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Visibility and intersection problems in plane geometry

Abstract

We develop new data structures for solving various visibility and intersection problems about a simple polygonP onn vertices. Among our results are a simpleO(n logn)-time algorithm for computing the illuminated subpolygon ofP from a luminous side, and anO(logn)-time algorithm for determining which side ofP is first hit by a bullet fired from a point in a certain direction. The latter method requires preprocessing onP which takes timeO(n logn) and spaceO(n). The two main tools in attacking these problems are geometric duality on the two-sided plane and fractional cascading.

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Additional information

Bernard Chazelle wishes to acknowledge the National Science Foundation for supporting this research in part under Grant CCR-8700917. A preliminary version of this paper was presented at the First Annual ACM Symposium on Computational Geometry, June 1985.

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Chazelle, B., Guibas, L.J. Visibility and intersection problems in plane geometry. Discrete Comput Geom 4, 551–581 (1989). https://doi.org/10.1007/BF02187747

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Keywords

  • Convex Polygon
  • Plane Geometry
  • Query Time
  • Intersection Problem
  • Simple Polygon