Geometric operations implemented by conformal geometric algebra neural\n nodes

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