2026-07-22T06:37:12Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:7216 2024-03-06T10:39:58Z ddc:004 open_access

Self-Approaching Paths in Simple Polygons Bose, Prosenjit Kostitsyna, Irina Langerman, Stefan self-approaching path simple polygon shortest path involute curve 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Prosenjit Bose and Irina Kostitsyna and Stefan Langerman 2017 Is Part Of LIPIcs, Volume 77, 33rd International Symposium on Computational Geometry (SoCG 2017) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.SoCG.2017.21 urn:nbn:de:0030-drops-72166 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2017.21 eng https://creativecommons.org/licenses/by/3.0/legalcode