Название: Dual Quaternions and Their Associated Clifford Algebras
Автор: Ronald Goldman
Издательство: CRC Press
Год: 2024
Страниц: 279
Язык: английский
Формат: pdf (true)
Размер: 10.1 MB

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.

Dual quaternions are much more powerful, yet much more obscure than classical quaternions. Quaternions were introduced by Hamilton to model rotations in 3-dimensions; dual quaternions were introduced by Clifford to model rigid motions – translations and rotations —in 3 dimensions. Quaternion multiplication can be used to compute rotations, reflections, and perspective projections in 3-dimensions; dual quaternion multiplication can be used to compute translations as well as rotations and reflections along with perspective projections in 3-dimensions. Quaternions are vectors in 4-dimensions; dual quaternions are vectors in 8-dimensions. Quaternions can be represented by a pair of complex numbers; dual quaternions can be represented by a pair of quaternions.

Thus dual quaternions are both more powerful and more complicated than quaternions. These two factors are motivation enough for an extended rigorous study of dual quaternions. Moreover, recently several authors have suggested that a Clifford algebra for dual quaternions is a more suitable framework for computer graphics than standard matrix algebra. These claims too motivate a renewed interest in dual quaternions and their associated Clifford algebras.

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.