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

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Abstract

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.

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Authors and Affiliations

  1. Computer Science Department, Stanford University, 94305, Stanford, CA, USA

    Leonidas Guibas & John Hershberger

  2. DEC/SRC, 130 Lytton Avenue, 94301, Palo Alto, CA, USA

    Leonidas Guibas

  3. School of Mathematical Sciences, Tel-Aviv University, 69978, Tel Aviv, Israel

    Daniel Leven & Micha Sharir

  4. Courant Institute of Mathematical Sciences, New York University, 10012, New York, NY, USA

    Micha Sharir

  5. Department of Computer Science, Princeton University, 08544, Princeton, NJ, USA

    Robert E. Tarjan

  6. AT&T Bell Laboratories, 07974, Murray Hill, NJ, USA

    Robert E. Tarjan

Authors
  1. Leonidas Guibas
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  2. John Hershberger
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  3. Daniel Leven
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  4. Micha Sharir
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  5. Robert E. Tarjan
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Additional information

Communicated by Bernard Chazelle.

Work on this paper by this author has been supported by Office of Naval Research Grant N00014-82-K-0381, National Science Foundation Grant No. NSF-DCR-83-20085, and by grants from the Digital Equipment Corporation, the IBM Corporation, and from the U.S.-Israel Binational Science Foundation.

Work on this paper by this author has been supported by National Science Foundation Grant DCR-86-05962.

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Guibas, L., Hershberger, J., Leven, D. et al. Linear-time algorithms for visibility and shortest path problems inside triangulated simple polygons. Algorithmica 2, 209–233 (1987). https://doi.org/10.1007/BF01840360

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  • DOI: https://doi.org/10.1007/BF01840360

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