Adaptive Enumeration of Implicit Surfaces with Affine Arithmetic

Adaptive Enumeration of Implicit Surfaces with Affine Arithmetic (1996) (Make Corrections) (8 citations)
Luiz Henrique de Figueiredo, Jorge StolfiComputer Graphics Forum

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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. We also describe applications of affine arithmetic to... (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...

Cited by: More
Implicit Linear Interval Estimations - Bühler (2002) (Correct)
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0.4: Robust Adaptive Approximation of Implicit Curves - Oliveira, de Figueiredo (2001) (Correct)
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7: Self-Validated Numerical Methods and Applications - Stolfi, de Figueiredo - 1997
6: Interval Analysis (context) - Moore - 1966
5: The Design and Analysis of Spatial Data Structures (context) - Samet - 1989

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
85 Space subdivision for fast ray tracing (context) - Glassner - 1984
83 Polygonization of implicit surfaces - Bloomenthal - 1988
66 Interval analysis for computer graphics - Snyder - 1992
52 Interval arithmetic and recursive subdivision for implicit f.. (context) - Duff - 1992
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
15 Adaptive polygonization of implicitly defined surfaces (context) - Hall, Warren - 1990
15 Contour tracing by piecewise linear approximations (context) - Dobkin, Levy et al. - 1990
14 Adaptive polygonization of implicit surfaces using simplicia.. (context) - Velho - 1986
13 Affine arithmetic and its applications to computer graphics - Comba, Stolfi - 1993
8 A tracking algorithm for implicitly defined curves (context) - Chandler - 1988
7 Quadtree algorithms for contouring functions of two variable.. (context) - Suffern - 1990
5 Boundary evaluation of CSG solids by simplicial subdivision (context) - Persiano, Salim et al. - 1990
4 Lectures Notes in Computer Science (context) - Matijasevich, interval - 1985
1 IEEE Computer Graphics & Applications (context) - Taubin, curves - 1994

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Instituto de Matematica Pura e Aplicada -- IMPA Estrada Dona.. - Ruben Jonas (Correct)
Computational Morphology of Implicit Curves - de Figueiredo (1992) (Correct)
A Methodology for Piecewise Linear Approximation of Surfaces - Velho, de Figueiredo, Gomes (1997) (Correct)

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