Foundations of Exact Rounding

Yap, Chee; Yu, Jihun

doi:10.1007/978-3-642-00202-1_2

Cited by 2 publications

(2 citation statements)

References 20 publications

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“…Bigfloat packages are efficient and widely available (e.g., GMP, LEDA or Core Library). More generally, F can be replaced by any "computational ring" [27] satisfying some basic axioms.…”

Section: Subdivision Methods Overviewmentioning

confidence: 99%

Adaptive isotopic approximation of nonsingular curves

Lin

Yap

2009

Proceedings of the Twenty-Fifth Annual Symposium on Computational Geometry

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We consider domain subdivision algorithms for computing isotopic approximations of nonsingular curves represented implicitly by an equation f (X, Y ) = 0. Two algorithms in this area are from Snyder (1992) and Plantinga & Vegter (2004). We introduce a new algorithm that combines the advantages of these two algorithms: like Snyder, we use the parametrizability criterion for subdivision, and like Plantinga & Vegter we exploit non-local isotopy. We further extend our algorithm in two important and practical directions: first, we allow subdivision cells to be rectangles with arbitrary but bounded aspect ratios. Second, we extend the input domains to be regions R0 with arbitrary geometry and which might not be simply connected. Our algorithm halts as long as the curve has no singularities in the region, and intersects the boundary of R0 transversally. Our algorithm is also easy to implement exactly. We report on very encouraging preliminary experimental results, showing that our algorithms can be much more efficient than both Plantinga & Vegter's and Snyder's algorithms.

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“…Bigfloat packages are efficient and widely available (e.g., GMP, LEDA or Core Library). More generally, F can be replaced by any "computational ring" [27] satisfying some basic axioms.…”

Section: Subdivision Methods Overviewmentioning

confidence: 99%

Adaptive isotopic approximation of nonsingular curves

Lin

Yap

2009

Proceedings of the Twenty-Fifth Annual Symposium on Computational Geometry

Self Cite

View full text Add to dashboard Cite

show abstract

“…Bigfloat number packages are efficient and widely available (e.g., GMP, LEDA, or Core Library). More generally, F can be replaced by any "computational ring" [31] satisfying some basic axioms to support exact real approximation.…”

Section: Our Computational Modelmentioning

confidence: 99%

Adaptive Isotopic Approximation of Nonsingular Curves: the Parameterizability and Nonlocal Isotopy Approach

Lin

Yap

2011

Discrete Comput Geom

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We consider domain subdivision algorithms for computing isotopic approximations of a nonsingular algebraic curve. The curve is given by a polynomial equation f (X, Y ) = 0. Two algorithms in this area are from Snyder (1992) SIG-GRAPH Comput. Graphics, 26(2), 121 and Plantinga and Vegter (2004) In Proc. Eurographics Symposium on Geometry Processing, pp. 245-254. We introduce a new algorithm that combines the advantages of these two algorithms: like Snyder, we use the parameterizability criterion for subdivision, and like Plantinga and Vegter, we exploit nonlocal isotopy. We further extend our algorithm in two important and practical directions: first, we allow subdivision cells to be rectangles with arbitrary but bounded aspect ratios. Second, we extend the input domains to be regions R 0 with arbitrary geometry and which might not be simply connected. Our algorithm halts as long as the curve has no singularities in the region, and intersects the boundary of R 0 transversally. Our algorithm is practical and easy to implement exactly. We report some very encouraging experimental results, showing that our algorithms can be much more efficient than the algorithms of Plantinga-Vegter and Snyder.

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Foundations of Exact Rounding

Cited by 2 publications

References 20 publications

Adaptive isotopic approximation of nonsingular curves

Adaptive isotopic approximation of nonsingular curves

Adaptive Isotopic Approximation of Nonsingular Curves: the Parameterizability and Nonlocal Isotopy Approach

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