Tutorial MATLAB : Geometric Algebra

GABLE: A Matlab Tutorial for Geometric AlgebraLeo Dorst, Stephen Mann, and Tim BoumaDecember 3, 2002AbstractIn this tutorial we give an introduction to geometric algebra, using our Matlab pack-age GABLE (Geometric AlgeBra Learning Environment). In the geometric algebra for 3-dimensional Euclidean space, we graphically demonstrate the ideas of the geometric product,the outer product, and the inner product, and the geometric operators that may be formed fromthem. We give several demonstrations of computations you can do using the geometric algebra,including projection and rejection, orthogonalization, interpolation of rotations, and intersec-tion of linear o set spaces such as lines and planes. We emphasize the importance of blades asrepresentations of subspaces, and the use of meet and join to manipulate them. We end withEuclidean geometry of 2-dimensional space as represented in the 3-dimensional homogeneousmodel.1GABLE Version 1.3 (revised tutorial) 2Contents1 Introduction 41.1 Getting started . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.2 Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 The products of geometric algebra 62.1 Scalar product . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.2 The outer product . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.2.1 De nition . . . . . . . . . . . . . . . . . . . . . . . . . . ...