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17
Approximating Polygons and Subdivisions with MinimumLink Paths
, 1991
"... We study several variations on one basic approach to the task of simplifying a plane polygon or subdivision: Fatten the given object and construct an approximation inside the fattened region. We investigate fattening by convolving the segments or vertices with disks and attempt to approximate object ..."
Abstract

Cited by 63 (12 self)
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We study several variations on one basic approach to the task of simplifying a plane polygon or subdivision: Fatten the given object and construct an approximation inside the fattened region. We investigate fattening by convolving the segments or vertices with disks and attempt to approximate objects with the minimum number of line segments, or with near the minimum, by using efficient greedy algorithms. We give some variants that have linear or O(n log n) algorithms approximating polygonal chains of n segments. We also show that approximating subdivisions and approximating with chains with no selfintersections are NPhard.
Computing the maximum bichromatic discrepancy, with applications to computer graphics and machine learning
 Journal of Computer and Systems Sciences
, 1996
"... ..."
Spaceefficient planar convex hull algorithms
 Proc. Latin American Theoretical Informatics
, 2002
"... A spaceefficient algorithm is one in which the output is given in the same location as the input and only a small amount of additional memory is used by the algorithm. We describe four spaceefficient algorithms for computing the convex hull of a planar point set. ..."
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Cited by 19 (1 self)
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A spaceefficient algorithm is one in which the output is given in the same location as the input and only a small amount of additional memory is used by the algorithm. We describe four spaceefficient algorithms for computing the convex hull of a planar point set.
Maintaining the Approximate Width of a Set of Points in the Plane (Extended Abstract)
, 1993
"... The width of a set of n points in the plane is the smallest distance between two parallel lines that enclose the set. We maintain the set of points under insertions and deletions of points and we are able to report an approximation of the width of this dynamic point set. Our data structure takes lin ..."
Abstract

Cited by 12 (1 self)
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The width of a set of n points in the plane is the smallest distance between two parallel lines that enclose the set. We maintain the set of points under insertions and deletions of points and we are able to report an approximation of the width of this dynamic point set. Our data structure takes linear space and allows for reporting the approximation with relative accuracy ffl in O( p 1=ffl log n) time; and the update time is O(log² n). The method uses the tentative pruneandsearch strategy of Kirkpatrick and Snoeyink.
Determining the Convex Hull in Large Multidimensional Databases
, 2001
"... Determining the convex hull of a point set is a basic operation for many applications of pattern recognition, image processing, statistics, and data mining. ..."
Abstract

Cited by 12 (1 self)
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Determining the convex hull of a point set is a basic operation for many applications of pattern recognition, image processing, statistics, and data mining.
Parallel Computational Geometry: An approach using randomization
 IN HANDBOOK OF COMPUTATIONAL GCOMETRY, EDITED BY J.R. SACK AND
, 1998
"... We describe very general methods for designing efficient parallel algorithms for problems in computational geometry. Although our main focus is the PRAM, we provide strong evidence that these techniques yield equally efficient algorithms in more concrete computing models like Butterfly networks. ..."
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Cited by 5 (0 self)
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We describe very general methods for designing efficient parallel algorithms for problems in computational geometry. Although our main focus is the PRAM, we provide strong evidence that these techniques yield equally efficient algorithms in more concrete computing models like Butterfly networks. The algorithms exploit random sampling and randomized techniques that result in very general strategies for solving a wide class of fundamental problems from computational geometry like convex hulls, voronoi diagrams, triangulation, pointlocation and arrangements. Our description emphasizes the algorithmic techniques rather than a detailed treatment of the individual problems.
Optimal inplace planar convex hull algorithms
 Proceedings of Latin American Theoretical Informatics (LATIN 2002), volume 2286 of Lecture Notes in Computer Science
, 2002
"... An inplace algorithm is one in which the output is given in the same location as the input and only a small amount of additional memory is used by the algorithm. In this paper we describe three inplace algorithms for computing the convex hull of a planar point set. All three algorithms are optima ..."
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Cited by 4 (2 self)
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An inplace algorithm is one in which the output is given in the same location as the input and only a small amount of additional memory is used by the algorithm. In this paper we describe three inplace algorithms for computing the convex hull of a planar point set. All three algorithms are optimal, some more so than others...
Computation on parametric curves with an application in grasping
 International Journal of Robotics Research
"... Curved shapes are frequent subjects of maneuvers by the human hand. In robotics it is well known that antipodal grasps exist on curved objects and guarantee force closure under proper finger contact conditions. This paper presents an efficient algorithm that computes, up to numerical resolution, all ..."
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Cited by 2 (1 self)
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Curved shapes are frequent subjects of maneuvers by the human hand. In robotics it is well known that antipodal grasps exist on curved objects and guarantee force closure under proper finger contact conditions. This paper presents an efficient algorithm that computes, up to numerical resolution, all pairs of antipodal points on a simple, closed, and twice continuously differentiable plane curve. Dissecting the curve into segments everywhere convex or everywhere concave, the algorithm marches simultaneously on a pair of such segments with provable convergence and interleaves marching with numerical bisection recursively. It makes use of new insights into the differential geometry at two antipodal points. We have avoided resorting to traditional nonlinear programming which would neither be quite as efficient nor guarantee to find all antipodal points. A byproduct of our result is a procedure that constructs all common tangent lines of two curves, achieving quadratic convergence rate. Dissection and the coupling of marching with bisection constitute an algorithm design scheme potentially applicable to computational problems involving curves and curved shapes. KEY WORDS—antipodal point, antipodal angle, inflection, monotonicity, common tangent, convergence rate, robot grasping 1
SpaceEfficient Planar Convex Hull Algorithms
"... A spaceefficient algorithm is one in which the output is given in the same location as the input and only a small amount of additional memory is used by the algorithm. We describe four spaceefficient algorithms for computing the convex hull of a planar point set. ..."
Abstract
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A spaceefficient algorithm is one in which the output is given in the same location as the input and only a small amount of additional memory is used by the algorithm. We describe four spaceefficient algorithms for computing the convex hull of a planar point set.
Maintaining the Approximate Width of a Set of Points in the Plane �
"... Jack Snoeyink x The width of a set of n points in the plane is the smallest distance between two parallel lines that enclose the set. We maintain the set of points under insertions and deletions of points and we are able to report an approximation of the width of this dynamic point set. Our data str ..."
Abstract
 Add to MetaCart
Jack Snoeyink x The width of a set of n points in the plane is the smallest distance between two parallel lines that enclose the set. We maintain the set of points under insertions and deletions of points and we are able to report an approximation of the width of this dynamic point set. Our data structure takes linear space and allows for reporting the approximation with relative accuracy � in O � p 1= � log n � time; and the update time is O�log 2 n�. The method uses the tentative pruneandsearch strategy of Kirkpatrick and Snoeyink. 1