Conformal geometric algebra

Summary

Conformal geometric algebra is the geometric algebra of $\R^{n+1,1}$, used as a model of Euclidean space $\R^n$. In it, points, spheres and planes are all represented by vectors. A point $x \in \R^n$ is embedded as a null vector $X$, and the inner product of two embedded points is $-\tfrac{1}{2}$ times their squared distance. Spheres and planes are the vectors orthogonal to the points that lie on them. All Möbius transformations of $\R^n \cup \set{\infty}$ act by conjugation with elements of the algebra. It is used in computer graphics and robotics, where rigid motions, intersections and tangencies become algebraic operations.