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Affine Arithmetic and its Applications to Computer Graphics
, 1993
"... We describe a new method for numeric computations, which we call affine arithmetic (AA). This model is similar to standard interval arithmetic, to the extent that it automatically keeps track of rounding and truncation errors for each computed value. However, by taking into account correlations betw ..."
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Cited by 77 (6 self)
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We describe a new method for numeric computations, which we call affine arithmetic (AA). This model is similar to standard interval arithmetic, to the extent that it automatically keeps track of rounding and truncation errors for each computed value. However, by taking into account correlations between operands and subformulas, AA is able to provide much tighter bounds for the computed quantities, with errors that are approximately quadratic in the uncertainty of the input variables. We also describe two applications of AA to computer graphics problems, where this feature is particularly valuable: namely, ray tracing and the construction of octrees for implicit surfaces.
Prague Copyright c
, 2000
"... fulfillment of the requirements for the degree of Doctor. Global illumination research aiming at the photorealistic image synthesis pushes forward research in computer graphics as a whole. The computation of visually plausible images is timeconsuming and far from being realtime at present. A signi ..."
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fulfillment of the requirements for the degree of Doctor. Global illumination research aiming at the photorealistic image synthesis pushes forward research in computer graphics as a whole. The computation of visually plausible images is timeconsuming and far from being realtime at present. A significant part of computation in global illumination algorithms involves repetitive computing of visibility queries. In the thesis, we describe our results in ray shooting, which is a wellknown problem in the field of visibility. The problem is difficult in spite of its simple definition: For a given oriented halfline and a set of objects, find out the first object intersected by the halfline if such an object exists. A naïve algorithm has the time complexity ¡£ ¢ N ¤ , where N is the number of objects. The naïve algorithm is practically inapplicable in global illumination applications for a scene with a high number of objects, due its huge time requirements. In this thesis we deal with heuristic ray shooting algorithms that use additional spatial data structures. We put stress on averagecase complexity and we particularly investigate the ray shooting algorithms based on spatial hierarchies. In the thesis we deal with two major topics.
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"... Interval arithmetic (IA), also known as interval analysis, isatechnique for numerical computation where each quantity is represented byaninterval of oatingpointnumbers. Those intervals are added, subtracted, ..."
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Interval arithmetic (IA), also known as interval analysis, isatechnique for numerical computation where each quantity is represented byaninterval of oatingpointnumbers. Those intervals are added, subtracted,
EFFICIENT POLYGONIZATION OF CSG SOLIDS USING BOUNDARY TRACKI:NG+
"... AbstractIn this paper, we propose a procedure that directly polygonizes the boundary surface of CSG solids. The procedure consists of a preprocessing step and a polygonization process followed by a postprocessing that recovers rounded edges and corners. In the preprocessing step, the minimum boundi ..."
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AbstractIn this paper, we propose a procedure that directly polygonizes the boundary surface of CSG solids. The procedure consists of a preprocessing step and a polygonization process followed by a postprocessing that recovers rounded edges and corners. In the preprocessing step, the minimum bounding volumes, called Sbounds, of all nodes in the given CSG tree are computed and then used as a basis for subdividing the Sbound of the tree’s root. In addition, a regular grid embedded on the root’s Sbound is constructed. The polygonization is performed in such a way that among leaf voxels of the space subdivision only voxels that overlap the solid’s boundary are traversed and inside such voxels only grid cells transversal to the solid’s boundary are tracked. The surface*dge intersections and vertex normals are computed directly from the exact boundary surfaces of the CSG solid. In the postprocessing step, rounded edges and corners are detected and recovered using primitive geometry. Q 1997 Elsevier Science Ltd. All rights reserved 1.