A Heuristic Homotopic Path Simplification Algorithm

  • Shervin Daneshpajouh
  • Mohammad Ghodsi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6784)


We study the well-known problem of approximating a polygonal path P by a coarse one, whose vertices are a subset of the vertices of P. In this problem, for a given error, the goal is to find a path with the minimum number of vertices while preserving the homotopy in presence of a given set of extra points in the plane. We present a heuristic method for homotopy-preserving simplification under any desired measure for general paths. Our algorithm for finding homotopic shortcuts runs in O( mlog(n + m) + nlogn log(nm) + k) time, where k is the number of homotopic shortcuts. Using this method, we obtain an O(n 2 + mlog(n + m) + nlogn log(nm)) time algorithm for simplification under the Hausdorff measure.


Computational Geometry Simplification Homotopy Path Line Curve Heuristic 


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© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Shervin Daneshpajouh
    • 1
  • Mohammad Ghodsi
    • 1
    • 2
  1. 1.Department of Computer EngineeringSharif University of TechnologyTehranIran
  2. 2.School of Computer ScienceInstitute for Research in Fundamental Sciences (IPM)TehranIran

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