Chapter 23: Helical polynomial curves
Chapter 24: Minkowski Pythagorean hodographs PART VI: ALGORITHMS Chapter 25: Planar Hermite interpolants
Chapter 26: Elastic bending energy
Chapter 27: Planar C^2 PH quintic splines
Chapter 28: Spatial Hermite interpolants PART VII: APPLICATIONS Chapter 29: Real-time CNC interpolators
Chapter 30: Rotation-minimizing frames Chapter 31: Closure References Index
Details
Erscheinungsjahr: 2010
Fachbereich: Geometrie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Reihe: Geometry and Computing
Inhalt: xvi
728 S.
204 s/w Illustr.
728 p. 204 illus.
ISBN-13: 9783642092435
ISBN-10: 3642092438
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Farouki, Rida T
Auflage: Softcover reprint of hardcover 1st ed. 2008
Hersteller: Springer-Verlag GmbH
Springer Berlin Heidelberg
Geometry and Computing
Maße: 235 x 155 x 40 mm
Von/Mit: Rida T Farouki
Erscheinungsdatum: 30.11.2010
Gewicht: 1,112 kg
Artikel-ID: 107175413
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
Preface Chapter 1: Introduction PART I: ALGEBRA Chapter 2: Preamble
Chapter 3: Polynomials
Chapter 4: Complex numbers
Chapter 5: Quaternions
Chapter 6: Clifford algebra PART II: GEOMETRY Chapter 7: Coordinate systems
Chapter 8: Differential geometry
Chapter 9: Algebraic geometry
Chapter 10: Non-Euclidean geometry PART III: COMPUTER-AIDED GEOMETRIC DESIGN Chapter 11: The Bernstein basis
Chapter 12: Numerical stability
Chapter 13: Bezier curves and surfaces
Chapter 14: C^2 cubic spline curves
Chapter 15: Spline basis functions PART IV: PLANAR PYTHAGOREAN-HODOGRAPH CURVES Chapter 16: Arc-length parameterization
Chapter 17: Pythagorean-hodograph curves
Chapter 18: Tschirnhausen's cubic
Chapter 19: Complex representation
Chapter 20: Rational Pythagorean-hodograph curves PART V: SPATIAL PYTHAGOREAN-HODOGRAPH CURVES Chapter 21: Pythagorean hodographs in R^3
Chapter 22: Quaternion representation
Chapter 23: Helical polynomial curves
Chapter 24: Minkowski Pythagorean hodographs PART VI: ALGORITHMS Chapter 25: Planar Hermite interpolants
Chapter 26: Elastic bending energy
Chapter 27: Planar C^2 PH quintic splines
Chapter 28: Spatial Hermite interpolants PART VII: APPLICATIONS Chapter 29: Real-time CNC interpolators
Chapter 30: Rotation-minimizing frames Chapter 31: Closure References Index
Details
Erscheinungsjahr: 2010
Fachbereich: Geometrie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Reihe: Geometry and Computing
Inhalt: xvi
728 S.
204 s/w Illustr.
728 p. 204 illus.
ISBN-13: 9783642092435
ISBN-10: 3642092438
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Farouki, Rida T
Auflage: Softcover reprint of hardcover 1st ed. 2008
Hersteller: Springer-Verlag GmbH
Springer Berlin Heidelberg
Geometry and Computing
Maße: 235 x 155 x 40 mm
Von/Mit: Rida T Farouki
Erscheinungsdatum: 30.11.2010
Gewicht: 1,112 kg
Artikel-ID: 107175413
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