Geometric Algebra: An Algebraic System for Computer Games and Animation

Geometric algebra is still treated as an obscure branch of algebra and most books have been written by competent mathematicians in a very abstract style. This restricts the readership of such books especially by programmers working in computer graphics, who simply want guidance on algorithm design.

Geometric algebra provides a unified algebraic system for solving a wide variety of geometric problems. John Vince reveals the beauty of this algebraic framework and communicates to the reader new and unusual mathematical concepts using colour illustrations, tabulations, and easy-to-follow algebraic proofs.

The book includes many worked examples to show how the algebra works in practice and is essential reading for anyone involved in designing 3D geometric algorithms.

From the reviews:

“Geometric algebra (GA), a truly fascinating area of mathematics, provides a powerful, unified language of exceptional clarity and generality to describe one-, two-, three-, and higher-dimensional geometries. … This book’s outstanding feature is the use of tables and colors to develop some arithmetical details. … The book is better suited for self-study than for the classroom. I recommend it for upper-level undergraduates, graduate students, teachers, researchers, and technical libraries.” (Edgar R. Chavez, ACM Computing Reviews, December, 2009)

“In the current volume, the author simplifies the presentation based on some of his new ideas on the subject. … The volume is self-contained and can be used by students and computer graphics professionals. … a good course in linear algebra and some mathematical maturity. Summing Up: Recommended. Computer graphics, computer animation, and computer games collections for upper-division undergraduates, graduate students, and professionals.” (D. Z. Spicer, Choice, Vol. 47 (7), March, 2010)

“Geometric algebra is a topic of current interest in mathematical research and in applications in physics, engineering, and computer science … . the book is directed to a computer programming audience. … this accessible, introductory book may convince some computer graphics programmers of the usefulness of geometric algebra … .” (Adam Coffman, Mathematical Reviews, Issue 2011 i)

“The book’s true value lies in describing important geometric transformations like reflection and rotation in a systematic way, and in listing many geometric primitives … . For people working in computer graphics or in game design, these topics could be of considerable value, and they certainly justify the book’s title.” (Rolf Klein, Zentralblatt MATH, Vol. 1226, 2012)