Hans Hagen

Visualization and Processing of Tensor Fields

Matrix-valued data sets so-called second order tensor fields have gained significant importance in scientific visualization and image processing due to recent developments such as diffusion tensor imaging. This book is the first edited volume that presents the state of the art in the visualization and processing of tensor fields. It contains some longer chapters dedicated to surveys and tutorials of specific topics, as well as a great deal of original work by leading experts that has not been published before. It serves as an overview for the inquiring scientist, as a basic foundation for developers and practitioners, and as as a textbook for specialized classes and seminars for graduate and doctoral students.

Efficient Computation and Visualization of Coherent Structures in Fluid Flow Applications

The recently introduced notion of Finite-Time Lyapunov Exponent to characterize Coherent Lagrangian Structures provides a powerful framework for the visualization and analysis of complex technical flows. Its definition is simple and intuitive, and it has a deep theoretical foundation. While the application of this approach seems straightforward in theory, the associated computational cost is essentially prohibitive. Due to the Lagrangian nature of this technique, a huge number of particle paths must be computed to fill the space-time flow domain. In this paper, we propose a novel scheme for the adaptive computation of FTLE fields in two and three dimensions that significantly reduces the number of required particle paths. Furthermore, for three-dimensional flows, we show on several examples that meaningful results can be obtained by restricting the analysis to a well-chosen plane intersecting the flow domain. Finally, we examine some of the visualization aspects of FTLE-based methods and introduce several new variations that help in the analysis of specific aspects of a flow.

Collaborative visualization: definition, challenges, and research agenda

The conflux of two growing areas of technology – collaboration and visualization – into a new research direction, collaborative visualization, provides new research challenges. Technology now allows us to easily connect and collaborate with one another – in settings as diverse as over networked computers, across mobile devices, or using shared displays such as interactive walls and tabletop surfaces. Digital information is now regularly accessed by multiple people in order to share information, to view it together, to analyze it, or to form decisions. Visualizations are used to deal more effectively with large amounts of information while interactive visualizations allow users to explore the underlying data. While researchers face many challenges in collaboration and in visualization, the emergence of collaborative visualization poses additional challenges, but it is also an exciting opportunity to reach new audiences and applications for visualization tools and techniques. The purpose of this article is (1) to provide a definition, clear scope, and overview of the evolving field of collaborative visualization, (2) to help pinpoint the unique focus of collaborative visualization with its specific aspects, challenges, and requirements within the intersection of general computer-supported cooperative work and visualization research, and (3) to draw attention to important future research questions to be addressed by the community. We conclude by discussing a research agenda for future work on collaborative visualization and urge for a new generation of visualization tools that are designed with collaboration in mind from their very inception.

FastBit: interactively searching massive data

As scientific instruments and computer simulations produce more and more data, the task of locating the essential information to gain insight becomes increasingly difficult. FastBit is an efficient software tool to address this challenge. In this article, we present a summary of the key underlying technologies, namely bitmap compression, encoding, and binning. Together these techniques enable FastBit to answer structured (SQL) queries orders of magnitude faster than popular database systems. To illustrate how FastBit is used in applications, we present three examples involving a high-energy physics experiment, a combustion simulation, and an accelerator simulation. In each case, FastBit significantly reduces the response time and enables interactive exploration on terabytes of data.

A topology simplification method for 2D vector fields

Topology analysis of plane, turbulent vector fields results in visual clutter caused by critical points indicating vortices of finer and finer scales. A simplification can be achieved by merging critical points within a prescribed radius into higher order critical points. After building clusters containing the singularities to merge, the method generates a piecewise linear representation of the vector field in each cluster containing only one (higher order) singularity. Any visualization method can be applied to the result after this process. Using different maximal distances for the critical points to be merged results in a hierarchy of simplified vector fields that can be used for analysis on different scales.

Continuous topology simplification of planar vector fields

Vector fields can present complex structural behavior, especially in turbulent computational fluid dynamics. The topological analysis of these data sets reduces the information, but one is usually still left with too many details for interpretation. In this paper, we present a simplification approach that removes pairs of critical points from the data set, based on relevance measures. In contrast to earlier methods, no grid changes are necessary, since the whole method uses small local changes of the vector values defining the vector field. An interpretation in terms of bifurcations underlines the continuous, natural flavor of the algorithm.

Curve and surface design

Part I. Curve Design: Properties of Minimal Energy Splines G. Brunnett Minimal Energy splines with Various End Constraints E. Jou and W. Han Interval Weighted Tau- splines D. Lasser and H. Hagen Curve and surface Interpolation using Quintic Weight Tau-splines D. Neuser Weighted splines Based on Piecewise Polynomial Weighted Functions K. Salkauskas Algorithms for Geometric spline Curves M. Eck On the Problem of Determining the distance Between parametric curves F. Fritsch and G. Nielson Part II. Non-Tensor Product Surfaces: A survey of scattered Data Fitting Using Triangular Interpolants T. De Rose Free-form surfaces from Partial Differential Equations M. I. G. Bloor and M. J. Wilson Modeling with Box spline surfaces M. Daehlen.

Topology Tracking for the Visualization of Time-Dependent Two-Dimensional Flows

The paper presents a topology-based visualization method for time-dependent two-dimensional vector elds. A time interpolation enables the accurate tracking of critical points and closed orbits as well as the detection and identication of structural changes. This completely characterizes the topology of the unsteady ow. Bifurcation theory provides the theoretical framework. The results are conveyed by surfaces that separate subvolumes of uniform ow behavior in a three-dimensional space-time domain.

Functional composition algorithms via blossoming

In view of the fundamental role that functional composition plays in mathematics, it is not surprising that a variety of problems in geometric modeling can be viewed as instances of the following composition problem: given representations for two functions <italic>F</italic> and <italic>G</italic>, compute a representation of the function <italic>H</italic> = <italic>F o G</italic>. We examine this problem in detail for the case when <italic>F</italic> and <italic>G</italic> are given in either Be´zier or B-spline form. Blossoming techniques are used to gain theoretical insight into the structure of the solution which is then used to develop efficient, tightly codable algorithms. From a practical point of view, if the composition algorithms are implemented as library routines, a number of geometric-modeling problems can be solved with a small amount of additional software.

Surface interrogation algorithms

Various visualization techniques that identify unwanted curvature regions, such as inflection points and dents, are reviewed. Orthotomics for the convexity test, isophotes for the geometric continuity test for the boundaries of a patchwork, reflection lines for the aesthetic quality of a surface, and local surfaces for the detection of undesired curvature situations on a surface are discussed.<<ETX>>