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

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.