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84
Over Two Decades of IntegrationBased, Geometric Flow
 EUROGRAPHICS 2009 / M. PAULY AND G. GREINER, STAR  STATE OF THE ART REPORT
, 2009
"... Flow visualization is a fascinating subbranch of scientific visualization. With ever increasing computing power, it is possible to process ever more complex fluid simulations. However, a gap between data set sizes and our ability to visualize them remains. This is especially true for the field of f ..."
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Cited by 31 (5 self)
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Flow visualization is a fascinating subbranch of scientific visualization. With ever increasing computing power, it is possible to process ever more complex fluid simulations. However, a gap between data set sizes and our ability to visualize them remains. This is especially true for the field of flow visualization which deals with large, timedependent, multivariate simulation datasets. In this paper, geometry based flow visualization techniques form the focus of discussion. Geometric flow visualization methods place discrete objects in the vector field whose characteristics reflect the underlying properties of the flow. A great amount of progress has been made in this field over the last two decades. However, a number of challenges remain, including placement, speed of computation, and perception. In this survey, we review and classify geometric flow visualization literature according to the most important challenges when considering such a visualization, a central theme being the seeding object upon which they are based. This paper details our investigation into these techniques with discussions on their applicability and their relative merits and drawbacks. The result is an uptodate overview of the current stateoftheart that highlights both solved and unsolved problems in this rapidly evolving branch of research. It also serves as a concise introduction to the field of flow visualization research.
Vector field editing and periodic orbit extraction using morse decomposition
 IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS
, 2007
"... Design and control of vector fields is critical for many visualization and graphics tasks such as vector field visualization, fluid simulation, and texture synthesis. The fundamental qualitative structures associated with vector fields are fixed points, periodic orbits, and separatrices. In this pa ..."
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Cited by 27 (13 self)
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Design and control of vector fields is critical for many visualization and graphics tasks such as vector field visualization, fluid simulation, and texture synthesis. The fundamental qualitative structures associated with vector fields are fixed points, periodic orbits, and separatrices. In this paper, we provide a new technique that allows for the systematic creation and cancellation of fixed points and periodic orbits. This technique enables vector field design and editing on the plane and surfaces with desired qualitative properties. The technique is based on Conley theory, which provides a unified framework that supports the cancellation of fixed points and periodic orbits. We also introduce a novel periodic orbit extraction and visualization algorithm that detects, for the first time, periodic orbits on surfaces. Furthermore, we describe the application of our periodic orbit detection and vector field simplification algorithms to engine simulation data demonstrating the utility of the approach. We apply our design system to vector field visualization by creating data sets containing periodic orbits. This helps us understand the effectiveness of existing visualization techniques. Finally, we propose a new streamlinebased technique that allows vector field topology to be easily identified.
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 20 (3 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
PLIC: Bridging the Gap Between Streamlines and LIC
 In Proceedings of Visualization ’99
, 1999
"... This paper lays the groundwork for comparing flow visualizations using streamlines and line integral convolution (LIC). Our approach is to identify and define relevant parameters in each of these flow visualization techniques. Mapping strategies are then designed to generate LIClike images from str ..."
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Cited by 19 (1 self)
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This paper lays the groundwork for comparing flow visualizations using streamlines and line integral convolution (LIC). Our approach is to identify and define relevant parameters in each of these flow visualization techniques. Mapping strategies are then designed to generate LIClike images from streamlines and streamlinelike images from LIC. The result is a technique which we call pseudoLIC or PLIC. The main contribution being reported in this paper is a methodology for flexibly generating flow visualizations that span the spectrum of streamlinelike to LIClike. Among the advantages are: performance speedups over LIC, applicability to time varying data sets, and variablespeed animation. Key Words and Phrases: unsteady flow, variable speed animation, jitter, texture mapping, comparative visualization. 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 17 (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
Strategies for Interactive Exploration of 3D Flow Using EvenlySpaced Illuminated Streamlines
, 2003
"... This paper presents several strategies to interactively explore 3D flow. Based on a fast illuminated streamlines algorithm, standard graphics hardware is sufficient to gain interactive rendering rates. Our approach does not require the user to have any prior knowledge of flow features. After the str ..."
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Cited by 17 (1 self)
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This paper presents several strategies to interactively explore 3D flow. Based on a fast illuminated streamlines algorithm, standard graphics hardware is sufficient to gain interactive rendering rates. Our approach does not require the user to have any prior knowledge of flow features. After the streamlines are computed in a short preprocessing time, the user can interactively change appearance and density of the streamlines to further explore the flow. Most important flow features like velocity or pressure not only can be mapped to all available streamline appearance properties like streamline width, material, opacity, but also to streamline density. To improve spatial perception of the 3D flow we apply techniques based on animation, depth cueing, and halos along a streamline if it is crossed by another streamline in the foreground. Finally, we make intense use of focus+context methods like magic volumes, region of interest driven streamline placing, and spotlights to solve the occlusion problem.
StateoftheArt Report 2002 in Flow Visualization
, 2002
"... Flow visualization has been a very attractive field within visualization research for a long time already. Usually huge datasets need to be processed, which often consist of multivariate data with a really large number of sample locations, often arranged in multiple timesteps. Recently, the ever ..."
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Cited by 15 (0 self)
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Flow visualization has been a very attractive field within visualization research for a long time already. Usually huge datasets need to be processed, which often consist of multivariate data with a really large number of sample locations, often arranged in multiple timesteps. Recently, the ever increasing performance of computers again has become a driving factor for a new boom in flow visualization (FlowViz), especially in FlowViz based on additional computation such as feature extraction, vector field clustering, and topology extraction. In this stateoftheart report, an attempt was made to (1) provide a useful categorization of FlowViz solutions, (2) give a surveylike overview about existing solutions, and (3) focus on recent work, especially in the field of FlowViz based on derived data. We give careful consideration as to how these topics are best organized for such a presentation. In separate sections we describe (a) direct FlowViz techniques such as using arrows, (b) FlowViz using integral object such as stream lines, (c) spacefilling FlowViz, including, spot noise or line integral convolution, and (d) FlowViz based on derived data such as flow topology. Within those sections, the discussion of FlowViz literature is substructured accoring to the dimensionality of the flow data (from 2D to 3D).
A Survey on Visualization of Vector Fields By TextureBased Methods
 Devel. Pattern Rec
, 2000
"... Visualization of vector data produced from application areas such as computational fluid dynamics (CFD), environmental sciences, and material engineering is a challenging task. Traditional visualization approaches, such as vector plot, particle tracing, stream surfaces, volume rendering, and so on, ..."
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Cited by 14 (0 self)
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Visualization of vector data produced from application areas such as computational fluid dynamics (CFD), environmental sciences, and material engineering is a challenging task. Traditional visualization approaches, such as vector plot, particle tracing, stream surfaces, volume rendering, and so on, often provide a rather coarse spatial resolution. This problem is tackled by texturebased algorithms, which can provide the flow visualization by high resolution output texture. Texturebased methods reveal to be effective, versatile, and suitable for a large spectrum of application. In this paper we review, outlining advantages and drawbacks, the most important texturebased techniques known in the literature for: 2D and 3D, steady and unsteady, regular and curvilinear vector grids. 1 INTRODUCTION Visualization of vector data has always been one of the most attractive challenges in the scientific visualization field; Figure 1 shows the classification of the main methodologies known in t...
Advanced visualization technology for terascale particle accelerator simulations
 In Proceedings of Supercomputing 2002 Conference
, 2002
"... This paper presents two new hardwareassisted rendering techniques developed for interactive visualization of the terascale data generated from numerical modeling of nextgeneration accelerator designs. The first technique, based on a hybrid rendering approach, makes possible interactive exploration ..."
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Cited by 14 (6 self)
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This paper presents two new hardwareassisted rendering techniques developed for interactive visualization of the terascale data generated from numerical modeling of nextgeneration accelerator designs. The first technique, based on a hybrid rendering approach, makes possible interactive exploration of largescale particle data from particle beam dynamics modeling. The second technique, based on a compact textureenhanced representation, exploits the advanced features of commodity graphics cards to achieve perceptually effective visualization of the very dense and complex electromagnetic fields produced from the modeling of reflection and transmission properties of open structures in an accelerator design. Because of the collaborative nature of the overall accelerator modeling project, the visualization technology developed is for both desktop and remote visualization settings. We have tested the techniques using both timevarying particle data sets containing up to one billion particles per time step and electromagnetic field data sets with millions of mesh elements.