Walking Your Dog in the Woods in Polynomial Time

Erin Wolf Chambers (1) , Eric Colin de Verdire (2) , Jeff Erickson (1) , Sylvain Lazard (3) , Francis Lazarus (4) , Shripad Thite (5)

1 UIUC - University of Illinois at Urbana-Champaign [Urbana]
2 ENS-PSL - École normale supérieure - Paris
3 VEGAS - Effective Geometric Algorithms for Surfaces and Visibility
4 GIPSA-GPIG - GIPSA - Géométrie, Perception, Images, Geste
5 CMI - Center for the Mathematics of Information

The Frechet 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 Frechet 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 Frechet distance between two given polygonal curves in the plane minus a given set of obstacles, which are either points or polygons.

Mots clés: Homotopic Frechet distance; geodesic leash map

Domaines: Géométrie algorithmique [cs.CG]

Erin Wolf Chambers, Eric Colin de Verdire, Jeff Erickson, Sylvain Lazard, Francis Lazarus, et al.. Walking Your Dog in the Woods in Polynomial Time. SoCG 2008 - 24th Annual Symposium on Computational Geometry, Jun 2008, College Park, Maryland, United States. pp.101--109, ⟨10.1145/1377676.1377694⟩. ⟨inria-00336497⟩