## Book description

Introduced 160 years ago as an attempt to generalize complex numbers to higher dimensions, quaternions are now recognized as one of the most important concepts in modern computer graphics. They offer a powerful way to represent rotations and compared to rotation matrices they use less memory, compose faster, and are naturally suited for efficient interpolation of rotations. Despite this, many practitioners have avoided quaternions because of the mathematics used to understand them, hoping that some day a more intuitive description will be available.
The wait is over. Andrew Hanson's new book is a fresh perspective on quaternions. The first part of the book focuses on visualizing quaternions to provide the intuition necessary to use them, and includes many illustrative examples to motivate why they are important—a beautiful introduction to those wanting to explore quaternions unencumbered by their mathematical aspects. The second part covers the all-important advanced applications, including quaternion curves, surfaces, and volumes. Finally, for those wanting the full story of the mathematics behind quaternions, there is a gentle introduction to their four-dimensional nature and to Clifford Algebras, the all-encompassing framework for vectors and quaternions.

* Richly illustrated introduction for the developer, scientist, engineer, or student in computer graphics, visualization, or entertainment computing.
* Covers both non-mathematical and mathematical approaches to quaternions.
* Companion website with an assortment of quaternion utilities and sample code, data sets for the book's illustrations, and Mathematica notebooks with essential algebraic utilities.

1. Front Cover (1/2)
2. Front Cover (2/2)
3. Visualizing Quaternions
5. Contents
7. Foreword
8. Preface (1/2)
9. Preface (2/2)
10. Acknowledgments
11. Part I: Elements of Quaternions
1. Chapter 1. The Discovery of Quaternions
2. Chapter 2. Folklore of Rotations
3. Chapter 3. Basic Notation
4. Chapter 4. What are Quaternions?
5. Chapter 5. Road Map to Quaternion Visualization
6. Chapter 6. Fundamentals of Rotations
7. Chapter 7. Visualizing Algebraic Structure
8. Chapter 8. Visualizing Spheres
9. Chapter 9. Visualizing Logarithms and Exponentials
10. Chapter 10. Visualizing Interpolation Methods
11. Chapter 11. Looking at Elementary Quaternion Frames
12. Chapter 12. Quaternions and the Belt Trick: Connecting to the Identity
13. Chapter 13. Quaternions and the Rolling Ball: Exploiting Order Dependence
14. Chapter 14. Quaternions and Gimbal Lock: Limiting the Available Space
12. Part II: Advanced Quaternion Topics
1. Chapter 15. Alternative Ways of Writing Quaternions
2. Chapter 16. Efficiency and Complexity Issues
3. Chapter 17. Advanced Sphere Visualization
4. Chapter 18. More on Logarithms and Exponentials
5. Chapter 19. Two-Dimensional Curves
6. Chapter 20. Three-Dimensional Curves
7. Chapter 21. 3D Surfaces
8. Chapter 22. Optimal Quaternion Frames
9. Chapter 23. Quaternion Volumes
10. Chapter 24. Quaternion Maps of Streamlines
11. Chapter 25. Quaternion Interpolation
12. Chapter 26. Quaternion Rotator Dynamics
13. Chapter 27. Concepts of the Rotation Group
14. Chapter 28. Spherical Riemannian Geometry
13. Part III: Beyond Quaternions
1. Chapter 29. The Relationship of 4D Rotations to Quaternions
2. Chapter 30. Quaternions and the Four Division Algebras
3. Chapter 31. Clifford Algebras
4. Chapter 32. Conclusions
14. Appendices
1. A. Notation
2. B. 2D Complex Frames
3. C. 3D Quaternion Frames
4. D. Frame and Surface Evolution
5. E. Quaternion Survival Kit (1/2)
6. E. Quaternion Survival Kit (2/2)
7. F. Quaternion Methods
8. G. Quaternion Path Optimization Using Surface Evolver
9. H. Quaternion Frame Integration
10. I. Hyperspherical Geometry
15. References (1/4)
16. References (2/4)
17. References (3/4)
18. References (4/4)
19. Index (1/3)
20. Index (2/3)
21. Index (3/3)

## Product information

• Title: Visualizing Quaternions
• Author(s): Andrew J. Hanson
• Release date: February 2006
• Publisher(s): Elsevier Science
• ISBN: None