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Geometric algebra is an optimal frame work for calculating with vectors. Thegeometric algebra of a space includes elements that represent all the itssubspaces (lines, planes, volumes, ...). Conformal geometric algebra expandsthis 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 likerepresentation for all proper and improper Euclidean transformations, includingreflections at spheres, general screw transformations and scaling. Expandingthe concepts of real and complex neurons we arrive at the new powerful conceptof conformal geometric algebra neurons. These neurons can easily take the abovementioned geometric objects or sets of these objects as inputs and apply a widerange of geometric transformations via the geometric algebra valued weights.

Geometric operations implemented by conformal geometric algebra neural nodes