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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.
SelfValidated Numerical Methods and Applications
, 1997
"... erical methods. We apologize to the reader for the length and verbosity of these notes but, like Pascal, 1 we didn't have the time to make them shorter. 1 "Je n'ai fait celleci plus longue que parce que je n'ai pas eu le loisir de la faire plus courte." Blaise Pascal, Lettres Provinciales, XV ..."
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Cited by 30 (0 self)
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erical methods. We apologize to the reader for the length and verbosity of these notes but, like Pascal, 1 we didn't have the time to make them shorter. 1 "Je n'ai fait celleci plus longue que parce que je n'ai pas eu le loisir de la faire plus courte." Blaise Pascal, Lettres Provinciales, XVI (1657). i ii Acknowledgements We thank the Organizing Committee of the 21 st Brazilian Mathematics Colloquium for the opportunity to present this course. We wish to thank Jo~ao Comba, who helped implement a prototype affine arithmetic package in Modula3, and Marcus Vinicius Andrade, who helped debug the C version and wrote an implicit surface raytracer based on it. Ronald van Iwaarden contributed an independent implementation of AA, and investigated its performance on branchandbound global optimization algorithms. Douglas Priest and Helmut Jarausch provided code and advice for rounding mode control. W
Reliable TwoDimensional Graphing Methods for Mathematical Formulae with Two Free Variables
, 2001
"... present s a series of new algorit hms for reliably graphingt wodimensional implicit equat ions and inequalit ies. A clear st andard for int erpret ingt he graphs generat ed byt wodimensional graphing soft ware is int roduced and used t o evaluat et he present ed algorit hms. The first approach pr ..."
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Cited by 11 (0 self)
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present s a series of new algorit hms for reliably graphingt wodimensional implicit equat ions and inequalit ies. A clear st andard for int erpret ingt he graphs generat ed byt wodimensional graphing soft ware is int roduced and used t o evaluat et he present ed algorit hms. The first approach present ed uses a st andard int erval arit hmet ic library. This approach is shownt o be fault y; an analysis oft he failure reveals a limit at ion of st andard int erval arit hmet ic. Subsequent algorit hms are developed in parallel wit h improvement s and ext#E sions t# t# e int erval ari t#met# c used byt he graphing algorit hms. Graphs exhibit ing a variet y of mat hemat ical and art ist ic phenomena are shownt o be graphed correct ly byt he present ed algorit hms. A brief comparison of t he final algorit hm present edt o ot her graphing algorit hms is included.
Interval Constraint Plotting for Interactive Visual Exploration of Implicitly Defined Relations
 Reliable Computing
, 1999
"... . Conventional plotting programs adopt techniques such as adaptive sampling to approximate, but not to guarantee, correctness and completeness in graphing functions. Moreover, implicitly defined mathematical relations can impose an even greater challenge as they either cannot be plotted directly, or ..."
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Cited by 10 (6 self)
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. Conventional plotting programs adopt techniques such as adaptive sampling to approximate, but not to guarantee, correctness and completeness in graphing functions. Moreover, implicitly defined mathematical relations can impose an even greater challenge as they either cannot be plotted directly, or otherwise are likely to be misrepresented. In this paper, we address these problems by investigating interval constraint plotting as an alternative approach that plots a hull of the specified curve. We present some empirical evidence that this hull property can be achieved by a O(n) algorithm. Practical experience shows that the hull obtained is the narrowest possible whenever the precision of the underlying floatingpoint arithmetic is adequate. We describe IASolver, a Java applet [9], that serves as testbed for this idea. Keywords: interval constraints, constraint propagation, interval arithmetic, implicitly defined relations, honest plotting, interactive plotting 1. Introduction Mathe...
Affine Arithmetic: Concepts and Applications
, 2003
"... Affine arithmetic is a model for selfvalidated numerical computation that affine arithmetic keeps track of firstorder correlations between computed and input quantities. We explain the main concepts in affine arithmetic and it handles the dependency problem in standard interval arithmetic. We also ..."
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Cited by 10 (1 self)
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Affine arithmetic is a model for selfvalidated numerical computation that affine arithmetic keeps track of firstorder correlations between computed and input quantities. We explain the main concepts in affine arithmetic and it handles the dependency problem in standard interval arithmetic. We also describe some of its applications.
Representing knowledge within the situation calculus using intervalvalued epistemic fluents
, 1999
"... The ability of interval arithmetic to provide a finite (and succinct) way to represent uncertainty about a large, possibly uncountable, set of alternatives turns out to be useful in building “intelligent ” autonomous agents. In particular, consider the two important issues of reasoning and sensing i ..."
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Cited by 9 (3 self)
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The ability of interval arithmetic to provide a finite (and succinct) way to represent uncertainty about a large, possibly uncountable, set of alternatives turns out to be useful in building “intelligent ” autonomous agents. In particular, consider the two important issues of reasoning and sensing in intelligent control for autonomous agents. Developing a principled way to combine the two raises complicated issues in knowledge representation. In this paper we describe a solution to the problem. The idea is to incorporate interval arithmetic into the situation calculus. The situation calculus is a well known formalism for describing changing worlds using sorted firstorder logic. It can also be used to describe how an agent’s knowledge of its world changes. Potentially, this provides a sound basis for incorporating sensing into logic programming. Previous work has relied on a possible worlds approach to knowledge. This leads to an elegant mathematical specification language. Unfortunately, there have been no proposals on how to implement the approach. This is because the number of possible worlds is potentially uncountable. We propose an alternative formalization of knowledge within the situation calculus. Our approach is based on intervals. The advantage is that it is straightforward to implement. Moreover, we can prove that it is sound and (sometimes) complete with respect to the previous possible worlds approach. 1
Cognitive Modeling:
, 1999
"... Recent work in behavioral animation has taken impressive steps toward autonomous, selfanimating characters for use in production animation and interactive games. It remains difficult, however, to direct autonomous characters to perform specific tasks. This paper addresses the challenge by introduci ..."
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Cited by 1 (0 self)
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Recent work in behavioral animation has taken impressive steps toward autonomous, selfanimating characters for use in production animation and interactive games. It remains difficult, however, to direct autonomous characters to perform specific tasks. This paper addresses the challenge by introducing cognitive modeling. Cognitive models go beyond behavioral models in that they govern what a character knows, how that knowledge is acquired, and how it can be used to plan actions. To help build cognitive models, we develop the cognitive modeling language CML. Using CML, we can imbue a character with domain knowledge, elegantly specified in terms of actions, their preconditions and their effects, and then direct the character's behavior in terms of goals. Our approach allows behaviors to be specified more naturally and intuitively, more succinctly and at a much higher level of abstraction than would otherwise be possible. With cognitively empowered characters, the animator need only speci...
On the Froissart phenomenon in multivariate homogeneous Padé approximation
"... In univariate Pade approximation we learn from the Froissart phenomenon that Pade approximants to perturbed Taylor series expansions of rational functions exhibit almost cancelling polezero combinations that are unwanted. The location of these polezero pairs is given by the socalled Froissart polyn ..."
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In univariate Pade approximation we learn from the Froissart phenomenon that Pade approximants to perturbed Taylor series expansions of rational functions exhibit almost cancelling polezero combinations that are unwanted. The location of these polezero pairs is given by the socalled Froissart polynomial. In this paper the occurrence of the Froissart phenomenon is explored for the first time in a multivariate setting. Several obvious questions arise. Which definition of Pade approximant is to be used? Which multivariate rational functions should be investigated? When considering univariate projections of these functions, our analysis confirms the univariate results obtained so far in [11], under the condition that the noise is added after projection. At the same time, it is apparent from section 4 that for the unprojected multivariate Froissart polynomial no conjecture can be formulated yet. Keywords: Pade approximation, noise, Froissart, floatingpoint AMS Subject Classification: 41...
Cognitive Modeling: Knowledge, Reasoning And . . .
, 1999
"... Recent work in behavioral animation has taken impressive steps toward autonomous, selfanimating characters for use in production animation and interactive games. It remains difficult, however, to direct autonomous characters to perform specific tasks. This paper addresses the challenge by introduci ..."
Abstract
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Recent work in behavioral animation has taken impressive steps toward autonomous, selfanimating characters for use in production animation and interactive games. It remains difficult, however, to direct autonomous characters to perform specific tasks. This paper addresses the challenge by introducing cognitive modeling. Cognitive models go beyond behavioral models in that they govern what a character knows, how that knowledge is acquired, and how it can be used to plan actions. To help build cognitive models, we develop the cognitive modeling language CML. Using CML, we can imbue a character with domain knowledge, elegantly specified in terms of actions, their preconditions and their effects, and then direct the character's behavior in terms of goals. Our approach allows behaviors to be specified more naturally and intuitively, more succinctly and at a much higher level of abstraction than would otherwise be possible. With cognitively empowered characters, the animator need only speci...