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2011
Let p and q be two points in a simple polygon P. This chapter provides the Chazelle algorithm for computing the ESP between p and q that is contained in P. It uses triangulation of simple polygons as presented in the previous chapter as a preprocessing step, and has a time complexity that is determined by that of the prior triangulation.
Reinhard Klette, Fajie Li
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Let p and q be two points in a simple polygon P. This chapter provides the Chazelle algorithm for computing the ESP between p and q that is contained in P. It uses triangulation of simple polygons as presented in the previous chapter as a preprocessing step, and has a time complexity that is determined by that of the prior triangulation.
Reinhard Klette, Fajie Li
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On Simple Polygonalizations with Optimal Area
Discrete & Computational Geometry, 2000The author studies the problem of finding a simple polygonalization for a given set of vertices P in the Euclidean plane that has optimal area. He shows that these problems are very closely related to problems of optimizing the number of points from a set Q in a simple polygon or a maximum weight polygon for a given vertex set.
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Compliant motion in a simple polygon
Proceedings of the ninth annual symposium on Computational geometry - SCG '93, 1989We consider motion planning under the compliant motion model, in which a robot directed to walk into a wall may slide along it. We examine several variants of compliant motion planning for a point robot inside a simple polygon with n sides, where the goal is a fixed vertex or edge.
Jack Snoeyink +2 more
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DETERMINING THE SEPARATION OF SIMPLE POLYGONS
International Journal of Computational Geometry & Applications, 1994Given simple polygons P and Q, their separation, denoted by σ(P, Q), is defined to be the minimum distance between their boundaries. We present a parallel algorithm for finding a closest pair among all pairs (p, q), p ∈ P and q ∈ Q. The algorithm runs in O ( log n) time using O(n) processors on a CREW PRAM, where n = |P| + |Q|.
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ON HAMILTONIAN TRIANGULATIONS IN SIMPLE POLYGONS
International Journal of Computational Geometry & Applications, 1999An n-vertex simple polygon P is said to have a Hamiltonian Triangulation if it has a triangulation whose dual graph contains a hamiltonian path. Such triangulations are useful in fast rendering engines in Computer Graphics. We give a new characterization of polygons with hamiltonian triangulations and use it to devise O(n log n)-time algorithms to ...
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Minimizing the Size of Vertexlights in Simple Polygons
MLQ, 2002Summary: We show that given a simple polygon \(P\) it is NP-hard to determine the smallest \(\alpha\in [0,\pi)\) such that \(P\) can be illuminated by \(\alpha\)-vertexlights, if we place exactly one \(\alpha\)-vertexlight in each vertex of \(P\).
Hans-Dietrich Hecker, Andreas Spillner
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Area optimization of simple polygons
Proceedings of the ninth annual symposium on Computational geometry - SCG '93, 1993We discuss problems of optimizing the area of a simple polygon for a given set of vertices P and show that these problems are very closely related to problems of optimizing the number of points from a set Q in a simple polygon with vertex set P. We prove that it is NP-complete to find a minimum weight polygon or a maximum weight polygon for a given ...
William R. Pulleyblank +1 more
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Triangulating Simple Polygons and Equivalent Problems
ACM Transactions on Graphics, 1984Summary: It has long been known that the complexity of triangulation of simple polygons having an upper bound of O(n log n) but a lower bound higher than \(\Omega\) (n) has not been proved yet. We propose here an easily implemented route to the triangulation of simple polygons through the trapezoidization of simple polygons, which is currently done in ...
Alain Fournier, D. Y. Montuno
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Intersection removal for simple polygons
International Journal of Computer Mathematics, 1997Given two intersecting simple polygons A and B and a direction, θ, we have to find the minimum distance by which B should be translated along direction θ so that A and B no longer intersect. We present two algorithms for this problem for the case that A and B are in 2 dimensions and one algorithm for the case that they are in 3 dimensions.
Kamala Krithivasan, Sumeet Lahorani
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Triangulating a simple polygon
Information Processing Letters, 1978David S. Johnson +3 more
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