Luiz Henrique Figueiredo and Jorge Stolfi. Adaptive enumeration of implicit surfaces with affine arithmetic. Computer Graphics Forum, 15(5):287--296, 1996. Home/Search Document Details and Download
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Ray-tracing Procedural Displacement Shaders - Heidrich, Seidel (1998) (9 citations) (Correct)
....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 affine arithmetic to obtain ....
....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 manipulating imprecise values, and for evaluating functions over intervals. It is also possible to keep track of truncation and round off errors. In contrast to interval arithmetic, affine arithmetic also maintains dependencies between ....
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Luiz Henrique Figueiredo and Jorge Stolfi. Adaptive enumeration of implicit surfaces with affine arithmetic. Computer Graphics Forum, 15(5):287--296, 1996.
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 ....
.... 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 used to manipulate imprecise values, and to evaluate functions over intervals. It is also possible to keep track of truncation and round off errors. In addition, affine arithmetic maintains dependencies between the sources of error, and ....
Luiz Henrique Figueiredo and Jorge Stolfi. Adaptive enumeration of implicit surfaces with affine arithmetic. Computer Graphics Forum, 15(5):287--296, 1996.
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