On the Curve Equipartition Problem: a brief exposition of basic issues
Costas PanagiotakisGeorge GeorgakopoulosGeorge Tziritas · 2006
We describe briefly the problem of partitioning a continuous curve into N parts with equal chords. (The length of a chord may be defined by any smooth distance metric applied on its endpoints-the Euclidean metric being one of them.) A have proved that a decision variation of this problem is NP-complete, yet for any continuous curve and any N there always exists at least one equipartition. In this work, we propose an approximate algorithm and also a steepest descent method that converges to an exact solution.