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27
Topologybased Simplification for Feature Extraction from 3D Scalar Fields
"... This paper describes a topological approach for simplifying continuous functions defined on volumetric domains. The MorseSmale complex provides a segmentation of the domain into monotonic regions having uniform gradient flow behavior. We present a combinatorial algorithm that simplifies the Morse ..."
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Cited by 35 (16 self)
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This paper describes a topological approach for simplifying continuous functions defined on volumetric domains. The MorseSmale complex provides a segmentation of the domain into monotonic regions having uniform gradient flow behavior. We present a combinatorial algorithm that simplifies the MorseSmale complex by repeated application of two atomic operations that removes pairs of critical points. The simplification procedure leaves important critical points untouched, and is therefore useful for extracting features. We present a visualization of the simplified topology.
Interactive rendering of large unstructured grids using dynamic levelofdetail
 In IEEE Visualization ’05
, 2005
"... We describe a new dynamic levelofdetail (LOD) technique that allows realtime rendering of large tetrahedral meshes. Unlike approaches that require hierarchies of tetrahedra, our approach uses a subset of the faces that compose the mesh. No connectivity is used for these faces so our technique eli ..."
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Cited by 32 (10 self)
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We describe a new dynamic levelofdetail (LOD) technique that allows realtime rendering of large tetrahedral meshes. Unlike approaches that require hierarchies of tetrahedra, our approach uses a subset of the faces that compose the mesh. No connectivity is used for these faces so our technique eliminates the need for topological information and hierarchical data structures. By operating on a simple set of triangular faces, our algorithm allows a robust and straightforward graphics hardware (GPU) implementation. Because the subset of faces processed can be constrained to arbitrary size, interactive rendering is possible for a wide range of data sets and hardware configurations.
Efficient Computation of MorseSmale Complexes for ThreeDimensional Scalar Functions
, 2007
"... The MorseSmale complex is an efficient representation of the gradient behavior of a scalar function, and critical points paired by the complex identify topological features and their importance. We present an algorithm that constructs the MorseSmale complex in a series of sweeps through the data, ..."
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Cited by 23 (11 self)
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The MorseSmale complex is an efficient representation of the gradient behavior of a scalar function, and critical points paired by the complex identify topological features and their importance. We present an algorithm that constructs the MorseSmale complex in a series of sweeps through the data, identifying various components of the complex in a consistent manner. All components of the complex, both geometric and topological, are computed, providing a complete decomposition of the domain. Efficiency is maintained by representing the geometry of the complex in terms of point sets.
A topological approach to simplification of threedimensional scalar functions
 IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS (SPECIAL ISSUE IEEE VISUALIZATION
, 2006
"... This paper describes an efficient combinatorial method for simplification of topological features in a 3D scalar function. The MorseSmale complex, which provides a succinct representation of a function’s associated gradient flow field, is used to identify topological features and their significance ..."
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Cited by 23 (11 self)
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This paper describes an efficient combinatorial method for simplification of topological features in a 3D scalar function. The MorseSmale complex, which provides a succinct representation of a function’s associated gradient flow field, is used to identify topological features and their significance. The simplification process, guided by the MorseSmale complex, proceeds by repeatedly applying two atomic operations that each remove a pair of critical points from the complex. Efficient storage of the complex results in execution of these atomic operations at interactive rates. Visualization of the simplified complex shows that the simplification preserves significant topological features and removes small features and noise.
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
A Practical Approach to MorseSmale Complex Computation: Scalability and Generality
"... Abstract—The MorseSmale (MS) complex has proven to be a useful tool in extracting and visualizing features from scalarvalued data. However, efficient computation of the MS complex for large scale data remains a challenging problem. We describe a new algorithm and easily extensible framework for co ..."
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Cited by 16 (3 self)
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Abstract—The MorseSmale (MS) complex has proven to be a useful tool in extracting and visualizing features from scalarvalued data. However, efficient computation of the MS complex for large scale data remains a challenging problem. We describe a new algorithm and easily extensible framework for computing MS complexes for large scale data of any dimension where scalar values are given at the vertices of a closurefinite and weak topology (CW) complex, therefore enabling computation on a wide variety of meshes such as regular grids, simplicial meshes, and adaptive multiresolution (AMR) meshes. A new divideandconquer strategy allows for memoryefficient computation of the MS complex and simplification onthefly to control the size of the output. In addition to being able to handle various data formats, the framework supports implementationspecific optimizations, for example, for regular data. We present the complete characterization of critical point cancellations in all dimensions. This technique enables the topology based analysis of large data on offtheshelf computers. In particular we demonstrate the first full computation of the MS complex for a 1 billion/1024 3 node grid on a laptop computer with 2Gb memory. Index Terms—Topologybased analysis, MorseSmale complex, large scale data. 1
Streaming simplification of tetrahedral meshes
 IEEE Transactions on Visualization and Computer Graphics
, 2005
"... Abstract—Unstructured tetrahedral meshes are commonly used in scientific computing to represent scalar, vector, and tensor fields in three dimensions. Visualization of these meshes can be difficult to perform interactively due to their size and complexity. By reducing the size of the data, we can ac ..."
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Cited by 13 (6 self)
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Abstract—Unstructured tetrahedral meshes are commonly used in scientific computing to represent scalar, vector, and tensor fields in three dimensions. Visualization of these meshes can be difficult to perform interactively due to their size and complexity. By reducing the size of the data, we can accomplish realtime visualization necessary for scientific analysis. We propose a twostep approach for streaming simplification of large tetrahedral meshes. Our algorithm arranges the data on disk in a streaming, I/Oefficient format that allows coherent access to the tetrahedral cells. A quadricbased simplification is sequentially performed on small portions of the mesh incore. Our output is a coherent streaming mesh which facilitates future processing. Our technique is fast, produces high quality approximations, and operates outofcore to process meshes too large for main memory. Index Terms—Computational geometry and object modeling, outofcore algorithms, streaming algorithms, mesh simplification, large meshes, tetrahedral meshes. 1
Progressive volume rendering of large unstructured grids
 IEEE Transactions on Visualization and Computer Graphics
, 2006
"... We describe a new progressive technique that allows realtime rendering of extremely large tetrahedral meshes. Our approach uses a clientserver architecture to incrementally stream portions of the mesh from a server to a client which refines the quality of the approximate rendering until it converg ..."
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Cited by 13 (3 self)
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We describe a new progressive technique that allows realtime rendering of extremely large tetrahedral meshes. Our approach uses a clientserver architecture to incrementally stream portions of the mesh from a server to a client which refines the quality of the approximate rendering until it converges to a full quality rendering. The results of previous steps are reused in each subsequent refinement, thus leading to an efficient rendering. Our novel approach keeps very little geometry on the client and works by refining a set of rendered images at each step. Our interactive representation of the dataset is efficient, lightweight, and high quality. We present a framework for the exploration of large datasets stored on a remote server with a thin client that is capable of rendering and managing full quality volume visualizations. 1
Interactive pointbased rendering of higherorder tetrahedral data
 IEEE Transactions on Visualization and Computer Graphics
, 2006
"... Computational simulations frequently generate solutions defined over very large tetrahedral volume meshes containing many millions of elements. Furthermore, such solutions may often be expressed using nonlinear basis functions. Certain solution techniques, such as discontinuous Galerkin methods, m ..."
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Cited by 11 (1 self)
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Computational simulations frequently generate solutions defined over very large tetrahedral volume meshes containing many millions of elements. Furthermore, such solutions may often be expressed using nonlinear basis functions. Certain solution techniques, such as discontinuous Galerkin methods, may even produce nonconforming meshes. Such data is difficult to visualize interactively, as it is far too large to fit in memory and many common data reduction techniques, such as mesh simplification, cannot be applied to nonconforming meshes. We introduce a pointbased visualization system for interactive rendering of large, potentially nonconforming, tetrahedral meshes. We propose methods for adaptively sampling points from nonlinear solution data and for decimating points at run time to fit GPU memory limits. Because these are streaming processes, memory consumption is independent of the input size. We also present an orderindependent point rendering method that can efficiently render volumes on the order of 20 million tetrahedra at interactive rates.
Simplification of Unstructured Tetrahedral Meshes by Point Sampling
, 2005
"... Tetrahedral meshes are widely used in scientific computing for representing threedimensional scalar, vector, and tensor fields. The size and complexity of some of these meshes can limit the performance of many visualization algorithms, making it hard to achieve interactive visualization. The use of ..."
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Cited by 7 (3 self)
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Tetrahedral meshes are widely used in scientific computing for representing threedimensional scalar, vector, and tensor fields. The size and complexity of some of these meshes can limit the performance of many visualization algorithms, making it hard to achieve interactive visualization. The use of simplified models is one way to enable the realtime exploration of these datasets. In this paper, we propose a novel technique for simplifying large unstructured meshes. Most current techniques simplify the geometry of the mesh using edge collapses. Our technique simplifies an underlying scalar field directly by segmenting the original scalar field into two pieces: the boundary of the original domain and the interior samples of the scalar field. We then simplify each piece separately, taking into account proper error bounds. Finally, we combine the simplified domain boundary and scalar field into a complete, simplified mesh that can be visualized with standard unstructureddata visualization tools. Our technique is much faster than edgecollapsebased simplification approaches. Furthermore, it is particularly suitable for aggressive simplification. Experiments show that isosurfaces and volume renderings of meshes produced by our technique have few noticeable visual artifacts.