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Applications of geometric
"... discrepancy in numerical analysis and statistics Josef Dick∗ In this paper we discuss various connections between geometric discrepancy measures, such as discrepancy with respect to convex sets (and convex sets with smooth boundary in particular), and applications to numerical analysis and statisti ..."
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discrepancy in numerical analysis and statistics Josef Dick∗ In this paper we discuss various connections between geometric discrepancy measures, such as discrepancy with respect to convex sets (and convex sets with smooth boundary in particular), and applications to numerical analysis
Point sets on the sphere S2 with small spherical cap discrepancy
 Discrete Comput. Geom
"... Abstract. In this paper we study the geometric discrepancy of explicit constructions of uniformly distributed points on the twodimensional unit sphere. We show that the spherical cap discrepancy of random point sets, of spherical digital nets and of spherical Fibonacci lattices converges with order ..."
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Cited by 4 (1 self)
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Abstract. In this paper we study the geometric discrepancy of explicit constructions of uniformly distributed points on the twodimensional unit sphere. We show that the spherical cap discrepancy of random point sets, of spherical digital nets and of spherical Fibonacci lattices converges
Bounds for the average L pextreme and the L ∞extreme discrepancy
"... The extreme or unanchored discrepancy is the geometric discrepancy of point sets in the ddimensional unit cube with respect to the set system of axisparallel boxes. For 2 ≤ p< ∞ we provide upper bounds for the average L pextreme discrepancy. With these bounds we are able to derive upper bounds ..."
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The extreme or unanchored discrepancy is the geometric discrepancy of point sets in the ddimensional unit cube with respect to the set system of axisparallel boxes. For 2 ≤ p< ∞ we provide upper bounds for the average L pextreme discrepancy. With these bounds we are able to derive upper
Hierarchical Image Caching for Accelerated Walkthroughs of Complex Environments
, 1996
"... We present a new method that utilizes path coherence to accelerate walkthroughs of geometrically complex static scenes. As a preprocessing step, our method constructs a BSPtree that hierarchically partitions the geometric primitives in the scene. In the course of a walkthrough, images of nodes at v ..."
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Cited by 184 (10 self)
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We present a new method that utilizes path coherence to accelerate walkthroughs of geometrically complex static scenes. As a preprocessing step, our method constructs a BSPtree that hierarchically partitions the geometric primitives in the scene. In the course of a walkthrough, images of nodes
Finding the Discrepancy of MRI images using the Second Moment and Geometric Comparison Techniques
"... This research investigates the technique of image subtraction to find the discrepancy between healthy and illness MRI images. The technique developed in this research moves the healthy MRI image to overlap with the illness MRI image. Then, the two MRI images are aligned to the same orientation. Afte ..."
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This research investigates the technique of image subtraction to find the discrepancy between healthy and illness MRI images. The technique developed in this research moves the healthy MRI image to overlap with the illness MRI image. Then, the two MRI images are aligned to the same orientation
Solving some discrepancy problems in NC
, 1997
"... We show that several discrepancylike problems can be solved in NC 2 nearly achieving the corresponding sequential bounds. For example, given a set system (X; S), where X is a ground set and S ` 2 X , a set R ` X can be computed in NC 2 so that, for each S 2 S, the discrepancy jjR " Sj \ ..."
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Cited by 4 (0 self)
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improve are lattice approximation, fflapproximations of range spaces of bounded VCexponent, sampling in geometric configuration spaces, and approximation of integer linear programs. 1 Introduction Problem and previous work. Discrepancy is an important concept in combinatorics, see e.g. [1, 5
Computing the maximum bichromatic discrepancy, with applications to computer graphics and machine learning
 J. Computer and Systems Sciences
, 1996
"... Computing the maximum bichromatic discrepancy is an interesting theoretical problem with important applications in computational learning theory, computational geometry and computer graphics. In this paper we give algorithms to compute the maximum bichromatic discrepancy for simple geometric ranges, ..."
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Cited by 36 (6 self)
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Computing the maximum bichromatic discrepancy is an interesting theoretical problem with important applications in computational learning theory, computational geometry and computer graphics. In this paper we give algorithms to compute the maximum bichromatic discrepancy for simple geometric ranges
Using LowDiscrepancy Sequences and the Crofton Formula to Compute Surface Areas of Geometric Models
, 2002
"... The surface area of a geometric model, like its volume, is an important integral property that needs to be evaluated frequently and accurately in practice. In this paper we present a new quasiMonte Carlo method using lowdiscrepancy sequences for computing the surface area of a 3D object. We sh ..."
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Cited by 11 (3 self)
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The surface area of a geometric model, like its volume, is an important integral property that needs to be evaluated frequently and accurately in practice. In this paper we present a new quasiMonte Carlo method using lowdiscrepancy sequences for computing the surface area of a 3D object. We
Geometric Potential
"... Following rapidly changing target objects is a challenging problem in fluid control, especially when the natural fluid motion should be preserved. The fluid should be responsive to the changing configuration of the target and, at the same time, its motion should not be overconstrained. In this paper ..."
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. In this paper, we introduce an efficient and effective solution by applying two different external force fields. The first one is a feedback force field which compensates for discrepancies in both shape and velocity. Its shape component is designed to be divergence free so that it can survive the velocity
LowDiscrepancy Sequences for Volume Properties in Solid Modelling
"... This paper investigates the use of lowdiscrepancy sequences for computing volume integrals in geometric modelling. An introduction to lowdiscrepancy point sequences is presented which explains how they can be used to replace random points in Monte Carlo methods. The relative advantages of usi ..."
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Cited by 5 (1 self)
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This paper investigates the use of lowdiscrepancy sequences for computing volume integrals in geometric modelling. An introduction to lowdiscrepancy point sequences is presented which explains how they can be used to replace random points in Monte Carlo methods. The relative advantages
Results 11  20
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317