  Geometric algebra is an optimal frame work for calculating with vectors. The
geometric algebra of a space includes elements that represent all the its
subspaces (lines, planes, volumes, ...). Conformal geometric algebra expands
this approach to elementary representations of arbitrary points, point pairs,
lines, circles, planes and spheres. Apart from including curved objects,
conformal geometric algebra has an elegant unified quaternion like
representation for all proper and improper Euclidean transformations, including
reflections at spheres, general screw transformations and scaling. Expanding
the concepts of real and complex neurons we arrive at the new powerful concept
of conformal geometric algebra neurons. These neurons can easily take the above
mentioned geometric objects or sets of these objects as inputs and apply a wide
range of geometric transformations via the geometric algebra valued weights.
