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16
Efficient algorithms for geometric optimization
 ACM Comput. Surv
, 1998
"... We review the recent progress in the design of efficient algorithms for various problems in geometric optimization. We present several techniques used to attack these problems, such as parametric searching, geometric alternatives to parametric searching, pruneandsearch techniques for linear progra ..."
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Cited by 114 (10 self)
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We review the recent progress in the design of efficient algorithms for various problems in geometric optimization. We present several techniques used to attack these problems, such as parametric searching, geometric alternatives to parametric searching, pruneandsearch techniques for linear programming and related problems, and LPtype problems and their efficient solution. We then describe a variety of applications of these and other techniques to numerous problems in geometric optimization, including facility location, proximity problems, statistical estimators and metrology, placement and intersection of polygons and polyhedra, and ray shooting and other querytype problems.
Approximation and Exact Algorithms for MinimumWidth Annuli and Shells
"... 1LetSbeasetofnpointsinRd.TheroundnessofS ..."
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Testing the Quality of Manufactured Disks and Cylinders
 IN PROCEEDINGS OF THE NINTH ANNUAL INTERNATIONAL SYMPOSIUM ON ALGORITHMS AND COMPUTATION (ISAAC'98
, 1998
"... We consider the problem of testing the roundness of a manufactured object using the finger probing model of Cole and Yap [2]. When the object being tested is a disk and it's center is known, we describe a procedure which uses O(n) probes and O(n) computation time. (Here n = j1=qj, where q ..."
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Cited by 5 (1 self)
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We consider the problem of testing the roundness of a manufactured object using the finger probing model of Cole and Yap [2]. When the object being tested is a disk and it's center is known, we describe a procedure which uses O(n) probes and O(n) computation time. (Here n = j1=qj, where q is the quality of the object.) When the center of the object is not known, a procedure using O(n) probes and O(n log n) computation time is described. When the object being tested is a cylinder of length l, a procedure is described which uses O(ln²) probes and O(ln 2 log ln) computation time. Lower bounds are also given which show that these procedures are optimal in terms of the number of probes used.
Testing the Quality of Manufactured Balls
, 1998
"... . We consider the problem of testing the roundness of a manufactured ball, using the nger probing model of Cole and Yap [4]. When the center of the object is known, a procedure requiring O(n 2 ) probes and O(n 2 ) computation time is described. (Here n = j1=qj, where q is the quality of the ..."
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Cited by 4 (0 self)
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. We consider the problem of testing the roundness of a manufactured ball, using the nger probing model of Cole and Yap [4]. When the center of the object is known, a procedure requiring O(n 2 ) probes and O(n 2 ) computation time is described. (Here n = j1=qj, where q is the quality of the object.) When the center of the object is not known, the procedure requires O(n 2 ) probes and O(n 4 ) computation time. We also give lower bounds that show that the number of probes used by these procedures is optimal. 1 Introduction The eld of metrology is concerned with measuring the quality of manufactured objects. A basic task in metrology is that of determining whether a given manufactured object is of acceptable quality. Usually this involves probing the surface of the object using a measuring device such as a coordinate measuring machine to get a set S of sample points, and then verifying, algorithmically, how well S approximates an ideal object. A special case of this pr...
A Nearquadratic algorithm for the alphaconnected twocenter decision problem
 Proc. of 14th Canadian Conference on Computational Geometry
"... Given a set S of n points in the plane and a constant α, the alphaconnected twocenter problem is to find two congruent closed disks of the smallest radius covering S, such that the distance of the two centers is at most 2(1 − α)r. We present an O(n 2 log 2 n) expectedtime algorithm for this probl ..."
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Cited by 2 (0 self)
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Given a set S of n points in the plane and a constant α, the alphaconnected twocenter problem is to find two congruent closed disks of the smallest radius covering S, such that the distance of the two centers is at most 2(1 − α)r. We present an O(n 2 log 2 n) expectedtime algorithm for this problem, improving substantially the previous O(n 5)time solution. The algorithm translates the alphaconnected twocenter problem into a distance problem between two circular hulls.
Testing the Quality of Manufactured Disks and Balls ∗
"... We consider the problem of testing the roundness of manufactured disks and balls using the finger probing model of Cole and Yap [6]. The running time of our procedures depends on the quality of the object being considered. Quality is a parameter that is negative when the object is not sufficiently r ..."
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We consider the problem of testing the roundness of manufactured disks and balls using the finger probing model of Cole and Yap [6]. The running time of our procedures depends on the quality of the object being considered. Quality is a parameter that is negative when the object is not sufficiently round and positive when it is. Quality values close to 0 represent objects that are close to the boundary between sufficiently round and insufficiently round. When the object being tested is a disk and its center is known, we describe a procedure that uses O(n) probes and O(n) computation time. (Here n = 1/q, where q is the quality of the object.) When the center of the object is not known, a procedure using O(n) probes and O(n log n) computation time is described. When the object is a ball, we describe a procedure that requires O(n 2) probes and O(n 4) computation time. Lower bounds are also given that show that these procedures are optimal in terms of the number of probes used. These results extend previous results in two directions by relaxing some of the assumptions required by previous results and by extending these results for 3dimensional objects. 1
Exact Construction of MinimumWidth Annulus of Disks in the Plane
"... The construction of a minimumwidth annulus of a set of objects in the plane has useful applications in diverse fields, such as tolerancing metrology and facility location. We present a novel implementation of an algorithm for obtaining a minimumwidth annulus containing a given set of disks in the ..."
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The construction of a minimumwidth annulus of a set of objects in the plane has useful applications in diverse fields, such as tolerancing metrology and facility location. We present a novel implementation of an algorithm for obtaining a minimumwidth annulus containing a given set of disks in the plane, in case one exists. The algorithm extends previously known methods for constructing minimumwidth annuli of sets of points. The algorithm for disks requires the construction of two Voronoi diagrams of different types, one of which we call the “farthestpoint farthestsite” Voronoi diagram and appears not to have been investigated before. The vertices of the overlay of these two diagrams are candidates for the annulus ’ center. The implementation employs an asymptotically nearoptimal randomized divideandconquer algorithm for constructing twodimensional Voronoi diagrams. Our software utilizes components from Cgal, the Computational Geometry Algorithms Library, and follows the exact computation paradigm. We do not assume general position. Namely, we handle degenerate input and produce exact results.
Author manuscript, published in "16th Discrete Geometry for Computer Imagery, Nancy: France (2011)" DOI: 10.1007/9783642198670_30 Optimal Consensus set for Annulus Fitting
, 2012
"... Abstract. An annulus is defined as a set of points contained between two circles. This paper presents a method for fitting an annulus to a given set of points in a 2D images in the presence of noise by maximizing the number of inliers, namely the consensus set, while fixing the thickness. We present ..."
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Abstract. An annulus is defined as a set of points contained between two circles. This paper presents a method for fitting an annulus to a given set of points in a 2D images in the presence of noise by maximizing the number of inliers, namely the consensus set, while fixing the thickness. We present a deterministic algorithm that searches the optimal solution(s) within a time complexity of O(N 4), N being the number of points.