Luiz Henrique Figueiredo and Jorge Stolfi. Adaptive enumeration of implicit surfaces with a#ne arithmetic. Computer Graphics Forum, 15(5):287--296, 1996. Home/Search Document Not in Database Summary Related Articles Check |
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Ray-tracing Procedural Displacement Shaders - Heidrich, Seidel (1998) (9 citations) (Correct)
....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 a#ne arithmetic, which they developed for this purpose. They showed that a#ne arithmetic produces significantly tighter bounds than interval arithmetic, although at a higher cost. In [12] we used a#ne arithmetic to obtain ....
....shaders. 4 A#ne Arithmetic A#ne 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, a#ne 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 o# errors. In contrast to interval arithmetic, a#ne arithmetic also maintains dependencies between the ....
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Luiz Henrique Figueiredo and Jorge Stolfi. Adaptive enumeration of implicit surfaces with a#ne arithmetic. Computer Graphics Forum, 15(5):287--296, 1996.
Sampling of Procedural Shaders Using Affine Arithmetic - Heidrich (1996) (5 citations) (Correct)
....since the convergence rate of Monte Carlo methods is only O( # 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 a#ne arithmetic [4, 6, 7]. We first give a brief overview of a#ne arithmetic in general before we describe the details of applying it to procedural shaders. 2 A#ne Arithmetic Since a#ne arithmetic has first been introduced in [4] it has been used as a replacement for interval arithmetic [16, 23, 24] in algorithms for ....
.... Since a#ne 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] a#ne 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 o# errors. In addition, a#ne arithmetic maintains dependencies between the sources of error, and thus ....
Luiz Henrique Figueiredo and Jorge Stolfi. Adaptive enumeration of implicit surfaces with a#ne arithmetic. Computer Graphics Forum, 15(5):287--296, 1996.
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