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Geometric and Arithmetic Culling Methods for Entire Ray Packets
, 2006
"... Recent interactive ray tracing performance has been mainly derived from the use of ray packets. Larger ray packets allow for significant amortization of both computations and memory accesses; however, the majority of primitives are still intersected by each ray in a packet. This paper discusses seve ..."
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Cited by 20 (9 self)
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Recent interactive ray tracing performance has been mainly derived from the use of ray packets. Larger ray packets allow for significant amortization of both computations and memory accesses; however, the majority of primitives are still intersected by each ray in a packet. This paper discusses several methods to cull entire ray packets against common primitives (box, triangle, and sphere) that allows an arbitrary number of rays to be tested by a single test. This provides cheap “all miss ” or “all hit ” tests and may substantially improve the performance of an interactive ray tracer. The paper surveys current methods, provides details on three particular approaches using interval arithmetic, bounding planes, and corner rays, describes how the respective bounding primitives can be easily and efficiently constructed, and points out the relation among the different fundamental concepts.
INNER APPROXIMATION OF THE RANGE OF VECTORVALUED FUNCTIONS
"... Abstract. No method for the computation of a reliable subset of the range of vectorvalued functions is available today. A method for computing such inner approximations is proposed in the specific case where both domain and codomain have the same dimension. A general sufficient condition for the i ..."
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Cited by 3 (1 self)
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Abstract. No method for the computation of a reliable subset of the range of vectorvalued functions is available today. A method for computing such inner approximations is proposed in the specific case where both domain and codomain have the same dimension. A general sufficient condition for the inclusion of a box inside the image of a box by a continuously differentiable vectorvalued is first provided. This sufficient condition is specialized to a more efficient one, which is used in a specific bisection algorithm that computes reliable inner and outer approximations of the image of a domain defined by constraints. Some experimentations are presented.
Quantifier Elimination versus Generalized Interval Evaluation: A comparison on a Special Class of Quantified Constraints
 in "Proc. of the 11th Information Processing and Management of Uncertainty International Conference, IPMU 2006
"... This paper presents and compares two methods for checking if a box is included inside the solution set of an equality constraint with existential quantification of its parameters. We focus on distance constraints, where each existentially quantified parameter has only one occurrence, because of thei ..."
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Cited by 2 (0 self)
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This paper presents and compares two methods for checking if a box is included inside the solution set of an equality constraint with existential quantification of its parameters. We focus on distance constraints, where each existentially quantified parameter has only one occurrence, because of their usefulness and their simplicity. The first method relies on a specific quantifier elimination based on geometric considerations whereas the second method relies on computations with generalized intervals— interval whose bounds are not constrained to be ordered. We show that on two dimension problems, the two methods yield equivalent results. However, when dealing with higher dimensions, generalized intervals are more efficient.
Efficient Handling of Universally Quantified Inequalities
, 2008
"... This paper introduces a new framework for solving quantified constraint satisfaction problems (QCSP) defined by universally quantified inequalities on continuous domains. This class of QCSPs has numerous applications in engineering and technology. We introduce a generic branch and prune algorithm to ..."
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This paper introduces a new framework for solving quantified constraint satisfaction problems (QCSP) defined by universally quantified inequalities on continuous domains. This class of QCSPs has numerous applications in engineering and technology. We introduce a generic branch and prune algorithm to tackle these continuous CSPs with parametric constraints, where the pruning and the solution identification processes are dedicated to universally quantified inequalities. Special rules are proposed to handle the parameter domains of the constraints. The originality of our framework lies in the fact that it solves the QCSP as a nonquantified CSP where the quantifiers are handled locally, at the level of each constraint. Experiments show that our algorithm outperforms the state of the art methods based on constraint techniques.
Modal Intervals Revisited Part 1: A Generalized Interval Natural Extension
 Reliable Computing
"... Modal interval theory is an extension of classical interval theory which provides richer interpretations (including in particular inner and outer approximations of the ranges of real functions). In spite of its promising potential, modal interval theory is not widely used today because of its origin ..."
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Modal interval theory is an extension of classical interval theory which provides richer interpretations (including in particular inner and outer approximations of the ranges of real functions). In spite of its promising potential, modal interval theory is not widely used today because of its original and complicated construction. The present paper proposes a new formulation of modal interval theory. New extensions of continuous real functions to generalized intervals (intervals whose bounds are not constrained to be ordered) are defined. They are called AEextensions. These AEextensions provide the same interpretations as the ones provided by modal interval theory, thus enhancing the interpretation of the classical interval extensions. The construction of AEextensions strictly follows the model of classical interval theory: starting from a generalization of the definition of the extensions to classical intervals, the minimal AEextensions of the elementary operations
EUSFLAT LFA 2005 Interval semimetric spaces for approximate distances
"... In accordance with the ideas of Interval Analysis, a notion of intervalvalued semimetric space is proposed. Also, the possibility of applying the resulting theory to some chapters of Computer Science is examined. ..."
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In accordance with the ideas of Interval Analysis, a notion of intervalvalued semimetric space is proposed. Also, the possibility of applying the resulting theory to some chapters of Computer Science is examined.
A Programming Language for Precision/Cost Tradeoffs
, 2009
"... Many computational systems need to deal with various forms of imprecision and uncertainty in their data; it is also the case that many systems, especially mobile and distributed systems, must be able to trade off the precision of their data and operations against the cost of performing those operati ..."
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Many computational systems need to deal with various forms of imprecision and uncertainty in their data; it is also the case that many systems, especially mobile and distributed systems, must be able to trade off the precision of their data and operations against the cost of performing those operations. Unfortunately, for many applications, trying to make these tradeoffs severely complicates the program, because there does not yet exist a programming model that gives the programmer the ability to easily describe the relevant tradeoffs between precision and cost of operations or to express in an algorithm what tradeoffs are appropriate under what circumstances. This paper lays a solid foundation for exploring
unknown title
, 2004
"... Fusion of imprecise, uncertain and conflicting beliefs with DSm rules of combination ..."
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Fusion of imprecise, uncertain and conflicting beliefs with DSm rules of combination
myjournal manuscript No. (will be inserted by the editor) A Survey on OR and Mathematical Methods Applied on GeneEnvironment Networks
"... Abstract In this paper we survey the recent advances and mathematical foundations of geneenvironment networks. We explain their interdisciplinary implications with special regard to human and life sciences as well as financial sciences. Special attention is paid to applications in Operational Resea ..."
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Abstract In this paper we survey the recent advances and mathematical foundations of geneenvironment networks. We explain their interdisciplinary implications with special regard to human and life sciences as well as financial sciences. Special attention is paid to applications in Operational Research and environmental protection. Originally developed in the context of modeling and prediction of geneexpression patterns, geneenvironment networks have proved to provide a conceptual framework for the modeling of dynamical systems with respect to errors and uncertainty as well as the influence of certain environmental items. Given the noiseprone measurement data we extract nonlinear differential equations to describe and investigate the interactions and regulating effects between the data items of interest and the environmental items. In particular, these equations reflect data uncertainty by the use of interval arithmetics and comprise unknown parameters resulting in a wide variety of the model. For an identification of these parameters Chebychev approximation and generalized semiinfinite optimization are applied. In addition, the timediscrete counterparts of the nonlinear equations
Noname manuscript No. (will be inserted by the editor) (Non)existence of Pleated Folds: How Paper Folds Between Creases
"... Abstract We prove that the pleated hyperbolic paraboloid, a familiar origami model known since 1927, in fact cannot be folded with the standard crease pattern in the standard mathematical model of zerothickness paper. In contrast, we show that the model can be folded with additional creases, sugges ..."
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Abstract We prove that the pleated hyperbolic paraboloid, a familiar origami model known since 1927, in fact cannot be folded with the standard crease pattern in the standard mathematical model of zerothickness paper. In contrast, we show that the model can be folded with additional creases, suggesting that real paper “folds ” into this model via small such creases. We conjecture that the circular version of this model, consisting simply of concentric circular creases, also folds without extra creases. At the heart of our results is a new structural theorem characterizing uncreased intrinsically flat surfaces—the portions of paper between the creases. Differential geometry has much to say about the local behavior of such surfaces when they are sufficiently smooth, e.g., that they are torsal ruled. But this classic result is simply false in the context of the whole surface. Our structural characterization tells the whole story, and even applies to surfaces with discontinuities in the second derivative. We use our theorem to prove fundamental properties about how paper folds, for example, that straight creases on the piece of paper must remain piecewisestraight (polygonal) by folding.