Quaternions for Computer Graphics

by John A. Vince

Sir William Rowan Hamilton was a genius, and will be remembered for his significant contributions to physics and mathematics. The Hamiltonian, which is used in quantum physics to describe the total energy of a system, would have been a major achievement for anyone, but Hamilton also invented quaternions, which paved the way for modern vector analysis. Quaternions are one of the most documented inventions in the history of mathematics, and this book is about their invention, and how they are used to rotate vectors about an arbitrary axis. Apart from introducing the reader to the features of quaternions and their associated algebra, the book provides valuable historical facts that bring the subject alive. Quaternions for Computer Graphics introduces the reader to quaternion algebra by describing concepts of sets, groups, fields and rings. It also includes chapters on imaginary quantities, complex numbers and the complex plane, which are essential to understanding quaternions. The book contains many illustrations and worked examples, which make it essential reading for students, academics, researchers and professional practitioners.

154 pages, Hardcover

First published January 1, 2011

Reviews

[Shaun Zhang · Rating 3 out of 5]

Very good introduction to quaternion, with history, detailed computations and explanations. Recommend for very beginners.

[Taneli · Rating 4 out of 5]

This is a great short read. It introduces quaternions and (as a requirement for understanding the former) complex numbers in an easy-to-understand style. This is however not a proper mathematical book, as it lacks rigorous proofs for its rules, and it is also not a programming book, since it includes no talk about how to implement quaternions and their calculations in programs. The previous sentence explains why I like this as a light(ish) read and a great introduction to the subject.