Testing the relative positions of several points on a circle

Abstract

This note introduces a programming technique that serves to facilitate the examination of the relative positions of several points on a circle, or—more generally—the relative positions of several entities that belong to a cyclic structure. The basic idea is to employ a function of the numerical representations of the individual positions which is invariant under rotation with regard to sign. The nature of the numerical representation makes it natural to introduce the term: cut-point-independent test procedure.