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31
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.
Hardwareaccelerated reconstruction of polygonal isosurface representations on unstructured grids
 In Proceedings of Pacific Graphics ’04
, 2004
"... Volume visualization using isosurface extraction is a wellresearched topic. Recent research demonstrated that even for unstructured grids peak performances of millions of tetrahedra per second can be achieved by exploiting the parallel processing capabilities of modern GPUs. In this paper we presen ..."
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Cited by 36 (0 self)
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Volume visualization using isosurface extraction is a wellresearched topic. Recent research demonstrated that even for unstructured grids peak performances of millions of tetrahedra per second can be achieved by exploiting the parallel processing capabilities of modern GPUs. In this paper we present a novel hardwareaccelerated solution that further improves the extraction performance. In contrary to existing approaches, our technique explicitly extracts the isosurface geometry in a fragment program by rendering only a single screensized quadrilateral. The extracted geometry is directly written to an onboard graphics memory object allowing for direct rendering without further bus transfers. Additionally, the geometry can be manipulated by shader programs or read back to the application for further processing. Examples and application scenarios are given that can benefit from our approach. 1.
A survey of GPUBased volume rendering of unstructured grids
 Brazilian Journal of Theoretic and Applied Computing (RITA
, 2005
"... Realtime rendering of large unstructured meshes is a major research goal in the scientific visualization community. While, for regular grids, texturebased techniques are wellsuited for current Graphics Processing Units (GPUs), the steps necessary for rendering unstructured meshes are not so easil ..."
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Cited by 18 (7 self)
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Realtime rendering of large unstructured meshes is a major research goal in the scientific visualization community. While, for regular grids, texturebased techniques are wellsuited for current Graphics Processing Units (GPUs), the steps necessary for rendering unstructured meshes are not so easily mapped to current hardware. This paper reviews volume rendering algorithm and techniques for unstructured grids aimed at exploiting highperformance GPUs. We discuss both the algorithms and their implementation details, including major shortcomings of existing approaches. Resumo: A visualização volumétrica de grandes malhas não estruturadas é uma das principais metas da comunidade de visualização científica. Enquanto que em grades regulares o uso de técnicas baseadas em textura são adequadas para as Unidades de Processamento Gráfico (GPUs) atuais, os passos necessários para exibir malhas não estruturas não são diretamente mapeadas para o hardware atual. Este artigo revisa algoritmos e técnicas de visualização volumétrica que exploram GPUs de alta performance. São discutidos tanto os algoritmos como seus detalhes de implementação, incluindo as principais dificuldades das abordagens atuais. 1
GPU construction and transparent rendering of isosurface
 Proceedings Vision, Modeling and Visualization 2005
, 2005
"... Isosurface construction and rendering on programmable graphics hardware has recently been shown for tetrahedral grids. In this paper, we present a novel edgebased approach that avoids redundant computations of edge–surface intersections. We show how to achieve a significant performance gain by con ..."
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Cited by 16 (1 self)
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Isosurface construction and rendering on programmable graphics hardware has recently been shown for tetrahedral grids. In this paper, we present a novel edgebased approach that avoids redundant computations of edge–surface intersections. We show how to achieve a significant performance gain by considering intrinsic features of recent GPUs. The isosurface extraction process is reformulated in a way that reduces both numerical computations and memory access operations. A spanspace data structure allows us to avoid the processing of elements not intersected by the selected surface. Finally, to allow for the rendering of transparent surfaces, a GPU sorting routine is integrated
A Generic and Scalable Pipeline for GPU Tetrahedral Grid Rendering
 IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS
, 2006
"... Recent advances in algorithms and graphics hardware have opened the possibility to render tetrahedral grids at interactive rates on commodity PCs. This paper extends on this work in that it presents a direct volume rendering method for such grids which supports both current and upcoming graphics ha ..."
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Cited by 13 (1 self)
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Recent advances in algorithms and graphics hardware have opened the possibility to render tetrahedral grids at interactive rates on commodity PCs. This paper extends on this work in that it presents a direct volume rendering method for such grids which supports both current and upcoming graphics hardware architectures, large and deformable grids, as well as different rendering options. At the core of our method is the idea to perform the sampling of tetrahedral elements along the view rays entirely in local barycentric coordinates. Then, sampling requires minimum GPU memory and texture access operations, and it maps efficiently onto a feedforward pipeline of multiple stages performing computation and geometry construction. We propose to spawn rendered elements from one single vertex. This makes the method amenable to upcoming Direct3D 10 graphics hardware which allows to create geometry on the GPU. By only modifying the algorithm slightly it can be used to render perpixel isosurfaces and to perform tetrahedral cell projection. As our method neither requires any preprocessing nor an intermediate grid representation it can efficiently deal with dynamic and large 3D meshes.
Edge transformations for improving mesh quality of marching cubes
 IEEE TVCG
"... Abstract—Marching Cubes is a popular choice for isosurface extraction from regular grids due to its simplicity, robustness, and efficiency. One of the key shortcomings of this approach is the quality of the resulting meshes, which tend to have many poorly shaped and degenerate triangles. This issue ..."
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Cited by 12 (4 self)
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Abstract—Marching Cubes is a popular choice for isosurface extraction from regular grids due to its simplicity, robustness, and efficiency. One of the key shortcomings of this approach is the quality of the resulting meshes, which tend to have many poorly shaped and degenerate triangles. This issue is often addressed through postprocessing operations such as smoothing. As we demonstrate in experiments with several data sets, while these improve the mesh, they do not remove all degeneracies and incur an increased and unbounded error between the resulting mesh and the original isosurface. Rather than modifying the resulting mesh, we propose a method to modify the grid on which Marching Cubes operates. This modification greatly increases the quality of the extracted mesh. In our experiments, our method did not create a single degenerate triangle, unlike any other method we experimented with. Our method incurs minimal computational overhead, requiring at most twice the execution time of the original Marching Cubes algorithm in our experiments. Most importantly, it can be readily integrated in existing Marching Cubes implementations and is orthogonal to many Marching Cubes enhancements (particularly, performance enhancements such as outofcore and acceleration structures). Index Terms—Meshing, marching cubes. Ç 1
Particle systems for efficient and accurate highorder finite element visualization
 IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS (UNDER REVIEW
, 2007
"... Visualization has become an important component of the simulation pipeline, providing scientists and engineers a visual intuition of their models. Simulations that make use of the highorder finite element method for spatial subdivision, however, present a challenge to conventional isosurface visua ..."
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Cited by 12 (3 self)
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Visualization has become an important component of the simulation pipeline, providing scientists and engineers a visual intuition of their models. Simulations that make use of the highorder finite element method for spatial subdivision, however, present a challenge to conventional isosurface visualization techniques. Highorder finite element isosurfaces are often defined by basis functions in reference space, which give rise to a worldspace solution through a coordinate transformation, which does not necessarily have a closedform inverse. Therefore, worldspace isosurface rendering methods such as marching cubes and ray tracing must perform a nested root finding, which is computationally expensive. We thus propose visualizing these isosurfaces with a particle system. We present a framework that allows particles to sample an isosurface in reference space, avoiding the costly inverse mapping of positions from world space when evaluating the basis functions. The distribution of particles across the reference space isosurface is controlled by geometric information from the worldspace isosurface such as the surface gradient and curvature. The resulting particle distributions can be distributed evenly or adapted to accommodate worldspace surface features. This provides compact, efficient, and accurate isosurface representations of these challenging data sets.
Seed sets and search structures for optimal isocontour extraction
 Texas Institute of Computational and Applied Mathematics
, 1999
"... The search for intersected cells in isocontouring can be accelerated using suitable range query data structures, such as the interval tree or segment tree. The storage overhead of such search structures can be significantly reduced by searching over a subset of the cells Ë, called a seed set, which ..."
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Cited by 9 (1 self)
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The search for intersected cells in isocontouring can be accelerated using suitable range query data structures, such as the interval tree or segment tree. The storage overhead of such search structures can be significantly reduced by searching over a subset of the cells Ë, called a seed set, which contains at least one cell per connected component of every isocontour. We present three algorithms for generating seed sets and compare their time complexity and performance in terms of the number of seed cells generated. The first two algorithms are applicable to both regular and irregular grids of arbitrary dimension, while the third is a specialization for regular grids. The first algorithm produces a nearly optimal seed set, minimizing the storage overhead for the search structure. While the second and third algorithms may produce a larger seed set, they are extremely fast, have the advantage of being suitable for extremely large datasets that cannot be kept in main memory (outofcore computation), and are amenable to parallelization. In each case the resulting seed sets are orders of magnitude smaller than the total number of cells, while the computational complexity remains optimal. We compare the results of the two new algorithms with previous results and recent new work. 2
Interactive Isosurface Ray Tracing of TimeVarying Tetrahedral Volumes
 SCI INSTITUTE, UNIVERSITY OF UTAH
, 2007
"... We describe a system for interactively rendering isosurfaces of tetrahedral finiteelement scalar fields using coherent ray tracing techniques on the CPU. By employing stateofthe art methods in polygonal ray tracing, namely aggressive packet/frustum traversal of a bounding volume hierarchy, we can ..."
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Cited by 8 (4 self)
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We describe a system for interactively rendering isosurfaces of tetrahedral finiteelement scalar fields using coherent ray tracing techniques on the CPU. By employing stateofthe art methods in polygonal ray tracing, namely aggressive packet/frustum traversal of a bounding volume hierarchy, we can accomodate large and timevarying unstructured data. In conjunction with this efficiency structure, we introduce a novel technique for intersecting ray packets with tetrahedral primitives. Ray tracing is flexible, allowing for dynamic changes in isovalue and time step, visualization of multiple isosurfaces, shadows, and depthpeeling transparency effects. The resulting system offers the intuitive simplicity of isosurfacing, guaranteedcorrect visual results, and ultimately a scalable, dynamic and consistently interactive solution for visualizing unstructured volumes.
Fast Ray Traversal of Tetrahedral and Hexahedral Meshes for Direct Volume Rendering
, 2006
"... The importance of highperformance rendering of unstructured or curvilinear data sets has increased significantly, mainly due to its use in scientific simulations such as computational fluid dynamics and finite element computations. However, the unstructured nature of these data sets lead to rather ..."
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Cited by 8 (1 self)
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The importance of highperformance rendering of unstructured or curvilinear data sets has increased significantly, mainly due to its use in scientific simulations such as computational fluid dynamics and finite element computations. However, the unstructured nature of these data sets lead to rather slow implementations for ray tracing. The approaches discussed in this paper are fast and scalable towards realtime ray tracing applications. We evaluate new algorithms for rendering tetrahedral and hexahedral meshes. In each algorithm, the first cell along a ray is found using common realtime ray tracing techniques. For traversing subsequent cells within the volume, Plücker coordinates as well as raybilinear patch intersection tests are used. Since the volume is rendered directly, all algorithms are applicable for isosurface rendering, maximumintensity projection, and emissionabsorption models.