Figure 1: The visualization of CFD simulation data from a cooling jacket: (left) texture-based flow visualization applied to the surface, (middle) semi-automatic extraction and visualization of vortex core lines using the moving cutting plane method and, (right) a feature-based, focus+context visualization showing regions of near-stagnant flow, specified interactively. Each snap-shot is accompanied by a close-up. 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 ideal-as-possible 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 texture-based flow visualization techniques as well as automatic feature extraction and interactive feature-based 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 feature-rich state-of-the-art flow visualization analysis applied to an important and complex data set from real-world computational fluid dynamics simulations.

Abstract—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 streamline-based technique that allows vector field topology to be easily identified. Index Terms—Vector field design, vector field visualization, vector field topology, vector field simplification, Morse decomposition, Conley index, periodic orbit detection, connection graphs. 1

Flow visualization research has made rapid advances in recent years, especially in the area of topology-based flow visualization. The ever increasing size of scientific data sets favors algorithms that are capable of extracting important subsets of the data, leaving the scientist with a more manageable representation that may be visualized interactively. Extracting the topology of a flow achieves the goal of obtaining a compact representation of a vector or tensor field while simultaneously retaining its most important features. We present the state of the art in topology-based flow visualization techniques. We outline numerous topology-based algorithms categorized according to the type and dimensionality of data on which they operate and according to the goal-oriented nature of each method. Topology tracking algorithms are also discussed. The result serves as a useful introduction and overview to research literature concerned with the study of topology-based flow visualization.

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 in-cylinder flows. The simulation data associated with in-cylinder tumble motion within a gas engine, given on an unstructured, time-varying and adaptive resolution CFD grid, demands robust visualization methods that apply to unsteady flow. We present a range of methods including integral, feature-based, and image-based schemes with the goal of extracting and visualizing these two important patterns of motion. We place a strong emphasis on automatic and semi-automatic methods, including topological analysis, that require little or no user input. We make effective use of animation to visualize the time-dependent simulation data and describe the challenges and some of the implementation measures necessary in an application of the presented methods to unstructured, time-varying and volumetric grids.

Flow visualization is a fascinating sub-branch 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 up-to-date overview of the current state-of-the-art 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.

Abstract — Existing topology-based 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 τ-maps, 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 τ-maps, 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 τ-maps in addition to the original temporal τ-maps. 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.

Configurations of dense locally parallel 3D curves occur in medical imaging, computer vision and graphics. Examples include white matter fibre tracts, textures, fur and hair. We develop a differential geometric characterization of such structures by considering the local behaviour of the associated 3D frame field, leading to the associated tangential, normal and bi-normal curvature functions. Using results from the theory of generalized minimal surfaces we adopt a generalized helicoid model as an osculating object and develop the connection between its parameters and these curvature functions. These developments allow for the construction of parametrized 3D vector fields (sampled osculating objects) to locally approximate these patterns. We apply these results to the analysis of diffusion MRI data via a type of 3D streamline flow. Experimental results on data from a human brain demonstrate the advantages of incorporating the full differential geometry. 1.

As the size of CFD simulation data sets expand, the job of the engineer to analyze, explore, and present the data becomes more challenging. The scientific visualization tools used by the engineer should evolve to meet the growing demands presented by large simulation data sets. Furthermore, no single visualization technique can meet each users needs. We present a detailed selection of recently developed direct, geometric, and texture-based flow visualization techniques. These techniques address the demand, set forth by engineers, for visualization solutions which provide insight into CFD simulation data. Included are algorithms for (1) the resampling of CFD simulation data, (2) fast, animated texture-based flow visualization, and (3) geometric flow visualization including dashed, animated-streamlines, oriented streamlines, streamlets, and streamcomets. Each approach is targeted at the visual analysis of computational fluid dynamics (CFD) simulation data. This relatively new selection of techniques provides valuable tools that allow engineers to gain insight into their CFD simulation results. Keywords computational fluid dynamics (CFD), flow visualization, vector field visualization, resampling, streamlines, texture advection

Abstract. Sensors such as video surveillance and weather monitoring systems record a significant amount of dynamic data which are represented by vector fields. We present a novel algorithm to measure the similarity of vector fields using global distributions that capture both vector field properties (e.g., vector orientation) and relational geometric information (e.g., the relative positions of two vectors in the field). We show that such global distributions are capable of distinguishing between vector fields of varying complexity and can be used to quantitatively compare similar fields.

Abstract—We present results from a user study that compared four visualization methods for three-dimensional vector data. Using visualizations from each method participants performed five simple but representative tasks: 1) determining whether a given point was a critical point, 2) identifying the type of a critical point, 3) determining whether a point advects through another, 4) determining whether there is swirling movement at a point, and 5) determining which of two points the vector field is moving faster at. The visualization methods were lines and tubes with both monoscopic and steroescopic viewing. While participants reported a preference for stereo lines, quantitative results showed varying performance by the methods among tasks. We found that users performed these tasks better with methods that: 1) gave a clear representation with no perceived occlusion and 2) clearly visualized curve speed and direction information. These results provide quantitative support for some of the anecdotal evidence concerning visualization methods. The tasks and testing framework also provide a basis for comparing other visualization methods, for creating more effective methods, and for defining additional tasks to further understand the tradeoffs among the methods. Index Terms—3D vector fields, visualization, user study, tubes, lines, stereoscopic and monoscopic viewing 1