Simplifying 3D Polygonal Chains Under the Discrete Fréchet Distance

  • Sergey Bereg
  • Minghui Jiang
  • Wencheng Wang
  • Boting Yang
  • Binhai Zhu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4957)


A well-known measure to characterize the similarity of two polygonal chains is the famous Fréchet distance. In this paper, for the first time, we consider the problem of simplifying 3D polygonal chains under the discrete Fréchet distance. We present efficient polynomial time algorithms for simplifying a single chain, including the first near-linear O(nlogn) time exact algorithm for the continuous min-# fitting problem. Our algorithms generalize to any fixed dimension d > 3. Motivated by the ridge-based model simplification we also consider simplifying a pair of chains simultaneously and we show that one version of the general problem is NP-complete.


Computational Geometry Steiner Point Greedy Method Tolerance Zone Polygonal Chain 
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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© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Sergey Bereg
    • 1
  • Minghui Jiang
    • 2
  • Wencheng Wang
    • 3
  • Boting Yang
    • 4
  • Binhai Zhu
    • 5
  1. 1.Department of Computer ScienceUniversity of Texas at DallasRichardsonUSA
  2. 2.Department of Computer ScienceUtah State UniversityLoganUSA
  3. 3.Institute of SoftwareChinese Academy of SciencesBeijingChina
  4. 4.Department of Computer ScienceUniversity of Regina, ReginaSaskatchewanCanada
  5. 5.Department of Computer ScienceMontana State UniversityBozemanUSA

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