Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable
Algebra and Geometry Inseparable
(Sprache: Englisch)
This book offers a comprehensive and self-contained treatment of the mathematical theory of Pythagorean-hodograph curves, including algorithms for their construction and examples of their practical applications.
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Produktinformationen zu „Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable “
This book offers a comprehensive and self-contained treatment of the mathematical theory of Pythagorean-hodograph curves, including algorithms for their construction and examples of their practical applications.
Klappentext zu „Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable “
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. It emphasizes the interplay of ideas from algebra and geometry and their historical origins and includes many figures, worked examples, and detailed algorithm descriptions.
Inhaltsverzeichnis zu „Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable “
Preface Chapter 1: Introduction PART I: ALGEBRA Chapter 2: PreambleChapter 3: PolynomialsChapter 4: Complex numbersChapter 5: QuaternionsChapter 6: Clifford algebra PART II: GEOMETRY Chapter 7: Coordinate systemsChapter 8: Differential geometryChapter 9: Algebraic geometryChapter 10: Non-Euclidean geometry PART III: COMPUTER-AIDED GEOMETRIC DESIGN Chapter 11: The Bernstein basisChapter 12: Numerical stabilityChapter 13: Bezier curves and surfacesChapter 14: C^2 cubic spline curvesChapter 15: Spline basis functions PART IV: PLANAR PYTHAGOREAN-HODOGRAPH CURVES Chapter 16: Arc-length parameterizationChapter 17: Pythagorean-hodograph curvesChapter 18: Tschirnhausen's cubicChapter 19: Complex representationChapter 20: Rational Pythagorean-hodograph curves PART V: SPATIAL PYTHAGOREAN-HODOGRAPH CURVES Chapter 21: Pythagorean hodographs in R^3Chapter 22: Quaternion representationChapter 23: Helical polynomial curvesChapter 24: Minkowski Pythagorean hodographs PART VI: ALGORITHMSChapter 25: Planar Hermite interpolantsChapter 26: Elastic bending energyChapter 27: Planar C^2 PH quintic splinesChapter 28: Spatial Hermite interpolants PART VII: APPLICATIONS Chapter 29: Real-time CNC interpolatorsChapter 30: Rotation-minimizing frames Chapter 31: Closure References Index
Bibliographische Angaben
- Autor: Rida T. Farouki
- 2008, 2008, 728 Seiten, mit Abbildungen, Masse: 16 x 24,1 cm, Gebunden, Englisch
- Verlag: Springer
- ISBN-10: 3540733973
- ISBN-13: 9783540733973
- Erscheinungsdatum: 11.10.2007
Sprache:
Englisch
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