Overview
- Fantastic new textbook on mathematical background to computer-aided geometric design.
- Includes supplementary material: sn.pub/extras
Part of the book series: Geometry and Computing (GC, volume 1)
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Table of contents (31 chapters)
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Computer Aided Geometric Design
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Planar Pythagorean-hodograph Curves
Keywords
About this book
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.
Reviews
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matter but also about the background material on algebra, geometry, and computer-aided geometric design, including historical references and quotes.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)
Authors and Affiliations
Bibliographic Information
Book Title: Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable
Authors: Rida T. Farouki
Series Title: Geometry and Computing
DOI: https://doi.org/10.1007/978-3-540-73398-0
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2008
Hardcover ISBN: 978-3-540-73397-3Published: 11 October 2007
Softcover ISBN: 978-3-642-09243-5Published: 30 November 2010
eBook ISBN: 978-3-540-73398-0Published: 01 February 2008
Series ISSN: 1866-6795
Series E-ISSN: 1866-6809
Edition Number: 1
Number of Pages: XVI, 728
Number of Illustrations: 204 b/w illustrations
Topics: Geometry, Computer-Aided Engineering (CAD, CAE) and Design, Computational Mathematics and Numerical Analysis, Algebra, Computer Imaging, Vision, Pattern Recognition and Graphics, Computational Intelligence