Geometric algebra: a computational framework for geometrical applications

Geometric algebra is a consistent computational framework in which to define geometric primitives and their relationships. This algebraic approach contains all geometric operators and permits specification of constructions in a totally coordinate-free manner. Since it contains primitives of any dimensionality (rather than just vectors) it has no special cases: all intersections of primitives are computed with one general incidence operator. We show that the quaternion representation of rotations is also naturally contained within the framework. Models of Euclidean geometry can be made which directly represent the algebra of spheres.