The study of vector fields obtained through simulation and measurement has a rich tradition in the Scientific Visualization community, which is explained by the ubiquity of vector fields across scientific, engineering, and medical application domains. The corresponding visualization techniques have in the past often focused on fluid flow phenomena. However, other application scenarios such as e.g. astrophysics, high-energy physics, geodynamics, and life sciences are gaining prominence in visualization practice, thus opening new avenues for vector field visualization research. In all these domains, numerical simulations produce large, time-varying, and highly complex vector fields. While the visual analysis of these four-dimensional datasets creates obvious issues of depiction and perception, the exploding data size coupled with the rapidly growing significance of Lagrangian methods poses unique challenges with respect to data management and computational scalability.

Obtaining insightful visualization in this setting is therefore both a key objective and an increasingly difficult task for application scientists. The aim of this tutorial is to provide an overview of modern approaches and specifically discuss their suitability for large vector field visualization. To address a broad range of interest and knowledge level, the included topics will encompass both theoretical material on the fundamentals of vector field visualization and insights into the efficient implementation and practical application of such methods.

The tutorial will be structured as follows. After a general introduction of the topic and the presenters, basic theoretical notions will be presented. In particular, numerical integration, integral lines, and integral surfaces will be discussed. Lagrangian and Eulerian perspectives will be considered next and the fundamental notion of a flow map will be used to explain the concept of Lagrangian coherent structures (LCS). Corresponding computational aspects will be mentioned before an in-depth presentation of the state of the art in the parallel implementation of numerical methods for scalable vector field visualization. The presentation will then turn to two scientific applications of these methods. The biomedical study of blood damage (or hemolysis) in artificial blood pumps will be described first, with a particular focus on the crucial role of vector field visualization in the process. This case study will be followed by a discussion of the practical benefit of LCS in understanding fundamental flow properties in aeronautics simulations and the challenges posed by their computation in emerging meshfree simulations. The tutorial will be concluded by an interactive Q&A session involving all presenters.

The originality of the present tutorial lies in its deliberate focus on large-scale problems, which are of paramount importance in research and industrial applications of vector fields. This setting raises fundamental challenges for visualization methods, which have yet to be properly addressed. Our goal is therefore to highlight recent success stories, document ongoing research efforts, and point out open problems.

The tutorial will be held during IEEE VisWeek 2010. All materials including presentation slides, links to available software and literature references, are available on the Materials page.

If you have any questions or comments, please email xmt@purdue.edu.