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Abstract: 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 sub-formulas, generally providing much tighter bounds for the computed quantities.... (Update)
Context of citations to this paper: More
.... 93 [2] as a tool for validated numerics [20] Since then, AA has been applied to the robust solution of several graphics problems [4,6,7,11,12], where it has successfully replaced interval arithmetic [16] In AA, a quantity x is represented as an affine form, x = x 0 x...
.... one of these tools, and its use in interval methods has resulted in faster algorithms for several problems in computer graphics [6, 5, 16, 15, 4]. A natural next step is to use affine arithmetic instead of interval arithmetic in the global processing algorithms we have...
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1.0: Surface intersection using affine arithmetic - de Figueiredo (1996) (Correct)
0.4: Robust Approximation of Offsets and Bisectors of Plane Curves - de Oliveira, de Figueiredo (2000) (Correct)
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0.2: Extensions of Affine Arithmetic: Application to Unconstrained.. - Messine (Correct)
0.2: Taylor Models and Affine Arithmetics - Towards a More.. - Bühler (2001) (Correct)
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5: Ray-tracing procedural displacement shaders - Heidrich, Seidel - 1998
5: Self-Validated Numerical Methods and Applications - Stolfi, de Figueiredo - 1997
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BibTeX entry: (Update)
L. H. de Figueiredo. Surface intersection using affine arithmetic. In Proceedings of Graphics Interface'96, pages 168-- 175, May 1996. http://citeseer.nj.nec.com/article/defigueiredo96surface.html More
@inproceedings{ defigueiredo96surface,
author = "Luiz Henrique {de Figueiredo}",
title = "Surface Intersection Using Affine Arithmetic",
booktitle = "Graphics Interface '96",
publisher = "Canadian Human-Computer Communications Society",
editor = "Wayne A. Davis and Richard Bartels",
pages = "168--175",
year = "1996",
url = "citeseer.nj.nec.com/article/defigueiredo96surface.html" }
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52 Interval arithmetic and recursive subdivision for implicit f.. (context) - Duff - 1992
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33 volume 120 of Lecture Notes in Computer Science (context) - Rall, Techniques - 1981
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22 Interval methods in computer graphics (context) - Suffern, Fackerell - 1991
21 Robust ray intersection with interval arithmetic (context) - Mitchell - 1990
17 Surface algorithms using bounds on derivatives (context) - Filip, Magedson et al. - 1986
13 Affine arithmetic and its applications to computer graphics - Comba, Stolfi - 1990
11 Adaptive enumeration of implicit surfaces with affine arithm.. (context) - de Figueiredo, Stolfi - 1995
10 Surfaces in computer-aided geometric design: A survey with n.. (context) - Barnhill - 1985
9 An interval refinement technique for surface intersection (context) - Gleicher, Kass - 1992
4 Local robustness and its applications to polyhedral intersec.. (context) - Stewart - 1994
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