Robert S. Laramee

The State of the Art in Flow Visualisation: Feature Extraction and Tracking

Flow visualisation is an attractive topic in data visualisation, offering great challenges for research. Very large data sets must be processed, consisting of multivariate data at large numbers of grid points, often arranged in many time steps. Recently, the steadily increasing performance of computers again has become a driving force for new advances in flow visualisation, especially in techniques based on texturing, feature extraction, vector field clustering, and topology extraction.

The State of the Art in Flow Visualization: Dense and Texture‐Based Techniques

Flow visualization has been a very attractive component of scientific visualization research for a long time. Usually very large multivariate datasets require processing. These datasets often consist of a large number of sample locations and several time steps. The steadily increasing performance of computers has recently become a driving factor for a reemergence in flow visualization research, especially in texture‐based techniques. In this paper, dense, texture‐based flow visualization techniques are discussed. This class of techniques attempts to provide a complete, dense representation of the flow field with high spatio‐temporal coherency. An attempt of categorizing closely related solutions is incorporated and presented. Fundamentals are shortly addressed as well as advantages and disadvantages of the methods.

Over Two Decades of Integration‐Based, Geometric Flow 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, time‐dependent, multivariate simulation data sets. In this paper, geometry‐based flow visualization techniques form the focus of discussion. Geometric flow visualization methods place discrete objects in the velocity 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 algorithm 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.

Topology-Based Flow Visualization, The State of the Art

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.

Vector Field Editing and Periodic Orbit Extraction Using Morse Decomposition

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.

Image space based visualization of unsteady flow on surfaces

We present a technique for direct visualization of unsteady flow on surfaces from computational fluid dynamics. The method generates dense representations of time-dependent vector fields with high spatio-temporal correlation using both Lagrangian-Eulerian advection and image based flow visualization as its foundation. While the 3D vector fields are associated with arbitrary triangular surface meshes, the generation and advection of texture properties is confined to image space. Frame rates of up to 20 frames per second are realized by exploiting graphics card hardware. We apply this algorithm to unsteady flow on boundary surfaces of, large, complex meshes from computational fluid dynamics composed of more than 250,000 polygons, dynamic meshes with time-dependent geometry and topology, as well as medical data.

Glyph-Based Visualization: Foundations, Design Guidelines, Techniques, and Applications

This state of the art report focuses on glyph-based visualization, a common form of visual design where a data set is depicted by a collection of visual objects referred to as glyphs. Its major strength is that patterns of multivariate data involving more than two attribute dimensions can often be more readily perceived in the context of a spatial relationship, whereas many techniques for spatial data such as direct volume rendering find difficult to depict with multivariate or multi-field data, and many techniques for non-spatial data such as parallel coordinates are less able to convey spatial relationships encoded in the data. This report fills several major gaps in the literature, drawing the link between the fundamental concepts in semiotics and the broad spectrum of glyph-based visualization, reviewing existing design guidelines and implementation techniques, and surveying the use of glyph-based visualization in many applications.

Investigating Swirl and Tumble Flow with a Comparison of Visualization Techniques

We investigate two important, common fluid flow patterns from computational fluid dynamics (CFD) simulations, namely, swirl and tumble motion typical of automotive engines. We study and visualize swirl and tumble flow using three different flow visualization techniques: direct, geometric, and texture-based. When illustrating these methods side-by-side, we describe the relative strengths and weaknesses of each approach within a specific spatial dimension and across multiple spatial dimensions typical of an engineers analysis. Our study is focused on steady-state flow. Based on this investigation we offer perspectives on where and when these techniques are best applied in order to visualize the behavior of swirl and tumble motion.

Efficient Morse Decompositions of Vector Fields

Existing topology-based vector field analysis techniques rely on the ability to extract the individual trajectories such as fixed points, periodic orbits, and separatrices that 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 MCGs, while fast, are overly conservative and usually result in MCGs 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 tau-maps, which typically provides finer MCGs than existing techniques. Furthermore, the choice of tau provides a natural trade-off between the fineness of the MCGs and the computational costs. We provide efficient implementations of Morse decomposition based on tau-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 tau-maps in addition to the original temporal tau-maps. These techniques provide additional trade-offs between the quality of the MCGs and the speed of computation. We demonstrate the utility of our technique with various examples in the plane and on surfaces including engine simulation data sets.

ISA and IBFVS: image space-based visualization of flow on surfaces

We present a side-by-side analysis of two recent image space approaches for the visualization of vector fields on surfaces. The two methods, image space advection (ISA) and image-based flow visualization for curved surfaces (IBFVS) generate dense representations of time-dependent vector fields with high spatio-temporal correlation. While the 3D vector fields are associated with arbitrary surfaces represented by triangular meshes, the generation and advection of texture properties is confined to image space. Fast frame rates are achieved by exploiting frame-to-frame coherency and graphics hardware. In our comparison of ISA and IBFVS, we point out the strengths and weaknesses of each approach and give recommendations as to when and where they are best applied.