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166
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
, 2005
"... 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 VCdimension ..."
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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 542 (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
IMPLEMENTATION OF AXISALIGNED BOUNDING BOX FOR OPENGL 3D VIRTUAL ENVIRONMENT
"... ABSTRACT This paper describes a simple and straight forward implementation of AxisAligned BoundingBox (AABB) for OpenGL 3Dimensional (3D) virtual environment for games and simulation purpose. The implementation of AABB is conducted in OpenGL graphic library version 1.2 with C++ programming langu ..."
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ABSTRACT This paper describes a simple and straight forward implementation of AxisAligned BoundingBox (AABB) for OpenGL 3Dimensional (3D) virtual environment for games and simulation purpose. The implementation of AABB is conducted in OpenGL graphic library version 1.2 with C++ programming
BoxTrees for Collision Checking in Industrial Installations
, 2002
"... A boxtree is a boundingvolume hierarchy that uses axisaligned boxes as bounding volumes. We describe a new algorithm to construct a boxtree for objects in a 3D scene, and we analyze its worstcase query time for approximate range queries. If the input scene has certain characteristics that we ..."
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Cited by 7 (4 self)
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A boxtree is a boundingvolume hierarchy that uses axisaligned boxes as bounding volumes. We describe a new algorithm to construct a boxtree for objects in a 3D scene, and we analyze its worstcase query time for approximate range queries. If the input scene has certain characteristics
Parallel MultiCore Geometric Algorithms in CGAL
"... We describe an approach to efficiently use multiple processing cores and shared memory for several geometric algorithms. The ddimensional algorithms we target are (a) spatial sorting of points, (b) kdtree construction, (c) axisaligned box intersection computation, and finally (d) bulk insertion o ..."
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We describe an approach to efficiently use multiple processing cores and shared memory for several geometric algorithms. The ddimensional algorithms we target are (a) spatial sorting of points, (b) kdtree construction, (c) axisaligned box intersection computation, and finally (d) bulk insertion
BoxTrees and Rtrees with NearOptimal Query Time
, 2001
"... A boxtree is a boundingvolume hierarchy that uses axisaligned boxes as bounding volumes. The query complexity of a boxtree with respect to a given type of query is the maximum number of nodes visited when answering such a query. We describe several new algorithms for constructing boxtrees with ..."
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Cited by 28 (6 self)
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A boxtree is a boundingvolume hierarchy that uses axisaligned boxes as bounding volumes. The query complexity of a boxtree with respect to a given type of query is the maximum number of nodes visited when answering such a query. We describe several new algorithms for constructing box
Results 1  10
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166