Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable

Softcover Nachdruck of hardcover 1. Auflage 2008
ISBN: 978-3-642-09243-5
Verlag: Springer

Buch, Englisch, Band 1, 728 Seiten, Paperback, Format (B × H): 155 mm x 235 mm, Gewicht: 1112 g

Reihe: Geometry and Computing

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.

Zielgruppe

Research

Autoren/Hrsg.

Farouki, Rida T

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik
• Mathematik | Informatik EDV | Informatik Professionelle Anwendung Computer-Aided Design (CAD)

Inhaltsverzeichnis

Algebra.- Preamble.- Polynomials.- Complex Numbers.- Quaternions.- Clifford Algebra.- Geometry.- Coordinate Systems.- Differential Geometry.- Algebraic Geometry.- Non—Euclidean Geometry.- Computer Aided Geometric Design.- The Bernstein Basis.- Numerical Stability.- Bézier Curves and Surfaces.- C2 Cubic Spline Curves.- Spline Basis Functions.- Planar Pythagorean-hodograph Curves.- Arc—length Parameterization.- Pythagorean—hodograph 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.- Real—time CNC Interpolators.- Rotation—minimizing Frames.- Closure.