This paper presents a strategy for seeding streamlines in 3D flow fields. Its main goal is to capture the essential flow patterns and to provide sufficient coverage in the field while reducing clutter. First, critical points of the flow field are extracted to identify regions with important flow patterns that need to be presented. Different seeding templates are then used around the vicinity of the different critical points. Because there is significant variability in the flow pattern even for the same type of critical point, our template can change shape depending on how far the critical point is from transitioning into another type of critical point. To accomplish this, we introduce the /spl alpha/-/spl beta/ map of 3D critical points. Next, we use Poisson seeding to populate the empty regions. Finally, we filter the streamlines based on their geometric and spatial properties. Altogether, this multi-step strategy reduces clutter and yet captures the important 3D flow features.

The use of remotely sensed images to map continuous biophysical variables, such as those related to terrestrial vegetation amount, sea surface temperature, and many other targets of NASA's Earth Observing System (EOS), includes variable, parametric, positional, spatial support and structural sources of uncertainty. A complete description of uncertainty will lead to a probability distribution at each location, allowing the exploration of the spatial dimension of uncertainty, that is, where the field is not well quantified. To achieve this purpose, convenient visualization tools are required. We have produced such a tool, called PDFVis, that facilitates the display of probability density functions (pdfs) on a per-grid-cell basis. The density estimate from Monte-Carlo generated realizations is interactively displayed as well as parametric and non-parametric summaries of the pdf field (such as mean, median, quartiles, standard deviation, number of modes, and locations of modes.) Shaded surface renderings of pdfs along a transect can also be projected onto a plane. This tool will become more useful as richer descriptions of spatial uncertainty become available.

Remote sensing analyses usually result in maps of discrete or continuous variables. Ideally, each value in such a map should be accompanied by an uncertainty description, that is, a quantitative statement about the probability of error. A full description of uncertainty at each pixel is usefully represented using a probability distribution. Such a probability distribution may be based on an understanding of potential errors in position, spatial support (the area measured by the sensor's field of view), model parameters, the model structure, and the input variables to the model. Visualizing uncertainty in the products of remote sensing analysis presents the challenge that at least four dimensions are required. These are the spatial dimensions (x and y), the dimension of the variable being mapped and finally the probability dimension. Current visualization tools and techniques do not support these data sets directly. Even animation, a logical choice to represent other four dimensional problems, is not fully satisfactory for probability distribution data sets. We have first addressed the problem of visualizing uncertainty by creating interactive maps of first, second and third order statistics summarizing the distributions. Next, we have experimented with shaded surface rendering of distributions from a user-selectable profile (row or column) in the image. We demonstrate these methods using a data set generated by a geostatistical conditional simulation algorithm and a single band image and we discuss the future promise of visualizing all four dimensions at once.

Box plot is a compact representation that encodes the minimum, maximum, mean, median, and quartile information of a distribution. In practice, a single box plot is drawn for each variable of interest. With the advent of more accessible computing power, we are now facing the problem of visualizing data where there is a distribution at each 2D spatial location. Simply extending the box plot technique to distributions over 2D domain is not straightforward. One challenge is reducing the visual clutter if a box plot is drawn over each grid location in the 2D domain. This paper presents and discusses two general approaches, using parametric statistics and shape descriptors, to present 2D distribution data sets. Both approaches provide additional insights compared to the traditional box plot technique.

The paper proposes the use of specially generated 3D procedural textures for visualizing steady state 2D flow fields. We use the flow field to advect and animate the texture over time. However, using standard texture advection techniques and arbitrary textures will introduce some undesirable effects such as: (a) expanding texture from a critical source point, (b) streaking pattern from the boundary of the flow field, (c) crowding of advected textures near an attracting spiral or sink, and (d) absent or lack of textures in some regions of the flow. The paper proposes a number of strategies to solve these problems. We demonstrate how the technique works using both synthetic data and computational fluid dynamics data.

Maps of biophysical and geophysical variables using Earth Observing System (EOS) satellite image data are an important component of Earth science. These maps have a single value derived at every grid cell and standard techniques are used to visualize them. Current tools fall short, however, when it is necessary to describe a distribution of values at each grid cell. Distributions may represent a frequency of occurrence over time, frequency of occurrence from multiple runs of an ensemble forecast or possible values from an uncertainty model. We identify these "distribution data sets" and present a case study to visualize such 2D distributions. Distribution data sets are different from multivariate data sets in the sense that the values are for a single variable instead of multiple variables. Data for this case study consists of multiple realizations of percent forest cover, generated using a geostatistical technique that combines ground measurements and satellite imagery to model uncertainty about forest cover. We present two general approaches for analyzing and visualizing such data sets. The first is a pixel-wise analysis of the probability density functions for the 2D image while the second is an analysis of features identified within the image. Such pixel-wise and feature-wise views will give Earth scientists a more complete understanding of distribution data sets. See www.cse.ucsc.edu/research/avis/nasa is for additional information.

The paper presents a seed placement strategy for streamlines based on flow features in the dataset. The primary goal of our seeding strategy is to capture flow patterns in the vicinity of critical points in the flow field, even as the density of streamlines is reduced. Secondary goals are to place streamlines such that there is sufficient coverage in non-critical regions, and to vary the streamline placements and lengths so that the overall presentation is aesthetically pleasing (avoid clustering of streamlines, avoid sharp discontinuities across several streamlines, etc.). The procedure is straightforward and non-iterative. First, critical points are identified. Next, the flow field is segmented into regions, each containing a single critical point. The critical point in each region is then seeded with a template depending on the type of critical point. Finally, additional seed points are randomly distributed around the field using a Poisson disk distribution to minimize closely spaced seed points. The main advantage of this approach is that it does not miss the features around critical points. Since the strategy is not image-guided, and hence not view dependent, significant savings are possible when examining flow fields from different viewpoints, especially for 3D flow fields.

This paper explores mapping strategies for generating LIC-like images from streamlines and streamline-like images from LIC. The main contribution of this paper is a technique which we call pseudo-LIC or PLIC. By adjusting a small set of key parameters, PLIC can generate flow visualizations that span the spectrum of streamline-like to LIC-like images. Among the advantages of PLIC are: image quality comparable with LIC, performance speedup over LIC, use of a template texture that is independent of the size of the flow field, handles the problem of multiple streamlines occupying the same pixel in image space, reduced aliasing, applicability to time varying data sets, and variable speed animation.

New challenges on vector field visualization emerge as time dependent numerical simulations become ubiquitous in the field of computational fluid dynamics (CFD). To visualize data generated from these simulations, traditional techniques, such as displaying particle traces, can only reveal flow phenomena in preselected local regions and thus, are unable to track the evolution of global flow features over time. The paper presents an algorithm, called UFLIC (Unsteady Flow LIC), to visualize vector data in unsteady flow fields. Our algorithm extends a texture synthesis technique, called Line Integral Convolution (LIC), by devising a new convolution algorithm that uses a time-accurate value scattering scheme to model the texture advection. In addition, our algorithm maintains the coherence of the flow animation by successively updating the convolution results over time. Furthermore, we propose a parallel UFLIC algorithm that can achieve high load balancing for multiprocessor computers with shared memory architecture. We demonstrate the effectiveness of our new algorithm by presenting image snapshots from several CFD case studies.

The paper presents an algorithm, UFLIC (Unsteady Flow LIC), to visualize vector data in unsteady flow fields. Using line integral convolution (LIC) as the underlying method, a new convolution algorithm is proposed that can effectively trace the flow's global features over time. The new algorithm consists of a time-accurate value depositing scheme and a successive feedforward method. The value depositing scheme accurately models the flow advection, and the successive feedforward method maintains the coherence between animation frames. The new algorithm can produce time-accurate, highly coherent flow animations to highlight global features in unsteady flow fields. CFD scientists, for the first time, are able to visualize unsteady surface flows using the algorithm.