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Hellytype theorems for hollow axisaligned boxes
 PROC. AMER. MATH. SOC
, 1999
"... A hollow axisaligned box is the boundary of the cartesian product of d compact intervals in R d. We show that for d ≥ 3, if any 2 d of a collection of hollow axisaligned boxes have nonempty intersection, then the whole collection has nonempty intersection; and if any 5 of a collection of hollow ..."
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Cited by 2 (2 self)
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A hollow axisaligned box is the boundary of the cartesian product of d compact intervals in R d. We show that for d ≥ 3, if any 2 d of a collection of hollow axisaligned boxes have nonempty intersection, then the whole collection has nonempty intersection; and if any 5 of a collection
Towards Faster LinearSized Nets for AxisAligned Boxes in the Plane
"... Abstract. Let B be any set of n axisaligned boxes in R d, d ≥ 1. We call a subset N ⊆ B a(1/c)net for B if any p ∈ R d contained in more than n/c boxes of B must be contained in a box of N, or equivalently if a point not contained in any box in N can only stab at most n/c boxes of B. General VCdi ..."
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Abstract. Let B be any set of n axisaligned boxes in R d, d ≥ 1. We call a subset N ⊆ B a(1/c)net for B if any p ∈ R d contained in more than n/c boxes of B must be contained in a box of N, or equivalently if a point not contained in any box in N can only stab at most n/c boxes of B. General VC
Dynamic FreeSpace Detection for Packing Algorithms
"... We present easytoimplement incremental algorithms for computing the union of axisaligned boxes. These algorithms can effectively be used for the implementation of packing algorithms which try to fit differently sized axis aligned boxes into a container modelled as a fixed point cloud. 1 ..."
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We present easytoimplement incremental algorithms for computing the union of axisaligned boxes. These algorithms can effectively be used for the implementation of packing algorithms which try to fit differently sized axis aligned boxes into a container modelled as a fixed point cloud. 1
FAST VOLUME RENDERING USING A SHEARWARP FACTORIZATION OF THE VIEWING TRANSFORMATION
, 1995
"... Volume rendering is a technique for visualizing 3D arrays of sampled data. It has applications in areas such as medical imaging and scientific visualization, but its use has been limited by its high computational expense. Early implementations of volume rendering used bruteforce techniques that req ..."
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Cited by 541 (2 self)
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casting algorithms because the latter must perform analytic geometry calculations (e.g. intersecting rays with axisaligned boxes). The new scanlineorder algorithm simply streams through the volume and the image in storage order. We describe variants of the algorithm for both parallel and perspective
Fast almostlinearsized nets for boxes in the plane
"... Let B be any set of n axisaligned boxes in R d, d ≥ 1. For any point p, we define the subset Bp of B as Bp = {B ∈ B: p ∈ B}. A box B in Bp is said to be stabbed by p. A subset N ⊆ B is a (1/c)net ..."
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Cited by 2 (0 self)
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Let B be any set of n axisaligned boxes in R d, d ≥ 1. For any point p, we define the subset Bp of B as Bp = {B ∈ B: p ∈ B}. A box B in Bp is said to be stabbed by p. A subset N ⊆ B is a (1/c)net
Fast almostlinearsized nets for boxes in the plane Herve ́ Brönnimann∗
"... Let B be any set of n axisaligned boxes in Rd, d ≥ 1. For any point p, we define the subset Bp of B as Bp = {B ∈ B: p ∈ B}. A box B in Bp is said to be stabbed by p. A subset N ⊆ B is a (1/c)net ..."
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Let B be any set of n axisaligned boxes in Rd, d ≥ 1. For any point p, we define the subset Bp of B as Bp = {B ∈ B: p ∈ B}. A box B in Bp is said to be stabbed by p. A subset N ⊆ B is a (1/c)net
Optimal Spanners for AxisAligned Rectangles
, 2004
"... this paper: we assume the topology of the network (the bridge graph) is given, and our only task is to place the bridges so as to minimize the dilation ..."
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Cited by 4 (2 self)
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this paper: we assume the topology of the network (the bridge graph) is given, and our only task is to place the bridges so as to minimize the dilation
Cuttings for Disks and AxisAligned Rectangles in ThreeSpace
"... We present new asymptotically tight bounds on cuttings, a fundamental data structure in computational geometry. For n objects in space and a parameter r ∈ N, an 1 rcutting is a covering of the space with simplices such that the interior of each simplex intersects at most n/rcutting of objects. For ..."
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. For n pairwise disjoint disks in R3 and a parameter r ∈ N, we construct a 1 r size O(r2). For n axisaligned rectangles in R3, we construct a 1 rcutting of size O(r3/2). As an application related to multipoint location in threespace, we present tight bounds on the cost of spanning trees across
Computing MinimumVolume Enclosing AxisAligned Ellipsoids
, 2007
"... Abstract Given a set of points S ={x 1,...,x m}⊂R n and ɛ>0, we propose and analyze an algorithm for the problem of computing a (1 + ɛ)approximation to the minimumvolume axisaligned ellipsoid enclosing S. We establish that our algorithm is polynomial for fixed ɛ. In addition, the algorithm ret ..."
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Abstract Given a set of points S ={x 1,...,x m}⊂R n and ɛ>0, we propose and analyze an algorithm for the problem of computing a (1 + ɛ)approximation to the minimumvolume axisaligned ellipsoid enclosing S. We establish that our algorithm is polynomial for fixed ɛ. In addition, the algorithm
Computing Minimum Volume Enclosing AxisAligned Ellipsoids
, 2006
"... Given a set of points S = {x 1,..., x m} ⊂ R n and ɛ> 0, we propose and analyze an algorithm for the problem of computing a (1 + ɛ)approximation to the the minimum volume axisaligned ellipsoid enclosing S. We establish that our algorithm is polynomial for fixed ɛ. In addition, the algorithm re ..."
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Given a set of points S = {x 1,..., x m} ⊂ R n and ɛ> 0, we propose and analyze an algorithm for the problem of computing a (1 + ɛ)approximation to the the minimum volume axisaligned ellipsoid enclosing S. We establish that our algorithm is polynomial for fixed ɛ. In addition, the algorithm
Results 1  10
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131,685