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The equipartition of curves Costas Panagiotakis
 

Summary: The equipartition of curves
Costas Panagiotakis
Computer Science Department, University of Crete, GR-71409 Iraklion, Greece
e-mail : cpanag@csd.uoc.gr
Konstantin Athanassopoulos
Department of Mathematics, University of Crete, GR-71409 Iraklion, Greece
e-mail : athanako@math.uoc.gr
Georgios Tziritas
Computer Science Department, University of Crete, GR-71409 Iraklion, Greece
e-mail : 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 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.

  

Source: Athanassopoulos, Konstantin - Department of Mathematics, University of Crete

 

Collections: Mathematics