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57
A Topology Simplification Method For 2D Vector Fields
, 2000
"... Topology analysis of plane, turbulent vector fields results in visual clutter caused by critical points indicating vortices of finer and finer scales. A simplification can be achieved by merging critical points within a prescribed radius into higher order critical points. After building clusters con ..."
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Cited by 64 (10 self)
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Topology analysis of plane, turbulent vector fields results in visual clutter caused by critical points indicating vortices of finer and finer scales. A simplification can be achieved by merging critical points within a prescribed radius into higher order critical points. After building clusters containing the singularities to merge, the method generates a piecewise linear representation of the vector field in each cluster containing only one (higher order) singularity. Any visualization method can be applied to the result after this process. Using different maximal distances for the critical points to be merged results in a hierarchy of simplified vector fields that can be used for analysis on different scales.
Vector and Tensor Field Topology Simplification, Tracking, and Visualization
 PhD. thesis, Schriftenreihe Fachbereich Informatik (3), Universität
, 2002
"... Abstract. Topologybased visualization of planar turbulent flows results in visual clutter due to the presence of numerous features of very small scale. In this paper, we attack this problem with a topology simplification method for vector and tensor fields defined on irregular grids. This is the ge ..."
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Cited by 44 (3 self)
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Abstract. Topologybased visualization of planar turbulent flows results in visual clutter due to the presence of numerous features of very small scale. In this paper, we attack this problem with a topology simplification method for vector and tensor fields defined on irregular grids. This is the generalization of previous work dealing with structured grids. The method works for all interpolation schemes. 1
TopologyBased Flow Visualization, The State of the Art. In
 Topologybased Methods in Visualization,
, 2007
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A LevelSet Method for Flow Visualization
 IN PROCEEDINGS OF VIZ2000, IEEE VISUALIZATION
, 2000
"... In this paper we propose a technique for visualizing steady flow. Using this technique, we first convert the vector field data into a scalar levelset representation. We then analyze the dynamic behavior and subsequent distortion of levelsets and interactively monitor the evolving structures by mea ..."
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Cited by 42 (1 self)
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In this paper we propose a technique for visualizing steady flow. Using this technique, we first convert the vector field data into a scalar levelset representation. We then analyze the dynamic behavior and subsequent distortion of levelsets and interactively monitor the evolving structures by means of texturebased surface rendering. Next, we combine geometrical and topological considerations to derive a multiscale representation and to implement a method for the automatic placement of a sparse set of graphical primitives depicting homogeneous streams in the fields. Using the resulting algorithms, we have built a visualization system that enables us to effectively display the flow direction and its dynamics even for dense 3D fields.
Flow Field Clustering via Algebraic Multigrid
 In Proc. IEEE Visualization Conf. ’04
, 2004
"... We present a novel multiscale approach for flow visualization. We define a local alignment tensor that encodes a measure for alignment to the direction of a given flow field. This tensor induces an anisotropic differential operator on the flow domain, which is discretized with a standard finite elem ..."
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Cited by 27 (4 self)
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We present a novel multiscale approach for flow visualization. We define a local alignment tensor that encodes a measure for alignment to the direction of a given flow field. This tensor induces an anisotropic differential operator on the flow domain, which is discretized with a standard finite element technique. The entries of the corresponding stiffness matrix represent the anisotropically weighted couplings of adjacent nodes of the domain mesh. We use an algebraic multigrid algorithm to generate a hierarchy of fine to coarse descriptions for the above coupling data. This hierarchy comprises a set of coarse grid nodes, a multiscale of basis functions and their corresponding supports. We use these supports to obtain a multilevel decomposition of the flow structure. Standard streamline icons are used to visualize this decomposition at any userselected level of detail. The method provides a single framework for vector field decomposition independent on the domain dimension or mesh type. Applications are shown in 2D, for flow fields on curved surfaces, and for 3D volumetric flow fields. 1
Comparative Flow Visualization
, 2004
"... There are many situations where one needs to compare two or more data sets. It may be to compare different models, different resolutions, differences in algorithms, different experimental results, etc. There is therefore a need for comparative visualization tools to help analyze the differences. Th ..."
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Cited by 27 (0 self)
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There are many situations where one needs to compare two or more data sets. It may be to compare different models, different resolutions, differences in algorithms, different experimental results, etc. There is therefore a need for comparative visualization tools to help analyze the differences. This paper focuses on comparative visualization tools for analyzing flow or vector data sets. The techniques presented allow one to compare individual streamlines and streamribbons as well as a dense field of streamlines. These comparison methods can also be used to study differences in vortex cores that are represented as polylines.
The state of the art in flow visualization: Partitionbased techniques
 In Simulation and Visualization 2008 Proceedings
, 2008
"... Flow visualization has been a very active subfield of scientific visualization in recent years. From the resulting large variety of methods this paper discusses partitionbased techniques. The aim of these approaches is to partition the flow in areas of common structure. Based on this partitioning, ..."
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Cited by 22 (2 self)
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Flow visualization has been a very active subfield of scientific visualization in recent years. From the resulting large variety of methods this paper discusses partitionbased techniques. The aim of these approaches is to partition the flow in areas of common structure. Based on this partitioning, subsequent visualization techniques can be applied. A classification is suggested and advantages/disadvantages of the different techniques are discussed as well. 1
A Phase Field Model for Continuous Clustering on Vector Fields
 IEEE Transactions on Visualization and Computer Graphics
"... A new method for the simplification of flow fields is presented. It is based on continuous clustering. A wellknown physical clustering model, the Cahn Hilliard model which describes phase separation, is modified to reflect the properties of the data to be visualized. Clusters are defined implicitly ..."
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Cited by 21 (3 self)
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A new method for the simplification of flow fields is presented. It is based on continuous clustering. A wellknown physical clustering model, the Cahn Hilliard model which describes phase separation, is modified to reflect the properties of the data to be visualized. Clusters are defined implicitly as connected components of the positivity set of a density function. An evolution equation for this function is obtained as a suitable gradient flow of an underlying anisotropic energy functional. Here, time serves as the scale parameter. The evolution is characterized by a successive coarsening of patterns — the actual clustering — during which the underlying simulation data specifies preferable pattern boundaries. We introduce specific physical quantities in the simulation to control the shape, orientation and distribution of the clusters, as a function of the underlying flow field. In addition the model is expanded involving elastic effects. Thereby in early stages of the evolution shear layer type representation of the flow field can be generated, whereas for later stages the distribution of clusters can be influenced. Furthermore, we incorporate upwind ideas to give the clusters an oriented drop–shaped appearance. Here we discuss the applicability of this new type of approach mainly for flow fields, where the cluster energy penalizes cross streamline boundaries. However, the method also carries provisions for other fields as well. The clusters can be displayed directly as a flow texture. Alternatively, the clusters can be visualized by iconic representations, which are positioned by using a skeletonization algorithm. 1
Higher Dimensional Vector Field Visualization: A Survey
, 2009
"... Vector field visualization research has evolved very rapidly over the last two decades. There is growing consensus amongst the research community that the challenge of twodimensional vector field visualization is virtually solved as a result of the tremendous amount of effort put into this problem. ..."
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Cited by 19 (9 self)
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Vector field visualization research has evolved very rapidly over the last two decades. There is growing consensus amongst the research community that the challenge of twodimensional vector field visualization is virtually solved as a result of the tremendous amount of effort put into this problem. Twodimensional flow, both steady and unsteady can be visualized in realtime, with complete coverage of the flow without much difficulty. However, the same cannot be said of flow in higherspatial dimensions, e.g. surfaces in 3D (2.5D) or volumetric flow (3D). We present a survey of higherspatial dimensional flow visualization techniques based on the presumption that little work remains for the case of twodimensional flow whereas many challenges still remain for the cases of 2.5D and 3D domains. This survey provides the most uptodate review of the stateoftheart of flow visualization in higher dimensions. The reader is provided with a highlevel overview of research in the field highlighting both solved and unsolved problems in this rapidly evolving direction of research.
Parallel Hierarchical Visualization of Large TimeVarying 3D Vector Fields
, 2007
"... We present the design of a scalable parallel pathline construction method for visualizing large timevarying 3D vector fields. A 4D (i.e., time and the 3D spatial domain) representation of the vector field is introduced to make a timeaccurate depiction of the flow field. This representation also all ..."
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Cited by 18 (0 self)
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We present the design of a scalable parallel pathline construction method for visualizing large timevarying 3D vector fields. A 4D (i.e., time and the 3D spatial domain) representation of the vector field is introduced to make a timeaccurate depiction of the flow field. This representation also allows us to obtain pathlines through streamline tracing in the 4D space. Furthermore, a hierarchical representation of the 4D vector field, constructed by clustering the 4D field, makes possible interactive visualization of the flow field at different levels of abstraction. Based on this hierarchical representation, a data partitioning scheme is designed to achieve high parallel efficiency. We demonstrate the performance of parallel pathline visualization using data sets obtained from terascale flow simulations. This new capability will enable scientists to study their timevarying vector fields at the resolution and interactivity previously unavailable to them.