Curves in ℤn

  • Grit Thürmer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2301)

Abstract

A new definition of closed curves in n-dimensional discrete space is proposed. This definition can be viewed as a generalization of closed quasi curves and is intended to overcome the limitations of known definitions for practical purposes. Following the proposed definition, a set of points forms a closed curve in discrete space if the set admits a parameterization, i.e. there exists a Hamiltonian cycle in the set. Adjacencies that do not indicate the parameterization are allowed only between points that are “close to each other” along the parameterization. Additionally, it is proven that discrete curves satisfying the new definition in two-dimensional discrete space have the Jordan property.

Keywords

Travel Salesman Problem Closed Curve Hamiltonian Cycle Discrete Space Endoscopic Sinus Surgery 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Grit Thürmer
    • 1
  1. 1.Computer Graphics, Visualization, Man-Machine Communication Group Faculty of MediaBauhaus-University WeimarWeimarGermany

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