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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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