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Abstract: We discuss adaptive enumeration and rendering methods for implicit surfaces, using octrees computed with affine arithmetic, a new tool 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. The resulting octrees are accordingly much smaller, and the rendering faster. Keywords: Cellular models; Interval arithmetic; Affine... (Update)
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.... 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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BibTeX entry: (Update)
L. H. de Figueiredo and J. Stolfi. Adaptive enumeration of implicit surfaces with affine arithmetic. Computer Graphics Forum, 15(5):287--296, 1996. http://citeseer.nj.nec.com/article/defigueiredo96adaptive.html More
@article{ defigueiredo96adaptive,
author = "Luiz Henrique {de Figueiredo} and Jorge Stolfi",
title = "Adaptive Enumeration of Implicit Surfaces with Affine Arithmetic",
journal = "Computer Graphics Forum",
volume = "15",
number = "5",
pages = "287--296",
year = "1996",
url = "citeseer.nj.nec.com/article/defigueiredo96adaptive.html" }
Citations (may not include all citations):312 Interval Analysis (context) - Moore - 1966
291 Display of surfaces from volume data (context) - Levoy - 1988
279 Multidimensional binary search trees used for associative se.. (context) - Bentley - 1975
179 On visible surface generation by a priori tree structures (context) - Fuchs, Kedem et al. - 1980
109 Applications of Spatial Data Structures (context) - Samet - 1990
85 Space subdivision for fast ray tracing (context) - Glassner - 1984
83 Polygonization of implicit surfaces - Bloomenthal - 1988
66 The complexity of partial derivatives (context) - Baur, Strassen - 1983
66 Interval analysis for computer graphics - Snyder - 1992
52 Interval arithmetic and recursive subdivision for implicit f.. (context) - Duff - 1992
51 Computer Methods for the Range of Functions (context) - Ratschek, Rokne - 1984
51 Numerical Continuation Methods: An Introduction (context) - Allgower, Georg - 1990
24 A generalized interval arithmetic (context) - Hansen - 1975
22 Interval methods in computer graphics (context) - Suffern, Fackerell - 1991
21 Field functions for implicit surfaces (context) - Wyvill, Wyvill - 1989
21 Robust ray intersection with interval arithmetic (context) - Mitchell - 1990
15 Contour tracing by piecewise linear approximations (context) - Dobkin, Levy et al. - 1990
14 Adaptive polygonization of implicit surfaces using simplicia.. (context) - Velho - 1990
13 Affine arithmetic and its applications to computer graphics - Comba, Stolfi - 1990
13 Adaptive polygonalization of implicitly defined surfaces (context) - Hall, Warren - 1990
9 An interval refinement technique for surface intersection (context) - Gleicher, Kass - 1992
8 A tracking algorithm for implicitly defined curves (context) - Chandler - 1988
7 Quadtree algorithms for contouring functions of two variable.. (context) - Suffern - 1990
6 Cutting cubes -- visualizing implicit surfaces by adaptive p.. (context) - Schmidt - 1993
5 Boundary evaluation of CSG solids by simplicial subdivision (context) - Persiano, Salim et al. - 1991
5 Surface intersection using affine arithmetic - de Figueiredo - 1996
5 Space division for ray tracing in CSG (context) - Wyvill, Kunii et al. - 1986
3 Rasterizing algebraic curves and surfaces (context) - Taubin - 1994
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