Proceedings of the Annual Meeting of the Cognitive Science Society

This paper outlines some preliminary results concerning the use of sinusoidal oscillations to represent vectors in two-dimensional space. The proposed representation scheme permits efficient implementation of translation and rotation, and immediate detection of such relations as collinearity and proximity of points. This scheme is then extended so that arbitrary convex regions of the plane are represented using a pair of signals varying over time. Finally, the advantages of representing convex regions in this way are shown to derive from the resulting ease with which such regions can be translated and rotated in the plane, and—more strikingly—from the simplicity of determining whether two such regions overlap.