Geodesic-preserving polygon simplification

Oswin Aichholzer, Thomas Hackl, Matias Korman, Alexander Pilz, Birgit Vogtenhuber

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

Polygons are a paramount data structure in computational geometry. While the com- plexity of many algorithms on simple polygons or polygons with holes depends on the size of the input polygon, the intrinsic complexity of the problems these algorithms solve is often related to the reex vertices of the polygon. In this paper, we give an easy-to- describe linear-time method to replace an input polygon P by a polygon P' such that (1) P' contains P, (2) P0 has its reex vertices at the same positions as P, and (3) the number of vertices of P' is linear in the number of reex vertices. Since the solutions of numerous problems on polygons (including shortest paths, geodesic hulls, separating point sets, and Voronoi diagrams) are equivalent for both P and P', our algorithm can be used as a preprocessing step for several algorithms and makes their running time dependent on the number of reex vertices rather than on the size of P. We describe several of these applications (including linear-time post-processing steps that might be necessary).

Original languageEnglish
Pages (from-to)307-323
Number of pages17
JournalInternational Journal of Computational Geometry and Applications
Volume24
Issue number4
DOIs
Publication statusPublished - 2014 Dec 26

Keywords

  • Polygon
  • Voronoi diagram
  • geodesic
  • geodesic hull
  • polygonal domain
  • shortest path
  • simple polygon

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

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