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Self-Approaching Paths in Simple Polygons

Authors Prosenjit Bose, Irina Kostitsyna, Stefan Langerman

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Prosenjit Bose
Irina Kostitsyna
Stefan Langerman

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Prosenjit Bose, Irina Kostitsyna, and Stefan Langerman. Self-Approaching Paths in Simple Polygons. In 33rd International Symposium on Computational Geometry (SoCG 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 77, pp. 21:1-21:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2017)


We study self-approaching paths that are contained in a simple polygon. A self-approaching path is a directed curve connecting two points 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 the properties, and present a characterization of shortest self-approaching paths. In particular, we show that a shortest self-approaching path connecting two points inside a 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 a self-approaching path inside a polygon connecting two points under a model of computation which assumes that we can calculate involute curves of high order. Lastly, we provide an 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 path
  • simple polygon
  • shortest path
  • involute curve


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