Journal ArticleDOI
Linear-time algorithms for visibility and shortest path problems inside triangulated simple polygons
Leonidas J. Guibas,John Hershberger,Daniel Leven,Micha Sharir,Micha Sharir,Robert E. Tarjan,Robert E. Tarjan +6 more
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Given a triangulation of a simple polygonP, linear-time algorithms for solving a collection of problems concerning shortest paths and visibility withinP are presented.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.read more
Citations
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Journal ArticleDOI
Capturing an evader in polygonal environments with obstacles: The full visibility case
TL;DR: It is proved that three pursuers are always sufficient and sometimes necessary to capture the evader and the bound is independent of the number of vertices or holes in the polygonal environment.
Journal ArticleDOI
Computing the visibility polygon from a convex set and related problems
TL;DR: The authors' algorithm for computing the complete visibility polygon of P from a convex set inside P leads to efficient algorithms for the following problems: Given a polygon Q of m vertices inside another polygon P of n vertices, construct a minimum nested convex polygon K between P and Q in O((n + m)log k) time, where k is the number of vertices.
Book
Computing the link center of a simple polygon
TL;DR: The link center of a simple polygon P is the set of points x inside P at which the maximal link-distance from x to any other point in P is minimized, where the link distance between two points x, y inside P is defined as the smallest number of straight edges in a polygonal path inside P connecting x to y.
Journal ArticleDOI
Generating random polygons with given vertices
TL;DR: An algorithm is given that generates a random monotone polygon in O(n) time and space after O(K) preprocessing time, where n is the number of vertices in a set of n vertices.
Journal ArticleDOI
A new algorithm for shortest paths among obstacles in the plane
TL;DR: A new algorithm for computing Euclidean shortest paths in the plane in the presence of polygonal obstacles is introduced, and a planar subdivision is built that supports efficient queries for shortest paths froms to any destination pointt.
References
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Journal ArticleDOI
Euclidean shortest paths in the presence of rectilinear barriers
Der-Tsai Lee,Franco P. Preparata +1 more
TL;DR: The goal is to find interesting cases for which the solution can be obtained without the explicit construction of the entire visibility graph, which solve the problems by constructing the shortest-path tree from the source to all the vertices of the obstacles and to the destination.