Mathematics for Computer Graphics pp 237-270 | Cite as

# Geometric Algebra

## Abstract

This can only be a brief introduction to geometric algebra as the subject really demands an entire book. Those readers who wish to pursue the subject further should consult the author’s books: *Geometric Algebra for Computer Graphics* or *Geometric Algebra: An Algebraic System for Computer Games and Animation*.

Although geometric algebra introduces some new ideas, the subject should not be regarded as difficult. If you have read and understood the previous chapters, you should be familiar with vectors, vector products, transforms, and the idea that the product of two transforms is sensitive to the transform sequence. For example, in general, scaling an object after it has been translated, is not the same as translating an object after it has been scaled. Similarly, given two vectors \(\textbf{r}\) and \(\textbf{s}\) their vector product \(\textbf{r} \times \textbf{ s}\) creates a third vector **t**, using the right-hand rule, perpendicular to the plane containing \(\textbf{r}\) and \(\textbf{s}\). However, just by reversing the vectors to \(\textbf{s} \times \textbf{ r}\), creates a similar vector but in the opposite direction \(-\textbf{t}\).