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Raytracing Procedural Displacement Shaders
 In Graphics Interface
, 1998
"... Displacement maps and procedural displacement shaders are a widely used approach of specifying geometric detail and increasing the visual complexity of a scene. While it is relatively straightforward to handle displacement shaders in pipeline based rendering systems such as the Reyesarchitecture, i ..."
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Displacement maps and procedural displacement shaders are a widely used approach of specifying geometric detail and increasing the visual complexity of a scene. While it is relatively straightforward to handle displacement shaders in pipeline based rendering systems such as the Reyesarchitecture, it is much harder to efficiently integrate displacementmapped surfaces in raytracers. Many commercial raytracers tessellate the surface into a multitude of small triangles. This introduces a series of problems such as excessive memory consumption and possibly undetected surface detail. In this paper we describe a novel way of raytracing procedural displacement shaders directly, that is, without introducing intermediate geometry. Affine arithmetic is used to compute bounding boxes for the shader over any range in the parameter domain. The method is comparable to the direct raytracing of B'ezier surfaces and implicit surfaces using B'ezier clipping and interval methods, respectively. Keyw...
An Introduction to Affine Arithmetic
, 2003
"... Affine arithmetic (AA) is a model for selfvalidated computation which, like standard interval arithmetic (IA), produces guaranteed enclosures for computed quantities, taking into account any uncertainties in the input data as well as all internal truncation and roundoff errors. Unlike standard I ..."
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Cited by 16 (0 self)
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Affine arithmetic (AA) is a model for selfvalidated computation which, like standard interval arithmetic (IA), produces guaranteed enclosures for computed quantities, taking into account any uncertainties in the input data as well as all internal truncation and roundoff errors. Unlike standard IA, the quantity representations used by AA are firstorder approximations, whose error is generally quadratic in the width of input intervals. In many practical applications, the higher asymptotic accuracy of AA more than compensates for the increased cost of its operations.
Affine Arithmetic: Concepts and Applications
, 2003
"... Affine arithmetic is a model for selfvalidated numerical computation that affine arithmetic keeps track of firstorder correlations between computed and input quantities. We explain the main concepts in affine arithmetic and it handles the dependency problem in standard interval arithmetic. We also ..."
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Cited by 14 (1 self)
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Affine arithmetic is a model for selfvalidated numerical computation that affine arithmetic keeps track of firstorder correlations between computed and input quantities. We explain the main concepts in affine arithmetic and it handles the dependency problem in standard interval arithmetic. We also describe some of its applications.
OpenFab: A programmable pipeline for multimaterial fabrication
 ACM Trans. on Graphics (SIGGRAPH
, 2013
"... Figure 1: Three rhinos, defined and printed using OpenFab. For each print, the same geometry was paired with a different fablet—a shaderlike program which procedurally defines surface detail and material composition throughout the object volume. This produces three unique prints by using displacemen ..."
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Cited by 11 (2 self)
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Figure 1: Three rhinos, defined and printed using OpenFab. For each print, the same geometry was paired with a different fablet—a shaderlike program which procedurally defines surface detail and material composition throughout the object volume. This produces three unique prints by using displacements, texture mapping, and continuous volumetric material variation as a function of distance from the surface. 3D printing hardware is rapidly scaling up to output continuous mixtures of multiple materials at increasing resolution over ever larger print volumes. This poses an enormous computational challenge: large highresolution prints comprise trillions of voxels and petabytes of data and simply modeling and describing the input with spatially varying material mixtures at this scale is challenging. Existing 3D printing software is insufficient; in particular, most software is designed to support only a few million primitives, with discrete material choices per object. We present OpenFab, a programmable pipeline for synthesis of multimaterial 3D printed objects that is inspired by RenderMan and modern GPU pipelines. The pipeline supports procedural evaluation of geometric detail and material composition, using shaderlike fablets, allowing models to be specified easily and efficiently. We describe a streaming architecture for OpenFab; only a small fraction of the final volume is stored in memory and output is fed to the printer with little startup delay. We demonstrate it on a variety of multimaterial objects.
Modified affine arithmetic is more accurate than centered interval arithmetic or affine arithmetic
 IMA Conference on the Mathematics of Surfaces 2003
, 2003
"... Abstract. In this paper we give mathematical proofs of two new results relevant to evaluating algebraic functions over a boxshaped region: (i) using interval arithmetic in centered form is always more accurate than standard affine arithmetic, and (ii) modified affine arithmetic is always more accu ..."
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Abstract. In this paper we give mathematical proofs of two new results relevant to evaluating algebraic functions over a boxshaped region: (i) using interval arithmetic in centered form is always more accurate than standard affine arithmetic, and (ii) modified affine arithmetic is always more accurate than interval arithmetic in centered form. Test results show that modified affine arithmetic is not only more accurate but also much faster than standard affine arithmetic. We thus suggest that modified affine arithmetic is the method of choice for evaluating algebraic functions, such as implicit surfaces, over a box.
Bounded clustering  finding good bounds on clustered light transport
 in: Proc. Pacific Graphics '98, IEEE Computer
, 1998
"... Clustering is a very e cient technique to applynite element methods to the computation of radiosity solutions of complex scenes. Both computation time and memory consumption can be reduced dramatically by grouping the primitives of the input scene into a hierarchy of clusters and allowing for light ..."
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Cited by 10 (3 self)
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Clustering is a very e cient technique to applynite element methods to the computation of radiosity solutions of complex scenes. Both computation time and memory consumption can be reduced dramatically by grouping the primitives of the input scene into a hierarchy of clusters and allowing for light exchange between all levels of this hierarchy. However, problems can arise due to clustering, when gross approximations about a cluster's content result in unsatisfactory solutions or unnecessary computations. In the clustering approach for di use global illumination described in this paper, light exchange between two objects  patches or clusters  is bounded by using geometrical and shading information provided by every object through a uniform interface. With this uniform view of various kinds of objects, comparable and reliable error bounds on the light exchange can be computed, which then guide a standard hierarchical radiosity algorithm. 1.
Approximating Parametric Curves with Strip Trees using Affine Arithmetic
"... We show how to use affine arithmetic to represent a parametric curve with a strip tree. The required bounding rectangles for pieces of the curve are computed by exploiting the linear correlation information given by affine arithmetic. As an application, we show how to compute approximate distance ..."
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Cited by 8 (3 self)
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We show how to use affine arithmetic to represent a parametric curve with a strip tree. The required bounding rectangles for pieces of the curve are computed by exploiting the linear correlation information given by affine arithmetic. As an application, we show how to compute approximate distance fields for parametric curves.
State of the Art in Procedural Noise Functions
, 2010
"... ProceduralnoisefunctionsarewidelyusedinComputerGraphics, from offlinerenderinginmovieproductionto interactivevideogames.Theabilitytoaddcomplexandintricate detailsatlowmemoryandauthoringcostisone of its main attractions. This stateoftheart report is motivated by the inherent importance of noise i ..."
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Cited by 7 (2 self)
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ProceduralnoisefunctionsarewidelyusedinComputerGraphics, from offlinerenderinginmovieproductionto interactivevideogames.Theabilitytoaddcomplexandintricate detailsatlowmemoryandauthoringcostisone of its main attractions. This stateoftheart report is motivated by the inherent importance of noise in graphics, thewidespreaduseofnoiseinindustry,andthefactthatmany recentresearchdevelopmentsjustifytheneedforan uptodatesurvey.Ourgoalistoprovidebothavaluableentrypointinto thefieldofproceduralnoisefunctions,as wellasacomprehensiveviewofthefieldtotheinformedreader. Inthisreport,wecoverproceduralnoisefunctions in all their aspects. We outline recent advances in research on this topic, discussing and comparing recent and well established methods. We first formally define procedural noise functions based on stochastic processes and then classify and review existing procedural noise functions. We discuss how procedural noise functions are used for modeling and how they are applied on surfaces. We then introduce analysis tools and apply them to evaluate andcompare the major approaches tonoisegeneration. We finally identify several directions for future work.
A survey Of procedural Noise functions
 VOLUME0(1981),NUMBER 0PP. 1–20 COMPUTER GRAPHICS FORUM
, 1981
"... ProceduralnoisefunctionsarewidelyusedinComputerGraphics, fromofflinerenderinginmovieproductionto interactivevideogames. Theabilitytoaddcomplexand intricatedetailsatlowmemory and authoring cost is one of its main attractions. This survey is motivated by the inherent importance of noise in graphics, ..."
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Cited by 4 (2 self)
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ProceduralnoisefunctionsarewidelyusedinComputerGraphics, fromofflinerenderinginmovieproductionto interactivevideogames. Theabilitytoaddcomplexand intricatedetailsatlowmemory and authoring cost is one of its main attractions. This survey is motivated by the inherent importance of noise in graphics, the widespread use of noise in industry, and the fact that many recent research developments justify the need for an uptodate survey. Our goal is to provide both a valuable entry point into the field of procedural noise functions, as well as a comprehensive view of the field to the informed reader. In this report, we cover procedural noise functions in all their aspects. We outline recent advances in research on this topic, discussing and comparing recent and well established methods. We first formally define procedural noise functions based on stochastic processes and then classify and review existing procedural noise functions. We discuss how procedural noise functions are used for modeling and how they are applied to surfaces. We then introduce analysis tools and apply them to evaluate and compare the major approaches to noise generation. We finally identify several directions for futur work.