Pythagorean-Hodograph Curves Algebra and Geometry Inseparable [Paperback]

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.

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.

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.

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: lÓ'