Inner Product of Two Oriented Points in Conformal Geometric Algebra in Detail

We study in full detail the inner product of oriented points in conformal geometric algebra and its geometric meaning. The notion of oriented point is introduced and the inner product of two general oriented points is computed, analyzed (including symmetry) and graphed in terms of point to point distance, and angles between the distance vector and the local orientation planes of the two points. Seven examples illustrate the results obtained. Finally, the results are extended from dimension three to arbitrary dimensions n.