Self-approaching paths in simple polygons

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

Research output: Contribution to journalArticleAcademicpeer-review

1 Citation (Scopus)
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Abstract

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.

Original languageEnglish
Article number101595
Number of pages24
JournalComputational Geometry
Volume87
DOIs
Publication statusPublished - Apr 2020

Keywords

  • Involute curves
  • Self-approaching paths
  • Shortest paths
  • Simple polygons

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