Interval Methods for Ray Casting Implicit Surfaces with Affine Arithmetic - Junior, de Figueiredo, Gattas (ResearchIndex)

Interval Methods for Ray Casting Implicit Surfaces with Affine Arithmetic (1999) (Make Corrections) (5 citations)
Affonso de Cusatis Junior, Luiz Henrique de Figueiredo, Marcelo Gattass

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Abstract: . We study the performance of affine arithmetic as a replacement for interval arithmetic in interval methods for ray casting implicit surfaces. Affine arithmetic is a variant of interval arithmetic designed to handle the dependency problem, and which has improved several interval algorithms in computer graphics. Keywords: image synthesis; root location; interval arithmetic; range analysis; self-validated computing. 1 Introduction Given a function h: R 3 ! R, the set S = fp 2 R 3 :... (Update)

Context of citations to this paper: More

.... has been successfully implemented in the following algorithms: Intersection of parametric surfaces: The algorithm presented in [7] is a modi cation of the subdivision algorithm presented in [13] that utilizes bounding boxes computed by direct interval evaluation of...

.... 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...

Cited by: More
Affine Arithmetic: Concepts and Applications - de Figueiredo, Stolfi (2003) (Correct)
Approximating Parametric Curves with Strip Trees using .. - de Figueiredo.. (Correct)
Robust Approximation of Offsets, Bisectors, and Medial Axes of.. - Oliveira (2002) (Correct)

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1.0: Robust Approximation of Offsets and Bisectors of Plane Curves - de Oliveira, de Figueiredo (2000) (Correct)
0.8: Robust Adaptive Polygonal Approximation of Implicit Curves - Oliveira, de Figueiredo (Correct)
0.8: Robust Adaptive Approximation of Implicit Curves - Oliveira, de Figueiredo (2001) (Correct)

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5: Ray-tracing procedural displacement shaders - Heidrich, Seidel - 1998
4: Sampling procedural shaders using affine arithmetic - Heidrich, Slusallek et al. - 1998
4: Surface intersection using affine arithmetic - de Figueiredo - 1996

BibTeX entry: (Update)

A. de Cusatis Junior, L.H. de Figueiredo, and M. Gattas. Interval methods for raycasting implicit surfaces with ane arithmetic. In Proceedings of XII SIBGRPHI, pages 1-7, 1999. http://citeseer.nj.nec.com/decusatis99interval.html More

@misc{ junior99interval,
  author = "A. Junior and L. de Figueiredo and M. Gattas",
  title = "Interval methods for raycasting implicit surfaces with ane arithmetic",
  text = "A. de Cusatis Junior, L.H. de Figueiredo, and M. Gattas. Interval methods
    for raycasting implicit surfaces with ane arithmetic. In Proceedings of
    XII SIBGRPHI, pages 1-7, 1999.",
  year = "1999",
  url = "citeseer.nj.nec.com/decusatis99interval.html" }

Citations (may not include all citations):
695 The Art of Scientific Computing (context) - Press, Teukolsky et al. - 1992
309 Interval Analysis (context) - Moore - 1966
155 An Introduction to Ray Tracing (context) - Glassner - 1989
66 Interval analysis for computer graphics - Snyder - 1992
63 Introduction to Implicit Surfaces (context) - Bloomenthal - 1997
52 Interval arithmetic and recursive subdivision for implicit f.. (context) - Duff - 1992
34 Lua: an extensible extension language - Ierusalimschy, de Figueiredo et al. - 1996
25 On ray tracing parametric surfaces (context) - Toth - 1985
23 Ray tracing algebraic surfaces (context) - Hanrahan - 1983
22 Interval methods in computer graphics (context) - Suffern, Fackerell - 1991
21 Robust ray intersection with interval arithmetic (context) - Mitchell - 1990
13 Ray-tracing procedural displacement shaders - Heidrich, Seidel - 1998
13 Affine arithmetic and its applications to computer graphics - Comba, Stolfi - 1993
12 Self-Validated Numerical Methods and Applications - Stolfi, de Figueiredo - 1997
10 Sampling procedural shaders using affine arithmetic - Heidrich, Slusallik et al. - 1998
8 Adaptive enumeration of implicit surfaces with affine arithm.. - de Figueiredo, Stolfi - 1996
8 Three applications of interval analysis in computer graphics (context) - Mitchell - 1991
7 Ray tracing general parametric surfaces using interval arith.. (context) - Barth, Lieger et al. - 1994
6 Surface intersection using affine arithmetic - de Figueiredo - 1996
6 A versatile precompiler for nonstandard arithmetics (context) - Crary - 1979
2 interval-comp/intsoft (context) - Kreinovich, http et al.
1 Solving quartics and cubics for graphics (context) - Herbison-Evans - 1995
1 Which root does the bisection algorithm find (context) - Corliss - 1977

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