Error-free boundary evaluation based on a lazy rational arithmetic: a detailed implementation

Benouamer, Mohand Ourabah; Michelucci, Dominique; Péroche, Bernard

doi:10.1016/0010-4485(94)90063-9

Cited by 32 publications

(30 citation statements)

References 9 publications

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“…Benouamer, Michelucci, and Peroche [2] implement a solid modeler using a filtered approach that differs from that of Fortune and van Wyk. Benouamer et al express each sequence of calculations as an expression dag, that is, a directed acyclic graph with operations at internal nodes and constants at the leaves.…”

Section: Literature Surveymentioning

confidence: 99%

Reliable Geometric Computations with Algebraic Primitives and Predicates

Foskey

Manocha

Culver

et al. 2002

Uncertainty in Geometric Computations

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Section: Literature Surveymentioning

confidence: 99%

Reliable Geometric Computations with Algebraic Primitives and Predicates

Foskey

Manocha

Culver

et al. 2002

Uncertainty in Geometric Computations

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“…Effects of this kind of the lazy evaluation strategy were reported in (Benouamer et al, 1993;Sugihara, 1997). 1.3.…”

Section: Acceleration By Lazy Evaluationmentioning

confidence: 99%

“…This principle has been used widely in numerically robust geometric computation (Ottmann et al, 1987;Sugihara and Iri, 1989;Karasick et al, 1991;Sugihara, 1992;Schorn, 1991;Benouamer et al, 1993;Fortune and von Wyk, 1993).…”

Section: Correct Judgement In Finite Precisionmentioning

confidence: 99%

“…The first group is the "exact-arithmetic approach", which relies on numerical computation absolutely (Sugihara and Iri, 1989;Ottmann et al, 1987;Karasick et al, 1991;Sugihara, 1992;Schorn, 1991;Benouamer et al, 1993;Fortune and von Wyk, 1993;Sugihara, 1997;Yap, 1995). The topological structure of a geometric object can be decided by the signs of the results of numerical computations.…”

Section: Introductionmentioning

confidence: 99%

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Degeneracy and Instability in Geometric Computation

Sugihara

2001

Geometric Modelling

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This paper describes main sources of instability in geometric computation, and reviews two mutually opposite approaches to this problem. Instability in geometric computation comes from numerical errors, which first cause misjudgements of geometric structure, and then generate topological inconsistency. One promising approach to this difficulty is the use of multiple precision arithmetic that is high enough to judge the topological structure always correctly. Another approach places high priority on the topological consistency, and use numerical values only when they do not contradict the topological structure. Merits and demerits of the two approaches are discussed with examples.

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“…Among the methods used to increase the efficiency of exact computations are those based on interval arithmetic [28,30], floating-point filters [18,19], lazy arithmetic [2], tuned computations [18,19], precision-driven computation [50], minimized intermediate computation [5,8], fast hardware computation [46], and modular arithmetic [5,18]. Libraries supporting basic exact computation have been developed, with LEDA [41] and CORE [29] being notable examples.…”

Section: Exact Computationmentioning

confidence: 99%

ESOLID---A System for Exact Boundary Evaluation

Keyser

Culver

Foskey³

et al. 2002

Proceedings of the Seventh ACM Symposium on Solid Modeling and Applications

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We present a system, ESOLID, that performs exact boundary evaluation of low-degree curved solids in reasonable amounts of time. ESOLID performs accurate Boolean operations using exact representations and exact computations throughout. The demands of exact computation require a different set of algorithms and efficiency improvements than those found in a traditional inexact floating-point based modeler. We describe the system architecture, representations, and issues in implementing the algorithms. We also describe a number of techniques that increase the efficiency of the system based on lazy evaluation, use of floating-point filters, arbitrary floating-point arithmetic with error bounds, and lower-dimensional formulation of subproblems.ESOLID has been used for boundary evaluation of many complex solids. These include both synthetic datasets and parts of a Bradley Fighting Vehicle designed using the BRL-CAD solid modeling system. It is shown that ESOLID can correctly evaluate the boundary of solids that are very hard to compute using a fixed-precision floating-point modeler. In terms of performance, it is about an order of magnitude slower as compared to a floating-point boundary evaluation system on most cases. q

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Error-free boundary evaluation based on a lazy rational arithmetic: a detailed implementation

Cited by 32 publications

References 9 publications

Reliable Geometric Computations with Algebraic Primitives and Predicates

Reliable Geometric Computations with Algebraic Primitives and Predicates

Degeneracy and Instability in Geometric Computation

ESOLID---A System for Exact Boundary Evaluation

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