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Geometric Algebra for Computer Graphics

  • John Vince

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Pages 1-3
  3. Pages 5-10
  4. Pages 11-22
  5. Pages 23-37
  6. Pages 39-48
  7. Pages 49-54
  8. Pages 55-77
  9. Pages 79-124
  10. Pages 199-230
  11. Pages 243-243
  12. Back Matter
    Pages 245-252

About this book

Introduction

Since its invention, geometric algebra has been applied to various branches of physics such as cosmology and electrodynamics, and is now being embraced by the computer graphics community where it is providing new ways of solving geometric problems. It took over two thousand years to discover this algebra, which uses a simple and consistent notation to describe vectors and their products.

John Vince (best-selling author of a number of books including ‘Geometry for Computer Graphics’ and ‘Vector Analysis for Computer Graphics’) tackles this new subject in his usual inimitable style, and provides an accessible and very readable introduction.

The first five chapters review the algebras of real numbers, complex numbers, vectors, and quaternions and their associated axioms, together with the geometric conventions employed in analytical geometry. As well as putting geometric algebra into its historical context, John Vince provides chapters on Grassmann’s outer product and Clifford’s geometric product, followed by the application of geometric algebra to reflections, rotations, lines, planes and their intersection. The conformal model is also covered, where a 5D Minkowski space provides an unusual platform for unifying the transforms associated with 3D Euclidean space.

Filled with lots of clear examples and useful illustrations, this compact book provides an excellent introduction to geometric algebra for computer graphics.

Keywords

3D Algebra Clifford Algebra Geometric algebra calculus computer graphics geometry reflection

Authors and affiliations

  • John Vince
    • 1
  1. 1.Bournemouth UniversityUK

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-84628-997-2
  • Copyright Information Springer London 2008
  • Publisher Name Springer, London
  • eBook Packages Computer Science
  • Print ISBN 978-1-84628-996-5
  • Online ISBN 978-1-84628-997-2
  • Buy this book on publisher's site
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