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Homotopic Fréchet Distance Between Curves or, Walking Your Dog in the Woods in Polynomial Time

Erin Wolf Chambers 1 Eric Colin de Verdière 2 Jeff Erickson 3 Sylvain Lazard 4 Francis Lazarus 5 Shripad Thite 6
1 UIUC - University of Illinois at Urbana Champaign
2 ENS Paris - École normale supérieure - Paris
3 Department. of Computer Science [Illinois]
4 VEGAS - Effective Geometric Algorithms for Surfaces and Visibility
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
5 GIPSA-AGPIG - GIPSA - Architecture, Géométrie, Perception, Images, Gestes
GIPSA-DIS - Département Images et Signal
6 CMI - Center for the Mathematics of Information
Abstract : The Fréchet distance between two curves in the plane is the minimum length of a leash that allows a dog and its owner to walk along their respective curves, from one end to the other, without backtracking. We propose a natural extension of Fréchet distance to more general metric spaces, which requires the leash itself to move continuously over time. For example, for curves in the punctured plane, the leash cannot pass through or jump over the obstacles (``trees''). We describe a polynomial-time algorithm to compute the homotopic Fréchet distance between two given polygonal curves in the plane minus a given set of polygonal obstacles.
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2010 Homotopic Frechet Distance Between Curves.png
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Submitted on : Thursday, December 3, 2009 - 4:58:14 PM
Last modification on : Friday, February 26, 2021 - 3:28:08 PM

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ENS-PARIS | UNIV-LORRAINE | INRIA | CNRS | LORIA | GIPSA | GIPSA-DIS | GIPSA-AGPIG | PSL | UGA

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Erin Wolf Chambers, Eric Colin de Verdière, Jeff Erickson, Sylvain Lazard, Francis Lazarus, et al.. Homotopic Fréchet Distance Between Curves or, Walking Your Dog in the Woods in Polynomial Time. Computational Geometry, Elsevier, 2010, Special Issue on 24th Annual Symposium on Computational Geometry (SoCG'08), 43 (3), pp.295-311. ⟨10.1016/j.comgeo.2009.02.008⟩. ⟨inria-00438463⟩

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