Dual Quaternions and Their Associated Clifford Algebras
Clifford algebra for dual quaternions has emerged recently as an alternative to standard matrix algebra as a computational framework for computer graphics. This book presents dual quaternions and their associated Clifford algebras in a new light, accessible to and geared toward the computer graphics community.
Collecting all the associated formulas and theorems in one place, this book provides an extensive and rigorous treatment of dual quaternions, as well as showing how two models of Clifford algebra emerge naturally from the theory of dual quaternions. Each section comes complete with a set of exercises to help readers sharpen and practice their understanding.
This book is accessible to anyone with a basic knowledge of quaternion algebra and is of particular use to forward-thinking members of the computer graphics community.
Part I. Dual Quaternions
1.1. Algebras and Dual Algebras
1.4. Rigid Motions
1.5. Rigid Motions as Rotations in 8-Dimensions
1.6. Screw Linear Interpolation (ScLERP)
1.7. Perspective and Pseudo-Perspective
1.8. Visualizing Quaternions and Dual Quaternions
1.9. Matrices versus Dual Quaternions
Part II. Clifford Algebras for Dual Quaternions
1. A Brief Review of Clifford Algebra
2. The Plane Model of Clifford Algebra for Dual Quaternions
3. The Point Model of Clifford Algebra for Dual Quaternions