 
Summary: The equipartition of curves
Costas Panagiotakis
Computer Science Department, University of Crete, GR71409 Iraklion, Greece
email : cpanag@csd.uoc.gr
Konstantin Athanassopoulos
Department of Mathematics, University of Crete, GR71409 Iraklion, Greece
email : athanako@math.uoc.gr
Georgios Tziritas
Computer Science Department, University of Crete, GR71409 Iraklion, Greece
email : tziritas@csd.uoc.gr
Abstract
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 nequipartition (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.
