Geometric Algebra: An Algebraic System for Computer Games and Animation

  • Authors
  • John Vince

Table of contents

  1. Front Matter
    Pages i-xviii
  2. Pages 1-3
  3. Pages 5-11
  4. Pages 13-32
  5. Pages 33-47
  6. Pages 49-64
  7. Pages 65-74
  8. Pages 75-101
  9. Pages 183-183
  10. Back Matter
    Pages 185-195

About this book

Introduction

The true power of vectors has never been exploited, for over a century, mathematicians, engineers, scientists, and more recently programmers, have been using vectors to solve an extraordinary range of problems. However, today, we can discover the true potential of oriented, lines, planes and volumes in the form of geometric algebra. As such geometric elements are central to the world of computer games and computer animation, geometric algebra offers programmers new ways of solving old problems.

John Vince (best-selling author of a number of books including Geometry for Computer Graphics, Vector Analysis for Computer Graphics and Geometric Algebra for Computer Graphics) provides new insights into geometric algebra and its application to computer games and animation.

The first two chapters review the products for real, complex and quaternion structures, and any non-commutative qualities that they possess. Chapter three reviews the familiar scalar and vector products and introduces the idea of ‘dyadics’, which provide a useful mechanism for describing the features of geometric algebra. Chapter four introduces the geometric product and defines the inner and outer products, which are employed in the following chapter on geometric algebra. Chapters six and seven cover all the 2D and 3D products between scalars, vectors, bivectors and trivectors. Chapter eight shows how geometric algebra brings new insights into reflections and rotations, especially in 3D. Finally, chapter nine explores a wide range of 2D and 3D geometric problems followed by a concluding tenth chapter.

Filled with lots of clear examples, full-colour illustrations and tables, this compact book provides an excellent introduction to geometric algebra for practitioners in computer games and animation.

Keywords

3D algebra algorithms animation computer computer graphics reflection

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-84882-379-2
  • Copyright Information Springer London 2009
  • Publisher Name Springer, London
  • eBook Packages Computer Science
  • Print ISBN 978-1-84882-378-5
  • Online ISBN 978-1-84882-379-2
  • About this book