, Volume 2, Issue 1–4, pp 209–233 | Cite as

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

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


Given a triangulation of a simple polygonP, we present linear-time algorithms for solving a collection of problems concerning shortest paths and visibility withinP. These problems include calculation of the collection of all shortest paths insideP from a given source vertexS to all the other vertices ofP, calculation of the subpolygon ofP consisting of points that are visible from a given segment withinP, preprocessingP for fast "ray shooting" queries, and several related problems.

Key words

Triangulation Simple polygon Visibility Shortest paths Ray shooting Computational geometry 


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Copyright information

© Springer-Verlag New York Inc. 1987

Authors and Affiliations

  • Leonidas Guibas
    • 1
    • 2
  • John Hershberger
    • 1
  • Daniel Leven
    • 3
  • Micha Sharir
    • 3
    • 4
  • Robert E. Tarjan
    • 5
    • 6
  1. 1.Computer Science DepartmentStanford UniversityStanfordUSA
  2. 2.DEC/SRCPalo AltoUSA
  3. 3.School of Mathematical SciencesTel-Aviv UniversityTel AvivIsrael
  4. 4.Courant Institute of Mathematical SciencesNew York UniversityNew YorkUSA
  5. 5.Department of Computer SciencePrinceton UniversityPrincetonUSA
  6. 6.AT&T Bell LaboratoriesMurray HillUSA

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