Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable [Hardcover]

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.

Algebra.- Preamble.- Polynomials.- Complex Numbers.- Quaternions.- Clifford Algebra.- Geometry.- Coordinate Systems.- Differential Geometry.- Algebraic Geometry.- NonEuclidean Geometry.- Computer Aided Geometric Design.- The Bernstein Basis.- Numerical Stability.- B?zier Curves and Surfaces.- C2 Cubic Spline Curves.- Spline Basis Functions.- Planar Pythagorean-hodograph Curves.- Arclength Parameterization.- Pythagoreanhodograph 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.- Realtime CNC Interpolators.- Rotationminimizing Frames.- Closure.

From the reviews:

This book is a learned treatise on Pythagorean-Hodograph curves & . The book is very well written and contains a wealth of interesting information, not only about its main subject matter but also about the background material on algebra, geometry, and computer-aided geometric design, incl£É