License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SoCG.2017.21
URN: urn:nbn:de:0030-drops-72166
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/7216/
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Bose, Prosenjit ; Kostitsyna, Irina ; Langerman, Stefan

Self-Approaching Paths in Simple Polygons

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LIPIcs-SoCG-2017-21.pdf (0.8 MB)

Abstract

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.

BibTeX - Entry

@InProceedings{bose_et_al:LIPIcs:2017:7216,
  author =	{Prosenjit Bose and Irina Kostitsyna and Stefan Langerman},
  title =	{{Self-Approaching Paths in Simple Polygons}},
  booktitle =	{33rd International Symposium on Computational Geometry (SoCG 2017)},
  pages =	{21:1--21:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-038-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{77},
  editor =	{Boris Aronov and Matthew J. Katz},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/7216},
  URN =		{urn:nbn:de:0030-drops-72166},
  doi =		{10.4230/LIPIcs.SoCG.2017.21},
  annote =	{Keywords: self-approaching path, simple polygon, shortest path, involute curve}
}

Keywords: self-approaching path, simple polygon, shortest path, involute curve
Collection: 33rd International Symposium on Computational Geometry (SoCG 2017)
Issue Date: 2017
Date of publication: 20.06.2017

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