We present an algorithm for the simplification of density maps in 3D. We assume that an input function specified at vertices of a triangulation and linearly interpolated within the tetrahedra. The fundamental operation in the simplification procedure is a topology preserving edge contraction. We describe simple and local conditions that can be used to check if an edge contraction preserves topology. These conditions are derived from the generic link conditions for 3-complexes described by Dey et. al. Besides providing a good approximation of the density map, the algorithm also aims to generate a mesh with good quality elements. We achieve this additional goal using a novel extension of the quadric error metric. We visualize isosurfaces extracted from the simplified density maps and use them along with an approximation error computation to evaluate the algorithm. We also develop validation tools to test the correctness of the simplified model and perform statistical measurements on the critical points of the density map to study the relationship between geometric and topological simplification.

We present a platform independent, generic and extensible framework for information visualization called ObVis. It allows reusing and customizing existing components (e.g., layout algorithms), supports a variety of data sources (e.g., data base system, files and Web documents) and allows integrating external applications and services. It is decomposed in five different component hierarchies. Recombining and adding components and utilizing the framework enables a rapid development of visual-based applications and visualization tools.

EmVis is an information visualization tool for the analysis of e-mail exchange among people in an organizaiton. A company-specific organizational hierarchy is used to provide the basic layout for a graph-based visualization of e-mail exchange. Various parameters are mapped to the nodes and edges in this graph: rank within the company, frequency/amount of e-mail exchange between subjects, possibly information content. The system we describe also supports more general graph-based visualizations not necessarily based on a company's hierarchy; it is possible to use EmVis for queries regarding any group of employees and the e-mail exchange among them. We employ geralizations of traditional information visualization concepts, such as cone tree and hyperbolic space representations

We present a method for the hierarchical representation of vector fields. Our approach is based on iterative refinement using cluster-ing and principal component analysis. The input to our algorithm is a discrete set of points with associated vectors. The algorithm generates a top-down segmentation of the discrete field by splitting clusters of points. We measure the error of the various approxima-tion levels by measuring the discrepancy between streamlines gen-erated by the original discrete field and its approximations based on much smaller discrete data sets. Our method assumes no particular structure of the field, nor does it require any topological connectiv-ity information. It is possible to generate multiresolution represen-tations of vector fields using this approach.

We present a multiresolution technique for interactive texture- based volume visualization of very large data sets. This method uses an adaptive scheme that renders the volume in a region-of- interest at a high resolution and the volume away from this region at progressively lower resolutions. The algorithm is based on the segmentation of texture space into an octree, where the leaves of the tree define the original data and the internal nodes define lower-resolution versions. Rendering is done adaptively by selecting high-resolution cells close to a center of attention and low-resolution cells away from this area. We limit the artifacts introduced by this method by modifying the transfer functions in the lower-resolution data sets and utilizing spherical shells as a proxy geometry. It is possible to use this technique to produce viewpoint-dependent renderings of very large data sets.

For types of data visualization where the cost of producing images is high, and the relationship between the rendering parameters and the image produced is less than clear, a visual representation of the exploration process can make the process more efficient and effective. Image graphs represent not only the results but also the process of data visualization. Each node in an image graph consists of an image and the corresponding visualization parameters used to produce it. Each edge in a graph shows the change in rendering parameters between the two nodes it connects. Image graphs are not just static representations: users can interact with a graph to review a previous visualization session or to perform new rendering. Operations which cause changes in rendering parameters can propagate through the graph. The user can take advantage of the information in image graphs to understand how certain rendering parameter changes affect visualization results. Users can share the image graphs they create to streamline the process of collaborative visualization. We have implemented a volume visualization system using the image graph interface. While our examples in the paper come from this implementation, we also discuss the applicability of image graphs to other problem domains.

Virtual Environments (VEs) have the potential to revolutionize traditional product design by enabling the transition from conventional CAD to fully digital product development. The presented prototype system targets closing the **digital gap'' as introduced by the need for physical models such as clay models or mockups in the traditional product design and evaluation cycle. We describe a design environment that provides an intuitive human-machine interface for the creation and manipulation of three-dimensional (3D) models in a semi-immersive design space, focussing on ease of use and increased productivity for both designer and CAD engineers.

We describe a system that supports real-time interactive visualization of computational fluid dynamics (CFD) simulations. The system allows a user to place and manipulate visualization primitives, such as isolines and streamlines, during an ongoing simulation process. A user can interactively select and designate regions of the computational mesh for refinement as the simulation progresses, perform remeshing, and see the effects of the refinement on the simulation in real time. The system is being used for the study of two open problems in compressible fluid dynamics. We can interactively explore solutions as they are computed, identify flow field regions containing features of interest, and refine the grid in those regions in order to obtain a better result locally. The ability to visualize live data, and to make changes to the computational setup in real time, has helped us to understand the underlying fundamental CFD simulation issues of these problems in shorter times than would otherwise have been possible.

We present a method for hierarchical data approximation using quadratic simplicial elements for domain decomposition and field approximation. Higher-order simplicial elements can approximate data better than linear elements. Thus, fewer quadratic elements are required to achieve similar approximation quality. We use quadratic basis functions and compute best quadratic simplicial spline approximations that are C0-continuous everywhere. We adaptively refine a simplicial approximation by identifying and bisecting simplicial elements with largest errors. It is possible to store multiple approximation levels of increasing quality. We have tested the suitability and efficiency of our hierarchical data approximation scheme by applying it to several data sets.