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A heuristic homotopic path simplification algorithm

Daneshpajouh, S ; Sharif University of Technology | 2011

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  1. Type of Document: Article
  2. DOI: 10.1007/978-3-642-21931-3_11
  3. Publisher: 2011
  4. Abstract:
  5. 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
  6. Keywords:
  7. Curve ; Heuristic ; Homotopies ; Line ; Path ; Simplification ; Algorithms ; Computational geometry ; Heuristic methods
  8. Source: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 20 June 2011 through 23 June 2011 ; Volume 6784 LNCS, Issue PART 3 , June , 2011 , Pages 132-140 ; 03029743 (ISSN) ; 9783642219306 (ISBN)
  9. URL: http://link.springer.com/chapter/10.1007%2F978-3-642-21931-3_11