A Phase Field Model for Continuous Clustering on Vector Fields

A new method for the simplification of flow fields is presented. It is based on continuous clustering. A well-known physical clustering model, the Cahn Hilliard model, which describes phase separation, is modified to reflect the properties of the data to be visualized. Clusters are defined implicitly as connected components of the positivity set of a density function. An evolution equation for this function is obtained as a suitable gradient flow of an underlying anisotropic energy functional. Here, time serves as the scale parameter. The evolution is characterized by a successive coarsening of patterns-the actual clustering-during which the underlying simulation data specifies preferable pattern boundaries. We introduce specific physical quantities in the simulation to control the shape, orientation and distribution of the clusters as a function of the underlying flow field. In addition, the model is expanded, involving elastic effects. In the early stages of the evolution shear layer type representation of the flow field can thereby be generated, whereas, for later stages, the distribution of clusters can be influenced. Furthermore, we incorporate upwind ideas to give the clusters an oriented drop-shaped appearance. Here, we discuss the applicability of this new type of approach mainly for flow fields, where the cluster energy penalizes cross streamline boundaries. However, the method also carries provisions for other fields as well. The clusters can be displayed directly as a flow texture. Alternatively, the clusters can be visualized by iconic representations, which are positioned by using a skeletonization algorithm.

Visualizing Magnitude and Direction in Flow Fields

In weather visualizations, it is common to see vector data represented by glyphs placed on grids. The glyphs either do not encode magnitude in readable steps, or have designs that interfere with the data. The grids form strong but irrelevant patterns. Directional, quantitative glyphs bent along streamlines are more effective for visualizing flow patterns. With the goal of improving the perception of flow patterns in weather forecasts, we designed and evaluated two variations on a glyph commonly used to encode wind speed and direction in weather visualizations. We tested the ability of subjects to determine wind direction and speed: the results show the new designs are superior to the traditional. In a second study we designed and evaluated new methods for representing modeled wave data using similar streamline-based designs. We asked subjects to rate the marine weather visualizations: the results revealed a preference for some of the new designs

Multiscale Image Based Flow Visualization

We present MIBFV, a method to produce real-time, multiscale animations of flow datasets. MIBFV extends the attractive features of the Image-Based Flow Visualization (IBFV) method, i.e. dense flow domain coverage with flow-aligned noise, real-time animation, implementation simplicity, and few (or no) user input requirements, to a multiscale dimension. We generate a multiscale of flow-aligned patterns using an algebraic multigrid method and use them to synthesize the noise textures required by IBFV. We demonstrate our approach with animations that combine multiple scale noise layers, in a global or level-of-detail manner

On the Optimization of Visualizations of Complex Phenomena

The problem of perceptually optimizing complex visualizations is a difficult one, involving perceptual as well as aesthetic issues. In our experience, controlled experiments are quite limited in their ability to uncover interrelationships among visualization parameters, and thus may not be the most useful way to develop rules-of-thumb or theory to guide the production of high-quality visualizations. In this paper, we propose a new experimental approach to optimizing visualization quality that integrates some of the strong points of controlled experiments with methods more suited to investigating complex highly-coupled phenomena. We use human-in-the-loop experiments to search through visualization parameter space, generating large databases of rated visualization solutions. This is followed by data mining to extract results such as exemplar visualizations, guidelines for producing visualizations, and hypotheses about strategies leading to strong visualizations. The approach can easily address both perceptual and aesthetic concerns, and can handle complex parameter interactions. We suggest a genetic algorithm as a valuable way of guiding the human-in-the-loop search through visualization parameter space. We describe our methods for using clustering, histogramming, principal component analysis, and neural networks for data mining. The experimental approach is illustrated with a study of the problem of optimal texturing for viewing layered surfaces so that both surfaces are maximally observable