Curve Reconstruction in Arbitrary Dimension and the Traveling Salesman Problem

  • Joachim Giesen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1568)

Abstract

Given a finite set of points sampled from a curve, we want to reconstruct the ordering of the points along the curve. Every ordering of the sample points can be defined by a polygon through these points. We show that for simple, regular curves Traveling Salesman Paths give the correct polygonal reconstruction, provided the points are sampled densely enough. In this case the polygonal reconstruction is part of the Delaunay Triangulation of the sample points. We use this observation to design an efficient algorithm for the reconstruction problem.

Keywords

Curve Reconstruction Traveling Salesman Problem Minimum Spanning Tree 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Joachim Giesen
    • 1
  1. 1.Institut für Theoretische InformatikETH ZürichZürichSwitzerland

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