Quaternions for Computer Graphics

1. Front Matter

   Pages i-xv

   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

    PDF

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.

• Computer Graphics
• Interpolating Quaternions
• Coding Quaternions
• Rotating with Quaternions
• Quaternions for Computer Graphics

• Bournemouth University, Poole, UK

  John Vince

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, computer science and virtual reality, including the following Springer titles:

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

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

• Imaginary Mathematics for Computer Science, (2018)

• Foundation Mathematics for Computer Science, 2^nd 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)