Jo~ao L. D. Comba and Jorge Stolfi. Affine arithmetic and its applications to computer graphics. In Anais do VII Sibgrapi, pages 9--18, 1993. Available from http://www.dcc.unicamp.br/~stolfi. Home/Search Document Details and Download
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Ray-tracing Procedural Displacement Shaders - Heidrich, Seidel (1998) (9 citations) (Correct)
....the value zero, the surface potentially passes through the cell, and the cell is subdivided in an octree fashion, unless it is already small enough. Unlike Lipschitz bounds, interval bounds can be automatically computed by specific implementations of the basic library functions. Comba and Stolfi [5] and Figueiredo and Stolfi [9] used a similar algorithm, but replaced interval arithmetic with affine arithmetic, which they developed for this purpose. They showed that affine arithmetic produces significantly tighter bounds than interval arithmetic, although at a higher cost. In [12] we used ....
....of the resulting point are at the same time bounding boxes for the geometry after the displacement. In the following we give a brief overview of affine arithmetic, and describe in more detail how it can be applied to procedural shaders. 4 Affine Arithmetic Affine arithmetic, first introduced in [5], is an extension of interval arithmetic [14] It has been successfully applied to several problems for which interval arithmetic had been used before [15, 22, 23] This includes the adaptive enumeration of implicit surfaces [9] Like interval arithmetic, affine arithmetic can be used for ....
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Jo~ao L. D. Comba and Jorge Stolfi. Affine arithmetic and its applications to computer graphics. In Anais do VII Sibgrapi, pages 9--18, 1993. Available from http://www.dcc.unicamp.br/~stolfi.
Bounded Clustering -- Finding Good Bounds on.. - Marc Stamminger.. (1997) (6 citations) (Correct)
....an upper and a lower bound on S and a proper approximation. The definition of addition, multiplication and division on the min max values is that of Interval Arithmetic [10] Using Interval Arithmetic for our computations is certainly not optimal. We are optimistic that using Affine Artihmetic [3] instead may result in better range computations, as it has been shown for other rendering applications [8, 7] The algorithm described below should be easy to transform. In the following, we describe how the light transport between two objects can be computed using the above definitions. We start ....
Jo~ao L. D. Comba and Jorge Stolfi. Affine arithmetic and its applications to computer graphics. In Anais do VII Sibgrapi, pages 9--18, 1993. Available from http://www.dcc.unicamp.br/¸stolfi/EXPORT/papers/affinearith.
Sampling of Procedural Shaders Using Affine Arithmetic - Heidrich, Slusallek, Seidel (1998) (5 citations) (Correct)
....since the convergence rate of Monte Carlo methods is only O( p N) 11] a relatively large number of samples is required to increase the certainty of these estimates. In this paper we describe a method for generating tight, conservative error bounds for procedural shaders using affine arithmetic [4, 6, 7]. We first give a brief overview of affine arithmetic in general before we describe the details of applying it to procedural shaders. 2 Affine Arithmetic Since affine arithmetic has first been introduced in [4] it has been used as a replacement for interval arithmetic [16, 23, 24] in algorithms ....
....tight, conservative error bounds for procedural shaders using affine arithmetic [4, 6, 7] We first give a brief overview of affine arithmetic in general before we describe the details of applying it to procedural shaders. 2 Affine Arithmetic Since affine arithmetic has first been introduced in [4], it has been used as a replacement for interval arithmetic [16, 23, 24] in algorithms for reliable intersection tests of rays with implicit surfaces and for the recursive enumeration of implicit surfaces in quad tree like structures [6, 7] Like interval arithmetic [15] affine arithmetic can be ....
[Article contains additional citation context not shown here]
Jo~ao L. D. Comba and Jorge Stolfi. Affine arithmetic and its applications to computer graphics. In Anais do VII Sibgrapi, pages 9--18, 1993.
Hierarchical Techniques for Global Illumination.. - Slusallek.. (Correct)
....to compute upper and lower bounds for any of the parameters that are used as input to the computation of the exchange coefficients. If tight conservative bounds are computed for the input parameters, the resulting exchange coefficients can also be bounded by applying interval or affine arithmetic [Moo66,CS93,Sny92]. The location of points and their normals can efficiently be bound with the cone of normals technique [SA93] and bounding boxes. Based on this data, bounds on the set of connecting rays, cosines factors, distances, and solid angles can be computed. Bounds can also be computed for visibility ....
Jo~ao L. D. Comba and Jorge Stolfi. Affine arithmetic and its applications to computer graphics. In Anais do VII Sibgrapi, pages 9--18, 1993. Available from http://www.dcc.unicamp.br/¸stolfi/EXPORT/papers/affine-arith.
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