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.
Self-approaching paths in simple polygons
2020-04-01
Bose , P , Kostitsyna , I & Langerman , S 2020 , ' Self-approaching paths in simple polygons ' , Computational Geometry , vol. 87 , 101595 . https://doi.org/10.1016/j.comgeo.2019.101595
Aufsatz (Zeitschrift)
Elektronische Ressource
Englisch
DDC: | 629 |
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