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Results 1 - 10
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166
Helly-type theorems for hollow axis-aligned boxes
- PROC. AMER. MATH. SOC
, 1999
"... A hollow axis-aligned 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 axis-aligned boxes have non-empty intersection, then the whole collection has non-empty intersection; and if any 5 of a collection of hollow ..."
Abstract
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Cited by 2 (2 self)
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A hollow axis-aligned 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 axis-aligned boxes have non-empty intersection, then the whole collection has non-empty intersection; and if any 5 of a collection
Towards Faster Linear-Sized Nets for Axis-Aligned Boxes in the Plane
, 2005
"... Let B be any set of n axis-aligned 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-dimension ..."
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Let B be any set of n axis-aligned 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 Free-Space Detection for Packing Algorithms
"... We present easy-to-implement incremental algorithms for computing the union of axis-aligned boxes. These algorithms can effectively be used for the implementa-tion 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 easy-to-implement incremental algorithms for computing the union of axis-aligned boxes. These algorithms can effectively be used for the implementa-tion 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 SHEAR-WARP 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 brute-force techniques that req ..."
Abstract
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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 axis-aligned boxes). The new scanline-order algorithm simply streams through the volume and the image in storage order. We describe variants of the algorithm for both parallel and perspective
Fast almost-linear-sized nets for boxes in the plane
"... Let B be any set of n axis-aligned 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 ..."
Abstract
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Cited by 2 (0 self)
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Let B be any set of n axis-aligned 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 almost-linear-sized nets for boxes in the plane Herve ́ Brönnimann∗
"... Let B be any set of n axis-aligned 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 ..."
Abstract
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Let B be any set of n axis-aligned 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 AXIS-ALIGNED BOUNDING BOX FOR OPENGL 3D VIRTUAL ENVIRONMENT
"... ABSTRACT This paper describes a simple and straight forward implementation of Axis-Aligned Bounding-Box (AABB) for OpenGL 3-Dimensional (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 Axis-Aligned Bounding-Box (AABB) for OpenGL 3-Dimensional (3D) virtual environment for games and simulation purpose. The implementation of AABB is conducted in OpenGL graphic library version 1.2 with C++ programming
Box-Trees for Collision Checking in Industrial Installations
, 2002
"... A box-tree is a bounding-volume hierarchy that uses axis-aligned boxes as bounding volumes. We describe a new algorithm to construct a box-tree for objects in a 3D scene, and we analyze its worst-case query time for approximate range queries. If the input scene has certain characteristics that we ..."
Abstract
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Cited by 7 (4 self)
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A box-tree is a bounding-volume hierarchy that uses axis-aligned boxes as bounding volumes. We describe a new algorithm to construct a box-tree for objects in a 3D scene, and we analyze its worst-case query time for approximate range queries. If the input scene has certain characteristics
Parallel Multi-Core Geometric Algorithms in CGAL
"... We describe an approach to efficiently use multiple processing cores and shared memory for several geometric algorithms. The d-dimensional algorithms we target are (a) spatial sorting of points, (b) kd-tree construction, (c) axis-aligned 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 d-dimensional algorithms we target are (a) spatial sorting of points, (b) kd-tree construction, (c) axis-aligned box intersection computation, and finally (d) bulk insertion
Box-Trees and R-trees with Near-Optimal Query Time
, 2001
"... A box-tree is a bounding-volume hierarchy that uses axis-aligned boxes as bounding volumes. The query complexity of a box-tree 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-trees with ..."
Abstract
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Cited by 28 (6 self)
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A box-tree is a bounding-volume hierarchy that uses axis-aligned boxes as bounding volumes. The query complexity of a box-tree 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
