Linear-time algorithms for visibility and shortest path problems inside triangulated simple polygons

Leonidas Guibas, John Hershberger, Daniel Leven, Micha Sharir, Robert E. Tarjan

Research output: Contribution to journalArticlepeer-review

Abstract

Given a triangulation of a simple polygon P, we present linear-time algorithms for solving a collection of problems concerning shortest paths and visibility within P. These problems include calculation of the collection of all shortest paths inside P from a given source vertex S to all the other vertices of P, calculation of the subpolygon of P consisting of points that are visible from a given segment within P, preprocessing P for fast "ray shooting" queries, and several related problems.

Original languageEnglish
Pages (from-to)209-233
Number of pages25
JournalAlgorithmica
Volume2
Issue number1-4
DOIs
StatePublished - Nov 1987

Keywords

  • Computational geometry
  • Ray shooting
  • Shortest paths
  • Simple polygon
  • Triangulation
  • Visibility

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