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  • Textbook
  • © 2008

Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable

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  • 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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eBook
USD 69.99
Price excludes VAT (USA)
  • ISBN: 978-3-540-73398-0
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD 89.99
Price excludes VAT (USA)
Hardcover Book
USD 119.99
Price excludes VAT (USA)

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Table of contents (31 chapters)

  1. Front Matter

    Pages I-XVI
  2. Algebra

    1. Introduction

      Pages 1-8
    2. Preamble

      Pages 11-28
    3. Polynomials

      Pages 29-43
    4. Complex Numbers

      Pages 45-60
    5. Quaternions

      Pages 61-77
    6. Clifford Algebra

      Pages 79-86
  3. Geometry

    1. Coordinate Systems

      Pages 89-129
    2. Differential Geometry

      Pages 131-196
    3. Algebraic Geometry

      Pages 197-230
    4. Non—Euclidean Geometry

      Pages 231-246
  4. Computer Aided Geometric Design

    1. The Bernstein Basis

      Pages 249-260
    2. Numerical Stability

      Pages 261-293
    3. C2 Cubic Spline Curves

      Pages 323-343
    4. Spline Basis Functions

      Pages 345-366
  5. Planar Pythagorean-hodograph Curves

    1. Tschirnhausen's Cubic

      Pages 393-406
    2. Complex Representation

      Pages 407-425

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.

Keywords

  • Augmented Reality
  • algorithm
  • algorithms
  • animation
  • computer graphics
  • computer-aided design (CAD)
  • construction
  • robotics
  • stability

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

  • Department of Mechanical and Aeronautical Engineering, University of California, Davis, USA

    Rida T. Farouki

Bibliographic Information

Buying options

eBook
USD 69.99
Price excludes VAT (USA)
  • ISBN: 978-3-540-73398-0
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD 89.99
Price excludes VAT (USA)
Hardcover Book
USD 119.99
Price excludes VAT (USA)