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On the boundary of the union of planar convex sets
 Discrete Comput. Geom
, 1999
"... We give two alternative proofs leading to dierent generalizations of the following theorem of [1]. Given n convex sets in the plane, such that the boundaries of each pair of sets cross at most twice, then the boundary of their union consists of at most 6n 12 arcs. (An arc is a connected piece of th ..."
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Cited by 2 (1 self)
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We give two alternative proofs leading to dierent generalizations of the following theorem of [1]. Given n convex sets in the plane, such that the boundaries of each pair of sets cross at most twice, then the boundary of their union consists of at most 6n 12 arcs. (An arc is a connected piece
INEQUALITIES FOR LATTICE CONSTRAINED PLANAR CONVEX SETS
"... ABSTRACT. Every convex set in the plane gives rise to geometric functionals such as the area, perimeter, diameter, width, inradius and circumradius. In this paper, we prove new inequalities involving these geometric functionals for planar convex sets containing zero or one interior lattice point. We ..."
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ABSTRACT. Every convex set in the plane gives rise to geometric functionals such as the area, perimeter, diameter, width, inradius and circumradius. In this paper, we prove new inequalities involving these geometric functionals for planar convex sets containing zero or one interior lattice point
Chords Halving The Area Of A Planar Convex Set
, 2005
"... Let K be a compact convex set in the plane. A halving chord of K is a line segment pp, p, p #K, which divides the area of K into two equal parts. For every direction v there exists exactly one halving chord. Its length hA (v) is the corresponding (area) halving distance. In this article we g ..."
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Cited by 4 (2 self)
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Let K be a compact convex set in the plane. A halving chord of K is a line segment pp, p, p #K, which divides the area of K into two equal parts. For every direction v there exists exactly one halving chord. Its length hA (v) is the corresponding (area) halving distance. In this article we
Inscribing an axially symmetric polygon and other approximation algorithms for planar convex sets
 Comput. Geom. Theory Appl
"... Abstract Given a planar convex set C, we give sublinear approximation algorithms to determine approximations of the largest axially symmetric convex set S contained in C, and the smallest such set S that contains C. More precisely, for any ε > 0, we find an axially symmetric convex polygon Q ⊂ C ..."
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Cited by 6 (5 self)
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Abstract Given a planar convex set C, we give sublinear approximation algorithms to determine approximations of the largest axially symmetric convex set S contained in C, and the smallest such set S that contains C. More precisely, for any ε > 0, we find an axially symmetric convex polygon Q
DISTANCES SETS THAT ARE A SHIFT OF THE INTEGERS AND FOURIER BASIS FOR PLANAR CONVEX SETS
, 709
"... Abstract. The aim of this paper is to prove that if a planar set A has a difference set ∆(A) satisfying ∆(A) ⊂ Z + + s for suitable s than A has at most 3 elements. This result is motivated by the conjecture that the disk has not more than 3 orthogonal exponentials. Further, we prove that if A is a ..."
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Abstract. The aim of this paper is to prove that if a planar set A has a difference set ∆(A) satisfying ∆(A) ⊂ Z + + s for suitable s than A has at most 3 elements. This result is motivated by the conjecture that the disk has not more than 3 orthogonal exponentials. Further, we prove that if A
Maximizing the Overlap of Two Planar Convex Sets under Rigid Motions
, 2006
"... Given two compact convex sets P and Q in the plane, we compute an image of P under a rigid motion that approximately maximizes the overlap with Q. More precisely, for any ε> 0, we compute a rigid motion such that the area of overlap is at least 1−ε times the maximum possible overlap. Our algorith ..."
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Cited by 12 (5 self)
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Given two compact convex sets P and Q in the plane, we compute an image of P under a rigid motion that approximately maximizes the overlap with Q. More precisely, for any ε> 0, we compute a rigid motion such that the area of overlap is at least 1−ε times the maximum possible overlap. Our
The Quickhull algorithm for convex hulls
 ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE
, 1996
"... The convex hull of a set of points is the smallest convex set that contains the points. This article presents a practical convex hull algorithm that combines the twodimensional Quickhull Algorithm with the generaldimension BeneathBeyond Algorithm. It is similar to the randomized, incremental algo ..."
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Cited by 713 (0 self)
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The convex hull of a set of points is the smallest convex set that contains the points. This article presents a practical convex hull algorithm that combines the twodimensional Quickhull Algorithm with the generaldimension BeneathBeyond Algorithm. It is similar to the randomized, incremental
Exact Matrix Completion via Convex Optimization
, 2008
"... We consider a problem of considerable practical interest: the recovery of a data matrix from a sampling of its entries. Suppose that we observe m entries selected uniformly at random from a matrix M. Can we complete the matrix and recover the entries that we have not seen? We show that one can perfe ..."
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Cited by 873 (26 self)
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perfectly recover most lowrank matrices from what appears to be an incomplete set of entries. We prove that if the number m of sampled entries obeys m ≥ C n 1.2 r log n for some positive numerical constant C, then with very high probability, most n × n matrices of rank r can be perfectly recovered
Convex Position Estimation in Wireless Sensor Networks
"... A method for estimating unknown node positions in a sensor network based exclusively on connectivityinduced constraints is described. Known peertopeer communication in the network is modeled as a set of geometric constraints on the node positions. The global solution of a feasibility problem fo ..."
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Cited by 493 (0 self)
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A method for estimating unknown node positions in a sensor network based exclusively on connectivityinduced constraints is described. Known peertopeer communication in the network is modeled as a set of geometric constraints on the node positions. The global solution of a feasibility problem
Results 1  10
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14,654