Geodesic order types

Oswin Aichholzer, Matias Korman, Alexander Pilz, Birgit Vogtenhuber

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

The geodesic between two points a and b in the interior of a simple polygon P is the shortest polygonal path inside P that connects a to b. It is thus the natural generalization of straight line segments on unconstrained point sets to polygonal environments. In this paper we use this extension to generalize the concept of the order type of a set of points in the Euclidean plane to geodesic order types. In particular, we show that, for any set S of points and an ordered subset B ⊂ S of at least four points, one can always construct a polygon P such that the points of B define the geodesic hull of S w.r.t. P, in the specified order. Moreover, we show that an abstract order type derived from the dual of the Pappus arrangement can be realized as a geodesic order type.

Original languageEnglish
Pages (from-to)112-128
Number of pages17
JournalAlgorithmica
Volume70
Issue number1
DOIs
Publication statusPublished - 2014 Sep
Externally publishedYes

Keywords

  • Geodesic
  • Order types
  • Pappus arrangement
  • Simple polygon
  • Stretchability

ASJC Scopus subject areas

  • Computer Science(all)
  • Computer Science Applications
  • Applied Mathematics

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