Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable
Springer Berlin (Verlag)
978-3-642-09243-5 (ISBN)
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.- 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.
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matter but also about the background material on algebra, geometry, and computer-aided geometric design, including historical references and quotes. The prime audience for this book is students, researchers, and professionals working in computer-aided design and manufacturing, but anyone interested in mathematics, geometric modeling, or computer graphics and animation will learn much interesting mathematics from it." (Luiz Henrique de Figueiredo, MathDL, January, 2008)
"Pythagorean hodograph (PH) curves form a remarkable subclass of polynomial curves. ... This is the first book which gives a comprehensive introduction to this active field of research ... . The organization of the book is excellent. ... style and the flavour of the presentation make it a real pleasure to read this book. It can be expected that this book will contribute to the advancement of the field of PH ... . very suitable for use as a textbook for courses on applied geometry." (Bert Jüttler, Mathematical Reviews, Issue 2008 k)
| Erscheint lt. Verlag | 30.11.2010 |
|---|---|
| Reihe/Serie | Geometry and Computing |
| Zusatzinfo | XVI, 728 p. 204 illus. |
| Verlagsort | Berlin |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Gewicht | 1128 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik | |
| Technik ► Fahrzeugbau / Schiffbau | |
| Schlagworte | Algebra • algorithm • algorithms • Animation • augmented reality • Computer-Aided Design (CAD) • computer aided geometric design • Computer Graphics • Construction • geometrical algorithms • Geometry • Kurven • Pythagoras • Pythagorean-Hodograph curves • Robotics • stability |
| ISBN-10 | 3-642-09243-8 / 3642092438 |
| ISBN-13 | 978-3-642-09243-5 / 9783642092435 |
| Zustand | Neuware |
| Haben Sie eine Frage zum Produkt? |
aus dem Bereich
