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.

Streamline seeding rakes are widely used in vector field visualization. We present new approaches for calculating similarity between integral curves (streamlines and pathlines). While others have used similarity distance measures, the computational expense involved with existing techniques is relatively high due to the vast number of euclidean distance tests, restricting interactivity and their use for streamline seeding rakes. We introduce the novel idea of computing streamline signatures based on a set of curve-based attributes. A signature produces a compact representation for describing a streamline. Similarity comparisons are performed by using a popular statistical measure on the derived signatures. We demonstrate that this novel scheme, including a hierarchical variant, produces good clustering results and is computed over two orders of magnitude faster than previous methods. Similarity-based clustering enables filtering of the streamlines to provide a nonuniform seeding distribution along the seeding object. We show that this method preserves the overall flow behavior while using only a small subset of the original streamline set. We apply focus + context rendering using the clusters which allows for faster and easier analysis in cases of high visual complexity and occlusion. The method provides a high level of interactivity and allows the user to easily fine tune the clustering results at runtime while avoiding any time-consuming recomputation. Our method maintains interactive rates even when hundreds of streamlines are used.

Visualization of 3D, unsteady flow (4D) is very difficult due to both perceptual challenges and the large size of 4D vector field data. One approach to this challenge is to use integral surfaces to visualize the 4D properties of the field. However the construction of streak surfaces has remained elusive due to problems stemming from expensive computation and complex meshing schemes. We present a novel streak surface construction algorithm that generates the surface using a quadrangular mesh. In contrast to previous approaches the algorithm offers a combination of speed for exploration of 3D unsteady flow, high precision, and places less restriction on data or mesh size due to its CPU-based implementation compared to a GPU-based method. The algorithm can be applied to large data sets because it is based on local operations performed on the quad primitives. We demonstrate the technique on a variety of 3D, unsteady simulation data sets to show its speed and robustness. We also present both a detailed implementation and a performance evaluation. We show that a technique based on quad meshes handles large data sets and can achieve interactive frame rates.

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Abstract-Uncertainty arises in all stages of the visualization pipeline. However, the majority of flow visualization applications convey no uncertainty information to the user. In tools where uncertainty is conveyed, the focus is generally on data, such as error that stems from numerical methods used to generate a simulation or on uncertainty associated with mapping visualization primitives to data. Our work is aimed at another source of uncertainty -that associated with user-controlled input parameters. The navigation and stability analysis of user-parameters has received increasing attention recently. This work presents an investigation of this topic for flow visualization, specifically for three-dimensional streamline and pathline seeding. From a dynamical systems point of view, seeding can be formulated as a predictability problem based on an initial condition. Small perturbations in the initial value may result in large changes in the streamline in regions of high unpredictability. Analyzing this predictability quantifies the perturbation a trajectory is subjugated to by the flow. In other words, some predictions are less certain than others as a function of initial conditions. We introduce novel techniques to visualize important user input parameters such as streamline and pathline seeding position in both space and time, seeding rake position and orientation, and inter-seed spacing. The implementation is based on a metric which quantifies similarity between stream and pathlines. This is important for Computational Fluid Dynamics (CFD) engineers as, even with the variety of seeding strategies available, manual seeding using a rake is ubiquitous. We present methods to quantify and visualize the effects that changes in user-controlled input parameters have on the resulting stream and pathlines. We also present various visualizations to help CFD scientists to intuitively and effectively navigate this parameter space. The reaction from a domain expert in fluid dynamics is also reported.

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Despite the clear benefits that stream and path surfaces bring when visualizing 3D vector fields, their use in both industry and for research has not proliferated. This is due, in part, to the complexity of previous construction algorithms. We introduce a novel algorithm for the construction of stream and path surfaces that is fast, simple and does not rely on any complicated data structures or surface parameterization, thus making it suitable for inclusion into any visualization application. We demonstrate the technique on a series of simulation data sets and show that a number of benefits stem naturally from this approach including: easy timelines and timeribbons, easy stream arrows and easy evenly-spaced flow lines. We also introduce a novel interaction tool called a surface painter in order to address the perceptual challenges associated with visualizing 3D flow. The key to our integral surface generation algorithm's simplicity is performing local computations on quad primitives.