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Volume Rendering
, 1988
"... A technique for rendering images Of volumes containing mixtures of materials is presented. The shading model allows both the interior of a material and the boundary between materials to be colored. Image projection is performed by simulating the absorption of light along the ray path to the eye. The ..."
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Cited by 384 (2 self)
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A technique for rendering images Of volumes containing mixtures of materials is presented. The shading model allows both the interior of a material and the boundary between materials to be colored. Image projection is performed by simulating the absorption of light along the ray path to the eye. The algorithms used are designed to avoid artifacts caused by aliasing and quantization and can be efficiently implemented on an image computer. Images from a variety of applications are shown.
Topological Considerations in Isosurface Generation
 ACM Transactions on Graphics
, 1994
"... A popular technique for rendition of isosurfaces in sampled data is to consider cells with sample points as corners and approximate the isosurface in each cell by one or more polygons whose vertices are obtained by interpolation of the sample data. That is, each polygon vertex is a point on a cell e ..."
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Cited by 96 (0 self)
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A popular technique for rendition of isosurfaces in sampled data is to consider cells with sample points as corners and approximate the isosurface in each cell by one or more polygons whose vertices are obtained by interpolation of the sample data. That is, each polygon vertex is a point on a cell edge, between two adjacent sample points, where the function is estimated to equal the desired threshold value. The two sample points have values on opposite sides of the threshold, and the interpolated point is called an intersection point. When one cell face has an intersection point ineach of its four edges, then the correct connection among intersection points becomes ambiguous. An incorrect connection can lead to erroneous topology in the rendered surface, and possible discontinuities. We show that disambiguation methods, to be at all accurate, need to consider sample values in the neighborhood outside the cell. This paper studies the problems of disambiguation, reports on some solutions, and presents some statistics on the occurrence of such ambiguities. A natural way to incorporate neighborhood information is through the use of calculated gradients at cell corners. They provide insight into the behavior of a function in wellunderstood ways. We introduce two gradientconsistency heuristics that use calculated gradients at the corners of ambiguous faces, as well as the function values at those corners, to disambiguate at a reasonable computational cost. These methods give the correct topology on several examples that caused problems for other methods we examined.
Ray casting implicit procedural noises with reduced affine arithmetic
 Dept. of Comp. Science, The University of Sheffield
, 2005
"... A method for ray casting implicit surfaces, defined with procedural noise models, is presented. The method is robust in that it is able to guarantee correct intersections at all image pixels and for all types of implicit surfaces. This robustness comes from the use of an affine arithmetic representa ..."
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Cited by 3 (3 self)
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A method for ray casting implicit surfaces, defined with procedural noise models, is presented. The method is robust in that it is able to guarantee correct intersections at all image pixels and for all types of implicit surfaces. This robustness comes from the use of an affine arithmetic representation for the quantity that expresses the variation of the implicit function along a ray. Affine arithmetic provides a bounding interval estimate which is tighter than the interval estimates returned by conventional interval arithmetic. Our ray casting method is also efficient due to a proposed modification in the data structure used to hold affine arithmetic quantities. This modified data structure ultimately leads to a reduced affine arithmetic model. We show that such a reduced affine arithmetic model is able to retain all the tight estimation capabilities of standard affine arithmetic, in the context of ray casting implicit procedural noises, while being faster to compute and more efficient to store. We also show that, without this reduced model, affine arithmetic would not have any advantage over the more conventional interval arithmetic for ray casting the class of implicit procedural surfaces that we are interested in visualizing.
A decomposable algorithm for contour surface display generation
 ACM Transactions on Graphics
, 1988
"... We present a study of a highly decomposable algorithm useful for the parallel generation of a contour surface display. The core component of this algorithm is a twodimensional contouring algorithm that operates on a single 2 X 2 subgrid of a larger grid. An intuitive procedure for the operations us ..."
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Cited by 1 (0 self)
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We present a study of a highly decomposable algorithm useful for the parallel generation of a contour surface display. The core component of this algorithm is a twodimensional contouring algorithm that operates on a single 2 X 2 subgrid of a larger grid. An intuitive procedure for the operations used to generate the contour lines for a subgrid is developed. A data structure, the contouring tree, is introduced as the basis of a new algorithm for generating the contour lines for the subgrid. The construction of the contouring tree is detailed. Space requirements for the contouring tree algorithm are described for particular implementations.
unknown title
"... A technique for rendering images Of volumes containing mixtures of materials is presented. The shading model allows both the interior of a material and the boundary between materials to be colored. Image projection is performed by simulating the absorption of light along the ray path to the eye. The ..."
Abstract
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A technique for rendering images Of volumes containing mixtures of materials is presented. The shading model allows both the interior of a material and the boundary between materials to be colored. Image projection is performed by simulating the absorption of light along the ray path to the eye. The algorithms used are designed to avoid artifacts caused by aliasing and quantization and can be efficiently implemented on an image computer. Images from a variety of applications are shown.
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, 2005
"... iii iv GOKUL VARADHAN: Accurate SamplingBased Algorithms for Surface Extraction and Motion Planning. (Under the direction of Dinesh Manocha.) Boolean operations, Minkowski sum evaluation, configuration space computation, and motion planning are fundamental problems in solid modeling and robotics. T ..."
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iii iv GOKUL VARADHAN: Accurate SamplingBased Algorithms for Surface Extraction and Motion Planning. (Under the direction of Dinesh Manocha.) Boolean operations, Minkowski sum evaluation, configuration space computation, and motion planning are fundamental problems in solid modeling and robotics. Their applications include computeraided design, numericallycontrolled machining, tolerance verification, packing, assembly planning, and dynamic simulation. Prior algorithms for solving these problems can be classified into exact and approximate approaches. The exact approaches are difficult to implement and are prone to robustness problems. Current approximate approaches may not solve these problems accurately. Our work aims to bridge this gap between exact and approximate approaches. We present a samplingbased approach to solve these geometric problems. Our approach
Accurate SamplingBased Algorithms for Surface Extraction and Motion Planning
, 2005
"... Boolean operations, Minkowski sum evaluation, configuration space computation, and motion planning are fundamental problems in solid modeling and robotics. Their applications include computeraided design, numericallycontrolled machining, tolerance verification, packing, assembly planning, and dyna ..."
Abstract
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Boolean operations, Minkowski sum evaluation, configuration space computation, and motion planning are fundamental problems in solid modeling and robotics. Their applications include computeraided design, numericallycontrolled machining, tolerance verification, packing, assembly planning, and dynamic simulation. Prior algorithms for solving these problems can be classified into exact and approximate approaches. The exact approaches are difficult to implement and are prone to robustness problems. Current approximate approaches may not solve these problems accurately. Our work aims to bridge this gap between exact and approximate approaches. We present a samplingbased approach to solve these geometric problems. Our approach
A Contour Display Generation Algorithm for VLSI Implementation
"... Recent articles have discussed the current trend towards designing raster graphics algorithms into VLSI chips. The purpose of these design efforts is to capture some of the realtime animation capability found in vector graphics systems. Currently, realtime vector graphics animation is limited prim ..."
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Recent articles have discussed the current trend towards designing raster graphics algorithms into VLSI chips. The purpose of these design efforts is to capture some of the realtime animation capability found in vector graphics systems. Currently, realtime vector graphics animation is limited primarily to operations involving coordinate transformations. In order to enhance this animation capability, frequently encountered vector graphics algorithms that require the high speed, parallel computation capability of VLSI must be identified. Realtime contour display generation from grid data is one such algorithm. This paper describes the specifics of a contour display generation algorithm, the architectural framework of a processor that performs this algorithm and the architectural requirements of such a processor. The contouring algorithm is based on a data structure, the contouring tree, whose regularity and amenability for parallel computation make it an ideal candidate for VLSI. The architectural framework for a contouring processor chip that performs this algoritkm for the realtime environment of interactive graphics is discussed, particularly the issues of memory size and data distribution. A model of the contouring process is created in order to determine the necessary physical parameters of the contouring processor in this architectural framework. Conclusions are drawn concerning the feasibility of producing a VLSI chip that performs this contouring algorithm.