Geometric Algebra for Computer Science

19 BASIS BLADES AND OPERATIONS

All geometric algebra implementations that represent multivectors as a weighted sum of basis blades will, at some point, have to compute products of basis blades. Among the various products, the capability to compute the geometric product (also for non-Euclidean metrics) is clearly the minimum requirement, as the outer product and various flavors of the inner products can be derived from it using the (anti-)symmetry or grade selection techniques of Chapter 6.

This chapter describes how to implement this geometric product of basis blades through a convenient representation of basis blades. The algorithms described are quite simple, yet intricate enough that we need (pseudo)code to describe them precisely. Instead ...