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Radiance Interpolants for Accelerated BoundedError Ray Tracing
 ACM Transactions on Graphics
, 1999
"... this paper, we present a system that exploits objectspace, rayspace, imagespace and temporal coherence to accelerate ray tracing. Our system uses persurface interpolants to approximate radiance, while conservatively bounding error. The techniques we introduce in this paper should enhance both int ..."
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Cited by 53 (5 self)
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this paper, we present a system that exploits objectspace, rayspace, imagespace and temporal coherence to accelerate ray tracing. Our system uses persurface interpolants to approximate radiance, while conservatively bounding error. The techniques we introduce in this paper should enhance both interactive and batch ray tracers.
Computation and Application of Taylor Polynomials with Interval Remainder Bounds
 Reliable Computing
, 1998
"... . The expansion of complicated functions of many variables in Taylor polynomials is an important problem for many applications, and in practice can be performed rather conveniently (even to high orders) using polynomial algebras. An important application of these methods is the field of beam physics ..."
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Cited by 34 (2 self)
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. The expansion of complicated functions of many variables in Taylor polynomials is an important problem for many applications, and in practice can be performed rather conveniently (even to high orders) using polynomial algebras. An important application of these methods is the field of beam physics, where often expansions in about six variables to orders between five and ten are used. However, often it is necessary to also know bounds for the remainder term of the Taylor formula if the arguments lie within certain intervals. In principle such bounds can be obtained by interval bounding of the (n+1)st derivative, which in turn can be obtained with polynomial algebra; but in practice the method is rather inefficient and susceptible to blowup because of the need of repeated interval evaluations of the derivative. Here we present a new method that allows the computation of sharp remainder intervals in parallel with the accumulation derivatives up to order n. The method is useful for a...
Adaptive Enumeration of Implicit Surfaces with Affine Arithmetic
 Computer Graphics Forum
, 1996
"... . We discuss adaptive enumeration and rendering methods for implicit surfaces, using octrees computed with affine arithmetic, a new tool for range analysis. Affine arithmetic is similar to standard interval arithmetic, but takes into account correlations between operands and subformulas, generally ..."
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Cited by 30 (15 self)
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. We discuss adaptive enumeration and rendering methods for implicit surfaces, using octrees computed with affine arithmetic, a new tool for range analysis. Affine arithmetic is similar to standard interval arithmetic, but takes into account correlations between operands and subformulas, generally providing much tighter bounds for the computed quantities. The resulting octrees are accordingly much smaller, and the rendering faster. We also describe applications of affine arithmetic to intersection and ray tracing of implicit surfaces. keywords: cellular models, interval analysis, rendering, implicit surfaces. 1 Introduction Implicit surfaces have recently become popular in computer graphics and solid modeling. In order to exploit existing hardware and algorithms, it is often necessary to approximate such surfaces by models with simpler geometry, such as polygonal meshes or voxel arrays. Let S be a surface defined implicitly by the equation h(x; y; z) = 0. A simple and general techn...
Granular Computing: An Emerging Paradigm
, 2001
"... We provide an overview of Granular Computing a rapidly growing area of information processing aimed at the construction of intelligent systems. We highlight the main features of Granular Computing, elaborate on the underlying formalisms of information granulation and discuss ways of their developme ..."
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Cited by 19 (0 self)
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We provide an overview of Granular Computing a rapidly growing area of information processing aimed at the construction of intelligent systems. We highlight the main features of Granular Computing, elaborate on the underlying formalisms of information granulation and discuss ways of their development. We also discuss the concept of granular modeling and present the issues of communication between formal frameworks of Granular Computing. © 2007 World Academic Press, UK. All rights reserved.
Surface Intersection Using Affine Arithmetic
 In Graphics Interface
, 1996
"... We describe a variant of a domain decomposition method proposed by Gleicher and Kass for intersecting and trimming parametric surfaces. Instead of using interval arithmetic to guide the decomposition, the variant described here uses affine arithmetic, a tool recently proposed for range analysis. Aff ..."
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Cited by 18 (7 self)
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We describe a variant of a domain decomposition method proposed by Gleicher and Kass for intersecting and trimming parametric surfaces. Instead of using interval arithmetic to guide the decomposition, the variant described here uses affine arithmetic, a tool recently proposed for range analysis. Affine arithmetic is similar to standard interval arithmetic, but takes into account correlations between operands and subformulas, generally providing much tighter bounds for the computed quantities. As a consequence, the quadtree domain decompositions are much smaller and the intersection algorithm runs faster. keywords: surface intersection, trimming surfaces, range analysis, interval analysis, CAGD.
Mean Value Analysis for Queueing Network Models with Intervals as Input Parameters
, 1998
"... Mean value analysis (MVA) is a wellknown solution technique for separable closed queueing networks used in performance modeling of computer and communication systems. In many cases, like for sensitivity analysis or with inaccurate model input parameters, intervals are more appropriate as model inpu ..."
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Cited by 14 (12 self)
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Mean value analysis (MVA) is a wellknown solution technique for separable closed queueing networks used in performance modeling of computer and communication systems. In many cases, like for sensitivity analysis or with inaccurate model input parameters, intervals are more appropriate as model inputs than single values. This paper presents a version of the MVA algorithm for separable closed queueing networks with one customer class consisting of loadindependent queueing centers as well as delay devices, which accepts both single values and intervals as input parameters in arbitrary combination. Monotonicity of the model outputs with respect to all input parameters is proved and these monotonicity properties are used to construct a low cost intervalversion of the MVA algorithm providing exact output intervals as results. Thus, dependency problems commonly arising with the interval evaluation of arithmetic expressions are avoided without significant increase in computation costs. Addit...
Automatic Computation of a Linear Interval Enclosure
 Reliable Computing
, 2001
"... Abstract. Recently, an alternative interval approximation F ( X) for enclosing a factorable function f(x) in a given box X has been suggested. The enclosure is in the form of an affine interval function n i=1 F ( X) = a X + B where only the additive term B is an interval, the coefficients ai being r ..."
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Cited by 14 (6 self)
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Abstract. Recently, an alternative interval approximation F ( X) for enclosing a factorable function f(x) in a given box X has been suggested. The enclosure is in the form of an affine interval function n i=1 F ( X) = a X + B where only the additive term B is an interval, the coefficients ai being real i i numbers. The approximation is applicable to continuously differentiable, continuous and even discontinuous functions. In this paper, a new algorithm for determining the coefficients ai and the interval B of F(X) is proposed. It is based on the introduction of a specific generalized representation of intervals which permits the computation of the enclosure considered to be fully automated. 1.
Towards Practical Interval Constraint Solving in Logic Programming
 IN LOGIC PROGRAMMING: PROCEEDINGS OF THE 1994 INTERNATIONAL SYMPOSIUM
, 1994
"... Existing interval constraint logic programming languages, such as BNR Prolog, work under the framework of interval narrowing and are deficient in solving linear systems, which constitute an important class of problems in engineering and other applications. In this paper, an interval linear equality ..."
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Cited by 13 (3 self)
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Existing interval constraint logic programming languages, such as BNR Prolog, work under the framework of interval narrowing and are deficient in solving linear systems, which constitute an important class of problems in engineering and other applications. In this paper, an interval linear equality solver, which is based on generalized interval arithmetic and Gaussian elimination, is proposed. We show how the solver can be adapted to incremental execution and incorporated into a constraint logic programming language already equipped with a nonlinear solver based on interval narrowing. The two solvers interact and cooperate during computation, resulting in a practical interval constraint arithmetic language CIAL. A prototype of CIAL, based on CLP(R), is constructed and compared favourably against several major constraint logic programming languages.
Performance Prediction and Scheduling for Parallel Applications on MultiUser Clusters
, 1998
"... ..."
Interval Linear Constraint Solving Using the Preconditioned Interval GaussSeidel Method
 IN PROCEEDINGS OF THE TWELFTH INTERNATIONAL CONFERENCE ON LOGIC PROGRAMMING, LOGIC PROGRAMMING
, 1994
"... We propose the use of the preconditioned interval GaussSeidel method as the backbone of an efficient linear equality solver in a CLP(Interval) language. The method, as originally designed, works only on linear systems with square coefficient matrices. Even imposing such a restriction, a naive incor ..."
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Cited by 12 (1 self)
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We propose the use of the preconditioned interval GaussSeidel method as the backbone of an efficient linear equality solver in a CLP(Interval) language. The method, as originally designed, works only on linear systems with square coefficient matrices. Even imposing such a restriction, a naive incorporation of the traditional preconditioning algorithm in a CLP language incurs a high worstcase time complexity of O(n^4), where n is the number of variables in the linear system. In this paper, we generalize the algorithm for general linear systems with m constraints and n variables, and give a novel incremental adaptation of preconditioning of O(n 2 (n + m)) complexity. The efficiency of the incremental preconditioned interval GaussSeidel method is demonstrated using largescale linear systems.