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Quaternions for Computer Graphics

  • Textbook
  • © 2021

Overview

Authors:
  1. John Vince

    1. Bournemouth University, Poole, UK

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  • Describes quaternions as a progression from 2-D complex numbers to a 3-D transform for rotating points in space
  • Includes a variety of matrices that permit quaternions to be easily coded into a family of library functions
  • Relevant historical events show how quaternions led to the invention of modern vector analysis

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-xv
    Download chapter PDF

  2. Introduction

    • John Vince
    Pages 1-3

  3. Number Sets and Algebra

    • John Vince
    Pages 5-16

  4. Complex Numbers

    • John Vince
    Pages 17-53

  5. The Complex Plane

    • John Vince
    Pages 55-70

  6. Triples and Quaternions

    • John Vince
    Pages 71-75

  7. Quaternion Algebra

    • John Vince
    Pages 77-103

  8. 3-D Rotation Transforms

    • John Vince
    Pages 105-127

  9. Quaternions in Space

    • John Vince
    Pages 129-175

  10. Conclusion

    • John Vince
    Pages 177-178

  11. Back Matter

    Pages 179-181
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Keywords

About this book

If you have ever wondered what quaternions are — then look no further, John Vince will show you how simple and useful they are. This 2nd edition has been completely revised and includes extra detail on the invention of quaternions, a complete review of the text and equations, all figures are in colour, extra worked examples, an expanded index, and a bibliography arranged for each chapter.

Quaternions for Computer Graphics includes chapters on number sets and algebra, imaginary and complex numbers, the complex plane, rotation transforms, and a comprehensive description of quaternions in the context of rotation. The book will appeal to students of computer graphics, computer science and mathematics, as well as programmers, researchers, academics and professional practitioners interested in learning about quaternions.

John Vince explains in an easy-to-understand language, with the aid of useful figures, how quaternions emerged, gave birth to modern vector analysis, disappeared, and reemerged to be adopted by the flight simulation industry and computer graphics. This book will give you the confidence to use quaternions within your every-day mathematics, and explore more advanced texts.


Authors and Affiliations

  • Bournemouth University, Poole, UK

    John Vince

About the author

Professor John Vince began working in computer graphics at Middlesex Polytechnic in 1968. His research activities centered on computer animation software and resulted in the PICASO and PRISM animation systems. Whilst at Middlesex, he designed the UK’s first MSc course in Computer Graphics and developed a popular program of short courses in computer animation for television designers. In 1986 he joined Rediffusion Simulation as a Research Consultant and worked on the development of real-time computer systems for commercial flight simulators. In 1992 he was appointed Chief Scientist of Thomson Training Simulation Ltd. In 1995 he was appointed Professor of Digital Media at the National Centre for Computer Animation at Bournemouth University and in 1999 he was made Head of Academic Group for Computer Animation. He was awarded a DSc by Brunel University in recognition of his work in computer graphics. He has written and edited over 45 books on computer graphics, computer animation, computerscience and virtual reality, including the following Springer titles:

• Mathematics for Computer Graphics, 5th edition (2017)

• Calculus for Computer Graphics, 2nd edition (2019)

• Imaginary Mathematics for Computer Science, (2018)

• Foundation Mathematics for Computer Science, 2nd edition (2015)

• Matrix Transforms for Computer Games and Animation (2012)

• Expanding the Frontiers of Visual Analytics and Visualization (2012)

• Quaternions for Computer Graphics (2011)

• Rotation Transforms for Computer Graphics (2011)

• Geometric Algebra: An Algebraic System for Computer Animation and Games (2009)

• Geometric Algebra for Computer Graphics (2008)

Bibliographic Information

  • Book Title: Quaternions for Computer Graphics

  • Authors: John Vince

  • DOI: https://doi.org/10.1007/978-1-4471-7509-4

  • Publisher: Springer London

  • eBook Packages: Computer Science, Computer Science (R0)

  • Copyright Information: Springer-Verlag London Ltd., part of Springer Nature 2021

  • Hardcover ISBN: 978-1-4471-7508-7Published: 03 September 2021

  • Softcover ISBN: 978-1-4471-7511-7Published: 04 September 2022

  • eBook ISBN: 978-1-4471-7509-4Published: 02 September 2021

  • Edition Number: 2

  • Number of Pages: XV, 181

  • Number of Illustrations: 1 b/w illustrations, 40 illustrations in colour

  • Topics: Computer Graphics, Mathematical Logic and Foundations, Mathematical Applications in Computer Science

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