Self-approaching paths in simple polygons

Prosenjit Bose, Irina Kostitsyna (Corresponding author), Stefan Langerman

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2 Citaten (Scopus)
175 Downloads (Pure)


We study the problem of connecting two points in a simple polygon with a self-approaching path. A self-approaching path is a directed curve such that the Euclidean distance between a point moving along the path and any future position does not increase, that is, for all points a, b, and c that appear in that order along the curve, |ac|≥|bc|. We analyze properties of self-approaching paths inside simple polygons, and characterize shortest self-approaching paths. In particular, we show that a shortest self-approaching path connecting two points in a simple polygon can be forced to follow a general class of non-algebraic curves. While this makes it difficult to design an exact algorithm, we show how to find the shortest self-approaching path under a model of computation which assumes that we can compute involute curves of high order. Lastly, we provide an efficient algorithm to test if a given simple polygon is self-approaching, that is, if there exists a self-approaching path for any two points inside the polygon.

Originele taal-2Engels
Aantal pagina's24
TijdschriftComputational Geometry
StatusGepubliceerd - apr. 2020


This work was begun at the CMO-BIRS Workshop on Searching and Routing in Discrete and Continuous Domains, October 11–16, 2015. I.K. was supported in part by the NWO under project no. 612.001.106 , and by F.R.S.-FNRS .

Fonds de la Recherche Scientifique
Nederlandse Organisatie voor Wetenschappelijk Onderzoek612.001.106


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