The equipartition of curves

In this paper we analyze the problem of partitioning a continuous curve into n parts with equal successive chords, the curve EquiPartition problem (EP). The goal is to locate n−1 consecutive curve points, so that the curve can be divided into n segments with equal chords under a distance function. We adopt a level set approach to prove that for any continuous injective curve in a metric space and any number n there always exists at least one n-equipartition (EP). A new approximate algorithm, that is the first EP algorithm, inspired from the level set approach is proposed for finding all solutions with high accuracy. Finally, EP based applications are presented and special properties of their solutions are discussed.