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LATIN 2008: Theoretical Informatics

Volume 4957 of the series Lecture Notes in Computer Science pp 630-641

Simplifying 3D Polygonal Chains Under the Discrete Fréchet Distance

  • Sergey BeregAffiliated withDepartment of Computer Science, University of Texas at Dallas
  • , Minghui JiangAffiliated withDepartment of Computer Science, Utah State University
  • , Wencheng WangAffiliated withInstitute of Software, Chinese Academy of Sciences
  • , Boting YangAffiliated withDepartment of Computer Science, University of Regina, Regina
  • , Binhai ZhuAffiliated withDepartment of Computer Science, Montana State University

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Abstract

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.