Geometric Algebra and Geometry

In this chapter we explore how GA can be used to resolve simple geometric problems in computer graphics. This is not to persuade you to adopt these methods, rather demonstrate that GA can be used alongside classic vectorial techniques. The classic vectorial approach often depends upon the scalar and cross products and normal vectors to lines and planes. The GA approach is to avoid such vectors and work with the inner, outer and geometric products, bivectors and trivectors. To begin, we investigate how the outer product can be used to test whether a point is inside a triangle.