E.S.M. Hitzer

**Geometric operations implemented by conformal geometric algebra neural nodes**

Proceedings of
*SICE Symposium on Systems and Information 2008*,
26-28 Nov. 2008, Himeji, Japan, pp. 357 ? 362 (2008).

**Abstract:**
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
neuronswe 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.

[ PDF ] 215K

[Geometric Calculus Japan index]