Which, simply put, is a way of representing objects in 3D space by using five dimensions.
Though this is a particular form of Geometric Algebra, it is said in various references that GA is substantially faster for computing than linear algebra for computations in up to nine dimensions. http://www.geometricalgebra.net/
Геометрическая алгебра - никому не понятный раздел математики, который, как я понял, позволяет в том числе и вычислять сложные отражения аналитически.
reflections It can be verified that forming P g(x) P gives a new direction on the null-cone, g(x' ), where x' corresponds to a reflection in the plane of points p in R3 that satisfy g(p) . P = 0. g(x) . A = 0 => P g(x) . A P = 0 => P g(x) P . P A P (and similarly for the wedge product), so the effect of applying P sandwich-fashion to any the quantities A in the section above is similarly to reflect the corresponding locus of points x, so the corresponding circles, spheres, lines and planes corresponding to particular types of A are reflected in exactly the same way that applying P to g(x) reflects a point x.