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Primitives for the manipulation of general subdivisions and the computations of Voronoi diagrams
 ACM Tmns. Graph
, 1985
"... The following problem is discussed: Given n points in the plane (the sites) and an arbitrary query point 4, find the site that is closest to q. This problem can be solved by constructing the Voronoi diagram of the given sites and then locating the query point in one of its regions. Two algorithms ar ..."
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Cited by 534 (11 self)
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to the separation of the geometrical and topological aspects of the problem and to the use of two simple but powerful primitives, a geometric predicate and an operator for manipulating the topology of the diagram. The topology is represented by a new data structure for generalized diagrams, that is, embeddings
Computing Dimensionally Parametrized Determinant Formulas
, 1997
"... We are interested in dimensionally parametrized determinant formulas for specially structured matrices. Applications of this question occur in the study of arbitrary dimensional geometric predicates. We will investigate determinant formulas for two important matrix classes and discuss the implementa ..."
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We are interested in dimensionally parametrized determinant formulas for specially structured matrices. Applications of this question occur in the study of arbitrary dimensional geometric predicates. We will investigate determinant formulas for two important matrix classes and discuss
Predication
 COGNITIVE SCIENCE
, 2001
"... In Latent Semantic Analysis (LSA) the meaning of a word is represented as a vector in a highdimensional semantic space. Different meanings of a word or different senses of a word are not distinguished. Instead, word senses are appropriately modified as the word is used in different contexts. In NV ..."
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Cited by 49 (4 self)
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In Latent Semantic Analysis (LSA) the meaning of a word is represented as a vector in a highdimensional semantic space. Different meanings of a word or different senses of a word are not distinguished. Instead, word senses are appropriately modified as the word is used in different contexts. In N
Adaptive Precision FloatingPoint Arithmetic and Fast Robust Geometric Predicates
 Discrete & Computational Geometry
, 1996
"... Exact computer arithmetic has a variety of uses including, but not limited to, the robust implementation of geometric algorithms. This report has three purposes. The first is to offer fast softwarelevel algorithms for exact addition and multiplication of arbitrary precision floatingpoint values. T ..."
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Cited by 169 (5 self)
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Exact computer arithmetic has a variety of uses including, but not limited to, the robust implementation of geometric algorithms. This report has three purposes. The first is to offer fast softwarelevel algorithms for exact addition and multiplication of arbitrary precision floatingpoint values
PREDICATES
"... In this paper we develop a semantic typology of gradable predicates, with special emphasis on deverbal adjectives. We argue for the linguistic relevance of this typology by demonstrating that the distribution and interpretation of degree modifiers is sensitive to its two major classificatory paramet ..."
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In this paper we develop a semantic typology of gradable predicates, with special emphasis on deverbal adjectives. We argue for the linguistic relevance of this typology by demonstrating that the distribution and interpretation of degree modifiers is sensitive to its two major classificatory
Robust Adaptive FloatingPoint Geometric Predicates
 in Proc. 12th Annu. ACM Sympos. Comput. Geom
, 1996
"... Fast C implementations of four geometric predicates, the 2D and 3D orientation and incircle tests, are publicly available. Their inputs are ordinary single or double precision floatingpoint numbers. They owe their speed to two features. First, they employ new fast algorithms for arbitrary precision ..."
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Cited by 58 (2 self)
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Fast C implementations of four geometric predicates, the 2D and 3D orientation and incircle tests, are publicly available. Their inputs are ordinary single or double precision floatingpoint numbers. They owe their speed to two features. First, they employ new fast algorithms for arbitrary
Reliable Geometric Computations With Algebraic Primitives And Predicates
"... this paper. Exact Computation as a Practical Approach. There is no question that EGC is slower than computation relying solely on machine precision arithmetic. The question is whether the slowdown is worth the gain in precision. Indeed, in many scientific or engineering applications the input data ..."
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this paper. Exact Computation as a Practical Approach. There is no question that EGC is slower than computation relying solely on machine precision arithmetic. The question is whether the slowdown is worth the gain in precision. Indeed, in many scientific or engineering applications the input data is inexact, and the question arises whether an exact result is even meaningful. But the main reason for using EGC is not exactness in itself, but rather reliability. A common cause of program failure is that rounding errors lead to inconsistent combinatorial decisions, e.g. about where a point lies with regard to a surface. By making a single interpretation of the data and performing calculations that are consistent with that interpretation, we can avoid this source of failure. Solving the problems of accuracy and consistency is the first step towards a general solution to the robustness problem, which also involves handling degeneracies and special cases
Automatic Generation of Staged Geometric Predicates
, 2002
"... Algorithms in Computational Geometry and Computer Aided Design are often developed for the Real RAM model of computation, which assumes exactness of all the input arguments and operations. In practice, however, the exactness imposes tremendous limitations on the algorithms – even the basic operation ..."
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Cited by 6 (0 self)
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with some estimate of the rounding error, and fall back to exact arithmetic only if this error is too big to determine the sign reliably. A particularly efficient variation on this approach has been used by Shewchuk in his robust implementations of Orient and InSphere geometric predicates. We extend
Realistic Animation of Rigid Bodies
 Computer Graphics Proc. SIGGRAPH
, 1988
"... The theoretical background and implementation for a computer animation system to model a general class of three dimensional dynamic processes for arbitrary rigid bodies is presented. The simulation of the dynamic interaction among rigid bodies takes into account various physical characteristics suc ..."
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Cited by 201 (8 self)
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The theoretical background and implementation for a computer animation system to model a general class of three dimensional dynamic processes for arbitrary rigid bodies is presented. The simulation of the dynamic interaction among rigid bodies takes into account various physical characteris
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