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© 2008

Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable

Textbook

Part of the Geometry and Computing book series (GC, volume 1)

Table of contents

  1. Front Matter
    Pages I-XVI
  2. Algebra

    1. Pages 1-8
    2. Pages 11-28
    3. Pages 29-43
    4. Pages 45-60
    5. Pages 61-77
    6. Pages 79-86
  3. Geometry

    1. Pages 89-129
    2. Pages 131-196
    3. Pages 197-230
    4. Pages 231-246
  4. Computer Aided Geometric Design

    1. Pages 249-260
    2. Pages 261-293
    3. Pages 323-343
    4. Pages 345-366
  5. Planar Pythagorean-hodograph Curves

About this book

Introduction

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

Authors and affiliations

  1. 1.Department of Mechanical and Aeronautical EngineeringUniversity of CaliforniaDavisUSA

Bibliographic information

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matter but also about the background material on algebra, geometry, and computer-aided geometric design, including historical references and quotes.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)