Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable
Authors: Farouki, Rida T
Free Preview- A comprehensive and self-contained treatment
- Special features include an emphasis on the interplay of ideas from algebra and geometry and their historical origins
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- About this Textbook
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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
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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matter but also about the background material on algebra, geometry, and computer-aided geometric design, including historical references and quotes.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)
- Table of contents (31 chapters)
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Introduction
Pages 1-8
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Preamble
Pages 11-28
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Polynomials
Pages 29-43
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Complex Numbers
Pages 45-60
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Quaternions
Pages 61-77
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Table of contents (31 chapters)
- Download Sample pages 1 PDF (2.2 MB)
- Download Table of contents PDF (200.8 KB)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable
- Authors
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- Rida T Farouki
- Series Title
- Geometry and Computing
- Series Volume
- 1
- Copyright
- 2008
- Publisher
- Springer-Verlag Berlin Heidelberg
- Copyright Holder
- Springer-Verlag Berlin Heidelberg
- eBook ISBN
- 978-3-540-73398-0
- DOI
- 10.1007/978-3-540-73398-0
- Hardcover ISBN
- 978-3-540-73397-3
- Softcover ISBN
- 978-3-642-09243-5
- Series ISSN
- 1866-6795
- Edition Number
- 1
- Number of Pages
- XVI, 728
- Number of Illustrations
- 204 b/w illustrations
- Topics
