Journal ArticleDOI
Computing the visibility polygon from a convex set and related problems
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TLDR
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.About:
This article is published in Journal of Algorithms.The article was published on 1991-01-02. It has received 74 citations till now. The article focuses on the topics: Convex polygon & Polygon covering.read more
Citations
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Computing minimum length paths of a given homotopy class
John Hershberger,Jack Snoeyink +1 more
TL;DR: It is shown that the universal covering space of a surface can be used to unify previous results on computing paths in a simple polygon and leads to simplified linear-time algorithms for shortest path trees, for minimum-link paths in simple polygons, and for paths restricted to c given orientations.
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Approximating polygons and subdivisions with minimum-link paths
TL;DR: This work investigates fattening by convolving the segments or vertices with disks and attempts to approximate objects with the minimum number of line segments, or with near the minimum, by using efficient greedy algorithms.
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Efficient piecewise-linear function approximation using the uniform metric
TL;DR: An anO(n logn)-time method for finding a bestk-link piecewise-linear function approximating ann-point planar point set using the well-known uniform metric to measure the error, ε≥0, of the approximation.
References
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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
TL;DR: Given a triangulation of a simple polygonP, linear-time algorithms for solving a collection of problems concerning shortest paths and visibility withinP are presented.
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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.
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Finding the convex hull of a simple polygon
TL;DR: An earlier convex hull finder of the authors' is limited to polygons which remain simple when locally non-convex vertices are removed, so this paper amended its earlier algorithm so that it finds with complexity O(m) the convex Hull of any simple polygon, while retaining much of the simplicity of the earlier algorithm.
Journal ArticleDOI
A linear algorithm for computing the visibility polygon from a point
H El Gindy,David Avis +1 more
TL;DR: A linear, and thus optimal, algorithm is exhibited for solving the hidden-line problem in two dimensions, a recurrent problem in computer graphics.
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Finding the convex hull of a simple polygon
Ron Graham,F. Frances Yao +1 more
TL;DR: A short linear-time algorithm for finding the convex hull when the points form the (ordered) vertices of a simple (i.e., non-self-intersecting) polygon is given.