VISUALIZING QUATERNIONS.

• PART I ELEMENTS OF QUATERNIONS
01 THE DISCOVERY OF QUATERNIONS
02 FOLKLORE OF ROTATIONS
03 BASIC NOTATION
04 WHAT ARE QUATERNIONS?
05 ROAD MAP TO QUATERNION VISUALIZATION
06 FUNDAMENTALS OF ROTATIONS
07 VISUALIZING ALGEBRAIC STRUCTURE
08 VISUALIZING SPHERES
09 VISUALIZING LOGARITHMS AND EXPONENTIALS
10 VISUALIZING INTERPOLATION METHODS
11 LOOKING AT ELEMENTARY QUATERNION FRAMES
12 QUATERNIONS AND THE BELT TRICK: CONNECTING TO THE IDENTITY
13 QUATERNIONS AND THE ROLLING BALL: EXPLOITING ORDER DEPENDENCE
• PART II ADVANCED QUATERNION TOPICS
15 ALTERNATIVE WAYS OF WRITING QUATERNIONS
16 EFFICIENCY AND COMPLEXITY ISSUES
17 ADVANCED SPHERE VISUALIZATION
18 MORE ON LOGARITHMS AND EXPONENTIALS
19 TWO-DIMENSIONAL CURVES
20 THREE-DIMENSIONAL CURVES
21 3D SURFACES
22 OPTIMAL QUATERNION FRAMES
23 QUATERNION VOLUMES
24 QUATERNION MAPS OF STREAMLINES
25 QUATERNION INTERPOLATION
26 QUATERNION ROTATOR DYNAMICS
27 CONCEPTS OF THE ROTATION GROUP
28 SPHERICAL RIEMANNIAN GEOMETRY
• PART III BEYOND QUATERNIONS
29 THE RELATIONSHIP OF 4D ROTATIONS TO QUATERNIONS
30 QUATERNIONS AND THE FOUR DIVISION ALGEBRAS
31 CLIFFORD ALGEBRAS
32 CONCLUSIONS

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.

Features:
• 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.

Author
Andrew J. Hanson, Indiana University, Bloomington, U.S.A.