One way to provide global illumination for the scientist who performs an interactive sweep through a 3D scalar dataset is to pre-compute global illumination, resample the radiance onto a 3D grid, then use it as a 3D texture. The basic approach of repeatedly extracting isosurfaces, illuminating them, and then building a 3D illumination grid suffers from the non-uniform sampling that arises from coupling the sampling of radiance with the sampling of isosurfaces. We demonstrate how the illumination step can be decoupled from the isosurface extraction step by illuminating the entire 3D scalar function as a 3-manifold in 4-dimensional space. By reformulating light transport in a higher dimension, one can sample a 3D volume without requiring the radiance samples to aggregate along individual isosurfaces in the pre-computed illumination grid.

Large datasets typically contain coarse features comprised of finer sub-features. Even if the shapes of the small structures are evident in a 3D display, the aggregate shapes they suggest may not be easily inferred. From previous studies in shape perception, the evidence has not been clear whether physically-based illumination confers any advantage over local illumination for understanding scenes that arise in visualization of large data sets that contain features at two distinct scales. In this paper we show that physically-based illumination can improve the perception for some static scenes of complex 3D geometry from flow fields. We perform human-subjects experiments to quantify the effect of physically-based illumination on participant performance for two tasks: selecting the closer of two streamtubes from a field of tubes, and identifying the shape of the domain of a flow field over different densities of tubes. We find that physically-based illumination influences participant performance as strongly as perspective projection, suggesting that physically-based illumination is indeed a strong cue to the layout of complex scenes. We also find that increasing the density of tubes for the shape identification task improved participant performance under physically-based illumination but not under the traditional hardware-accelerated illumination model.

We describe how to count the cases that arise in a family of visualization techniques, including Marching Cubes, Sweeping Simplices, Contour Meshing, Interval Volumes, and Separating Surfaces. Counting the cases is the first step toward developing a generic visualization algorithm to produce substitopes (geometric substitutions of polytopes). We demonstrate the method using "GAP," a software system for computational group theory. The case-counts are organized into a table that provides a taxonomy of members of the family; numbers in the table are derived from actual lists of cases, which are computed by our methods. The calculations confirm previously reported case-counts for four dimensions that are too large to check by hand and predict the number of cases that will arise in substitope algorithms that have not yet been invented. We show how Pólya theory produces a closed-form upper bound on the case counts.

We describe how to count the cases that arise in a family of visualization techniques, including marching cubes, sweeping simplices, contour meshing, interval volumes, and separating surfaces. Counting the cases is the first step toward developing a generic visualization algorithm to produce substitopes (geometric substitution of polytopes). We demonstrate the method using a software system ("GAP") for computational group theory. The case-counts are organized into a table that provides taxonomy of members of the family; numbers in the table are derived from actual lists of cases, which are computed by our methods. The calculation confirms previously reported case-counts for large dimensions that are too large to check by hand, and predicts the number of cases that will arise in algorithms that have not yet been invented.

The complex geometry of the human brain contains many folds and fissures, making it impossible to view the entire surface at once. Since most of the cortical activity occurs on these folds, it is desirable to be able to view the entire surface of the brain in a single view. This can be achieved using quasi-conformal flat maps of the cortical surface. Computational and visualization tools are now needed to be able to interact with these flat maps of the brain to gain information about spatial and functional relationships that might not otherwise be apparent. Such information can contribute to earlier diagnostic tools for diseases and improved treatment. Our group is developing visualization and analysis tools that will help elucidate new information about the human brain through the interaction between a cortical surface and its corresponding quasiconformal flat map.

Vortices are important features in many research and engineering fields. Visualization is an important step in gaining more understanding and control of vortices. Vortex detection criteria fall into two categories: point based scalar quantities, calculated at single points, and curve based geometric criteria, calculated for, e.g., streamlines. The first category is easy to compute, but does not work in all cases. The second category is more intuitive and should work in all cases, but currently only works in 2D (or 3D projected) flows. We show applications of both approaches in hydrodynamic flows.

We describe a multidisciplinary effort for creating interactive 3D graphical modules for visualizing optical phenomena. These modules are designed for use in an upper-level undergraduate course. The modules are developed in Open Inventor, which allows them to run under both Unix and Windows. The work is significant in that it applies contemporary interactive 3D visualization techniques to instructional courseware, which represents a considerable advance compared to the current state of the practice.

Sampling and analysis of subsurface contaminants comprise the first steps toward environmental remediation of hazardous spills. We have developed software tools to support the analysis phase, using three different schemes for interpolating scattered 3D soil-quality data onto a grid suitable for viewing in an interactive visualization system. A good interpolation scheme is one that respects the distribution of the original data. We find that the original data can be decimated by up to seventy percent while exhibiting graceful degradation in quality. A prototype software system is being deployed to allow technicians to visually determine, while in the field with their monitoring equipment, where the highest concentrations of contaminants lie. The system is now in use by the U.S. Army Corps of Engineers.

We present a way to visualize a flow field using Line Integral Convolution (LIC) with a multi frequency noise texture. A broad range of feature sizes can enhance a user's perception of the magnitudes and direction of the flow. In addition, the multiple scales of feature size help a user clarify the motion of the flow in an animation.

An isovalue contour of a function of two complex variables defines a surface in four-space. We present a robust technique for creating polygonal contours of complex-valued functions. The technique, contour meshing, generalizes well to larger dimensions.

We describe an interactive, immersive 3D system called Tracktur, which allows a viewer to track the development of a turbulent flow. Tracktur displays time-varying vortex structures extracted from a numerical flow simulation. The user navigates the space and probes the data within a windy 3D landscape. In order to sustain a constant frame rate, we enforce a fixed polygon budget on the geometry. In actual use by a fluid dynamicist, Tracktur has yielded new insights into the transition to turbulence of a laminar flow.

Presents a method for visualizing unsteady flow by displaying its vortices. The vortices are identified by using a vorticity-predictor pressure-corrector scheme that follows vortex cores. The cross-sections of a vortex at each point along the core can be represented by a Fourier series. A vortex can be faithfully reconstructed from the series as a simple quadrilateral mesh, or its reconstruction can be enhanced to indicate helical motion. The mesh can reduce the representation of the flow features by a factor of 1000 or more compared with the volumetric dataset. With this amount of reduction, it is possible to implement an interactive system on a graphics workstation to permit a viewer to examine, in 3D, the evolution of the vortical structures in a complex, unsteady flow.>

This paper considers an idealized subclass of surface reflectivities; namely a simple superposition of ideal diffuse and ideal specular, restricted to point light sources. The paper derives a model of diffuse and specular illumination in arbitrarily large dimensions, based on a few characteristics of material and light in 3-space. It describes how to adjust for the anomaly of excess brightness in large codimensions. If a surface is grooved or furry, it can be illuminated with a hybrid model that incorporates both the ID geometry (the grooves or fur) and the 2D geometry (the surface).

A new algorithm for identifying vortices in complex flows is presented. The scheme uses both the vorticity and pressure fields. A skeleton line along the center of a vortex is produced by a two-step predictor-corrector scheme. The technique uses the vector field to move in the direction of the skeleton line and the scalar field to correct the location in the plane perpendicular to the skeleton line. With an economical description of the vortex tube's cross-section, the skeleton compresses the representation of the flow by a factor of 4000 or more. We show how the reconstructed geometry of vortex tubes can be enhanced to help visualize helical motion.>