Computing the visibility polygon of an island in a polygonal domain

Authors:
Danny Z. Chen;Haitao Wang
Affiliations:
Department of Computer Science and Engineering, University of Notre Dame, Notre Dame, IN;Department of Computer Science and Engineering, University of Notre Dame, Notre Dame, IN
Venue:
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Year:
2012

Citing 12
Cited 1

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Worst-case optimal algorithms for constructing visibility polygons with holes

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Corrections to Lee's visibility polygon algorithm

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Visibility and intersection problems in plane geometry

Discrete & Computational Geometry
Computing the visibility polygon from a convex set and related problems

Journal of Algorithms
An optimal parallel algorithm for the visibility of a simple polygon from a point

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Triangulating a simple polygon in linear time

Discrete & Computational Geometry
An output-sensitive algorithm for computing visibility

SIAM Journal on Computing
An Optimal Algorithm for Computing Visibility in the Plane

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Planar rectilinear shortest path computation using corridors

Computational Geometry: Theory and Applications
A nearly optimal algorithm for finding L1shortest paths among polygonal obstacles in the plane

ESA'11 Proceedings of the 19th European conference on Algorithms

Visibility and ray shooting queries in polygonal domains

WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures

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Abstract

Given a set $\mathcal{P}$ of h pairwise-disjoint polygonal obstacles of totally n vertices in the plane, we study the problem of computing the (weakly) visibility polygon from a polygonal obstacle P* (an island) in $\mathcal{P}$. We give an O(n2h2) time algorithm for it. Previously, the special case where P* is a line segment was solved in O(n4) time, which is worst-case optimal. In addition, when all obstacles in $\mathcal{P}$ (including P*) are convex, our algorithm runs in O(n+h4) time.