Adaptive Enumeration of Implicit Surfaces with Affine Arithmetic

Adaptive Enumeration of Implicit Surfaces with Affine Arithmetic (1995) (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)

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7: Self-Validated Numerical Methods and Applications - Stolfi, de Figueiredo - 1997
6: Interval Analysis (context) - Moore - 1966
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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/defigueiredo95adaptive.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/defigueiredo95adaptive.html" }

Citations (may not include all citations):
321 Interval Analysis (context) - Moore - 1966
293 Display of surfaces from volume data (context) - Levoy - 1988
286 Multidimensional binary search trees used for associative se.. (context) - Bentley - 1975
184 On visible surface generation by a priori tree structures (context) - Fuchs, Kedem et al. - 1980
112 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 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
21 Field functions for implicit surfaces (context) - Wyvill, Wyvill - 1989
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
10 IEEE Computer Graphics and Applications (context) - Taubin, curves - 1994
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. - 1991
5 Lecture Notes in Computer Science (context) - Matijasevich, interval - 1985

The graph only includes citing articles where the year of publication is known.

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