ABSTRACT

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|111 pages

Dual Quaternions

chapter 1.1|8 pages

Algebras and Dual Algebras

chapter 1.2|8 pages

Algebra

chapter 1.3|14 pages

Geometry

chapter 1.4|28 pages

Rigid Motions

chapter 1.5|4 pages

Rigid Motions as Rotations in 8-Dimensions

chapter 1.6|8 pages

Screw Linear Interpolation (ScLERP)

chapter 1.7|12 pages

Perspective and Pseudo-Perspective

chapter 1.8|5 pages

Visualizing Quaternions and Dual Quaternions

chapter 1.9|10 pages

Matrices versus Dual Quaternions

chapter 1.10|2 pages

Insights

chapter 1.11|9 pages

Formulas

part II|135 pages

Clifford Algebras for Dual Quaternions