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Approximate ESPs on Surfaces of Polytopes Using a Rubberband Algorithm

  • Fajie Li
  • Reinhard Klette
  • Xue Fu
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4872)

Abstract

Let p and q be two points on the surface of a polytope Π. This paper provides a rubberband algorithm for computing a Euclidean shortest path between p and q (a so-called surface ESP) that is contained on the surface of Π. The algorithm has \(\kappa_1(\varepsilon) \cdot \kappa_2(\varepsilon) \cdot {\cal O}(n^2)\) time complexity, where n is the number of vertices of Π, κ i (ε) = (L 0 i  − L i )/ε, for the true length L i of some shortest path with initial (polygonal path) length L 0 i (used when approximating this shortest path), for i = 1, 2. Rubberband algorithms follow a straightforward design strategy, and the proposed algorithm is easy to implement and thus of importance for applications, for example, when analyzing 3D objects in 3D image analysis, such as in biomedical or industrial image analysis, using 3D image scanners.

Keywords

Rubberband algorithm Euclidean shortest path surface ESP 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Fajie Li
    • 1
  • Reinhard Klette
    • 2
  • Xue Fu
    • 3
    • 4
  1. 1.Institute for Mathematics and Computing Science, University of Groningen, P.O. Box 800, 9700 AV GroningenThe Netherlands
  2. 2.Computer Science Department, The University of Auckland, Private Bag 92019, Auckland 1142New Zealand
  3. 3.Faculty of Economics, University of Groningen, P.O. Box 800, 9700 AV GroningenThe Netherlands
  4. 4.School of Public Finance, Jiangxi University of Finance and Economy, Nanchang, 330013China

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