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Over Two Decades of IntegrationBased, Geometric Flow Visualization
 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 75 (13 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 59 (33 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.
Visual Analysis and Exploration of Fluid Flow in a Cooling Jacket
 In Proceedings IEEE Visualization 2005
, 2005
"... Figure 1: The visualization of CFD simulation data from a cooling jacket: (left) texturebased flow visualization applied to the surface, (middle) semiautomatic extraction and visualization of vortex core lines using the moving cutting plane method and, (right) a featurebased, focus+context visual ..."
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Cited by 49 (29 self)
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Figure 1: The visualization of CFD simulation data from a cooling jacket: (left) texturebased flow visualization applied to the surface, (middle) semiautomatic extraction and visualization of vortex core lines using the moving cutting plane method and, (right) a featurebased, focus+context visualization showing regions of nearstagnant flow, specified interactively. Each snapshot is accompanied by a closeup. We present a visual analysis and exploration of fluid flow through a cooling jacket. Engineers invest a large amount of time and serious effort to optimize the flow through this engine component because of its important role in transferring heat away from the engine block. In this study we examine the design goals that engineers apply in order to construct an idealaspossible cooling jacket geometry and use a broad range of visualization tools in order to analyze, explore, and present the results. We systematically employ direct, geometric, and texturebased flow visualization techniques as well as automatic feature extraction and interactive featurebased methodology. And we discuss the relative advantages and disadvantages of these approaches as well as the challenges, both technical and perceptual with this application. The result is a featurerich stateoftheart flow visualization analysis applied to an important and complex data set from realworld computational fluid dynamics simulations.
Efficient Morse Decompositions of Vector Fields
"... Abstract — Existing topologybased vector field analysis techniques rely on the ability to extract the individual trajectories such as fixed points, periodic orbits and separatrices which are sensitive to noise and errors introduced by simulation and interpolation. This can make such vector field an ..."
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Cited by 35 (19 self)
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Abstract — Existing topologybased vector field analysis techniques rely on the ability to extract the individual trajectories such as fixed points, periodic orbits and separatrices which are sensitive to noise and errors introduced by simulation and interpolation. This can make such vector field analysis unsuitable for rigorous interpretations. We advocate the use of Morse decompositions, which are robust with respect to perturbations, to encode the topological structures of a vector field in the form of a directed graph, called a Morse connection graph (MCG). While an MCG exists for every vector field, it need not be unique. Previous techniques for computing MCG’s, while fast, are overly conservative and usually results in MCG’s that are too coarse to be useful for the applications. To address this issue, we present a new technique for performing Morse decomposition based on the concept of τmaps, which typically provides finer MCG’s than existing techniques. Furthermore, the choice of τ provides a natural tradeoff between the fineness of the MCG’s and the computational costs. We provide efficient implementations of Morse decomposition based on τmaps, which include the use of forward and backward mapping techniques and an adaptive approach in constructing better approximations of the images of the triangles in the meshes used for simulation.Furthermore, we propose the use of spatial τmaps in addition to the original temporal τmaps. These techniques provide additional tradeoffs between the quality of the MCG’s and the speed of computation. We demonstrate the utility of our technique with various examples in plane and on surfaces including engine simulation datasets. Index Terms — Vector field topology, Morse decomposition, τmaps, Morse connection graph, flow combinatorialization.
Overview of flow visualization
 The Visualization Handbook
, 2005
"... With increasing computing power, it is possible to process more complex fluid simulations. However, a gap between increasing data size and our ability to visualize them still remains. Despite the great amount of progress that has been made in the field of flow visualization over the last two decades ..."
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Cited by 30 (13 self)
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With increasing computing power, it is possible to process more complex fluid simulations. However, a gap between increasing data size and our ability to visualize them still remains. Despite the great amount of progress that has been made in the field of flow visualization over the last two decades, a number of challenges remain. Whilst the visualization of 2D flow has many good solutions, the visualization of 3D flow still poses many problems. Challenges such as domain coverage, speed of computation, and perception remain key directions for further research. Flow visualization with a focus on surfacebased techniques forms the basis of this literature survey, including surface construction techniques and visualization methods applied to surfaces. We detail our investigation into these algorithms with discussions of their applicability and their relative strengths and drawbacks. We review the most important challenges when considering such visualizations. The result is an uptodate overview of the current stateoftheart that highlights both solved and unsolved problems in this rapidly evolving branch of research.
Asymmetric Tensor Analysis for Flow Visualization
 IEEE Trans. on Visualization and Computer Graphics
"... Abstract—The gradient of a velocity vector field is an asymmetric tensor field which can provide critical insight that is difficult to infer from traditional trajectorybased vector field visualization techniques. We describe the structures in the eigenvalue and eigenvector fields of the gradient te ..."
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Cited by 21 (13 self)
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Abstract—The gradient of a velocity vector field is an asymmetric tensor field which can provide critical insight that is difficult to infer from traditional trajectorybased vector field visualization techniques. We describe the structures in the eigenvalue and eigenvector fields of the gradient tensor and how these structures can be used to infer the behaviors of the velocity field that can represent either a 2D compressible flow or the projection of a 3D compressible or incompressible flow onto a 2D manifold. To illustrate the structures in asymmetric tensor fields, we introduce the notions of eigenvalue manifold and eigenvector manifold. These concepts afford a number of theoretical results that clarify the connections between symmetric and antisymmetric components in tensor fields. In addition, these manifolds naturally lead to partitions of tensor fields, which we use to design effective visualization strategies. Moreover, we extend eigenvectors continuously into the complex domains which we refer to as pseudoeigenvectors. We make use of evenly spaced tensor lines following pseudoeigenvectors to illustrate the local linearization of tensors everywhere inside complex domains simultaneously. Both eigenvalue manifold and eigenvector manifold are supported by a tensor reparameterization with physical meaning. This allows us to relate our tensor analysis to physical quantities such as rotation, angular deformation, and dilation, which provide a physical interpretation of our tensordriven vector field analysis in the context of fluid mechanics. To demonstrate the utility of our approach, we have applied our visualization techniques and interpretation to the study of the Sullivan Vortex as well as computational fluid dynamics simulation data. Index Terms—Tensor field visualization, flow analysis, asymmetric tensors, flow segmentation, tensor field topology, surfaces. Ç 1
Stable Morse Decompositions for Piecewise Constant Vector Fields on Surfaces
, 2011
"... Numerical simulations and experimental observations are inherently imprecise. Therefore, most vector fields of interest in scientific visualization are known only up to an error. In such cases, some topological features, especially those not stable enough, may be artifacts of the imprecision of the ..."
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Cited by 21 (6 self)
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Numerical simulations and experimental observations are inherently imprecise. Therefore, most vector fields of interest in scientific visualization are known only up to an error. In such cases, some topological features, especially those not stable enough, may be artifacts of the imprecision of the input. This paper introduces a technique to compute topological features of userprescribed stability with respect to perturbation of the input vector field. In order to make our approach simple and efficient, we develop our algorithms for the case of piecewise constant (PC) vector fields. Our approach is based on a supertransition graph, a common graph representation of all PC vector fields whose vector value in a mesh triangle is contained in a convex set of vectors associated with that triangle. The graph is used to compute a Morse decomposition that is coarse enough to be correct for all vector fields satisfying the constraint. Apart from computingstableMorsedecompositions, ourtechniquecanalsobeused to estimate the stability of Morse sets with respect to perturbation of the vector field or to compute topological features of continuous vector fields using the PC framework.
Extraction and visualization of swirl and tumble motion from engine simulation data
"... An optimal combustion process within an engine block is central to the performance of many motorized vehicles. Associated with this process are two important patterns of flow: swirl and tumble motion, which optimize the mixing of fluid within each of an engine’s cylinders. Good visualizations are n ..."
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Cited by 15 (7 self)
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An optimal combustion process within an engine block is central to the performance of many motorized vehicles. Associated with this process are two important patterns of flow: swirl and tumble motion, which optimize the mixing of fluid within each of an engine’s cylinders. Good visualizations are necessary to analyze these incylinder flows. The simulation data associated with incylinder tumble motion within a gas engine, given on an unstructured, timevarying and adaptive resolution CFD grid, demands robust visualization methods that apply to unsteady flow. We present a range of methods including integral, featurebased, and imagebased schemes with the goal of extracting and visualizing these two important patterns of motion. We place a strong emphasis on automatic and semiautomatic methods, including topological analysis, that require little or no user input. We make effective use of animation to visualize the timedependent simulation data and describe the challenges and some of the implementation measures necessary in an application of the presented methods to unstructured, timevarying and volumetric grids.
H.: Geometric Flow Visualization Techniques for CFD Simulation Data. In submitted to COMPUTER GRAPHICS Forum (1/2010). T. McLoughlin et al
 Over Two Decades of IntegrationBased, Geometric Flow Visualization 21 Proceedings of the 21st Spring Conference on Computer Graphics
, 2005
"... Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of ..."
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Cited by 10 (3 self)
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Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, to republish, to post on servers, or to redistribute to lists, requires prior specific permission and/or a fee.