J. Comba, J. Stolfi, A#ne arithmetic and its applications to computer graphics, Proc. VI SIBGRAPI (1993) 9--18. (Brazilian Symposium on Computer Graphics and Image Processing).  Home/Search   Document Not in Database   Summary   Related Articles   Check

....2 2 1 4. The estimates provided by interval arithmetic are too conservative; in complex expressions having many coupled sub expressions, these estimates can quickly become useless. An alternative to interval arithmetic, called a#ne arithmetic, has been proposed to overcome this problem [8]. A#ne arithmetic does handle coupling in expressions and is therefore able to provide better estimates. Adaptive enumeration of implicit objects using a#ne arithmetic is a promising technique, specially for rendering [9] Fig. 6) to appear in Computer Graphics 20 #3 (1996) special issue ....

J. Comba, J. Stolfi, A#ne arithmetic and its applications to computer graphics, Proc. VI SIBGRAPI (1993) 9--18. (Brazilian Symposium on Computer Graphics and Image Processing).

....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 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 ....

....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 a#ne arithmetic, and describe in more detail how it can be applied to procedural 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 ....

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Joao L. D. Comba and Jorge Stolfi. A#ne arithmetic and its applications to computer graphics. In Anais do VII Sibgrapi, pages 9--18, 1993. Available from http://www.dcc.unicamp.br/stolfi.

....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 ....

....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 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 ....

[Article contains additional citation context not shown here]

Joao L. D. Comba and Jorge Stolfi. A#ne arithmetic and its applications to computer graphics. In Anais do VII Sibgrapi, pages 9--18, 1993.

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