
Walking Your Dog in the Woods in Polynomial Time - vector_spaces
https://hal.inria.fr/inria-00438463/en
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carapace
> Abstract

> 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 polygonal obstacles.

