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2007 | Buch

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Topology-based Methods in Visualization

herausgegeben von: Helwig Hauser, Hans Hagen, Holger Theisel

Verlag: Springer Berlin Heidelberg

Buchreihe : Mathematics and Visualization

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

Enabling insight into large and complex datasets is a prevalent theme in visualization research for which different approaches are pursued.

Topology-based methods are built on the idea of abstracting characteristic structures such as the topological skeleton from the data and to construct the visualizations accordingly. There are currently new demands for and renewed interest in topology-based visualization solutions. This book presents 13 peer-reviewed papers as written results from the 2005 workshop “Topology-Based Methods in Visualization” that was initiated to enable additional stimulation in this field. It contains a longer chapter dedicated to a survey of the state-of-the-art, as well as a great deal of original work by leading experts that has not been published before, spanning both theory and applications. It captures key concepts and novel ideas and serves as an overview of current trends in topology-based visualization research.

Inhaltsverzeichnis

Frontmatter

Topology-Based Flow Visualization, The State of the Art

Summary

Flow visualization research has made rapid advances in recent years, especially in the area of topology-based flow visualization. The ever increasing size of scientific data sets favors algorithms that are capable of extracting important subsets of the data, leaving the scientist with a more manageable representation that may be visualized interactively. Extracting the topology of a flow achieves the goal of obtaining a compact representation of a vector or tensor field while simultaneously retaining its most important features. We present the state of the art in topology-based flow visualization techniques. We outline numerous topology-based algorithms categorized according to the type and dimensionality of data on which they operate and according to the goal-oriented nature of each method. Topology tracking algorithms are also discussed. The result serves as a useful introduction and overview to research literature concerned with the study of topology-based flow visualization.

Robert S. Laramee, Helwig Hauser, Lingxiao Zhao, Frits H. Post

Topology-guided Visualization of Constrained Vector Fields

Summary

In this study we explore ways of using precomputed vector field topology as a guide for interactive feature-based visualization of flow simulation data. Beyond streamline seeding based on critical points, we focus mainly on computing special stream surfaces related to critical points and periodic orbits. We address the special case of divergence-free vector fields which is often met in practical CFD data, and we extend the topological analysis to no-slip boundaries by treating 3D velocity and 2D wall shear stress in a unified way. Finally we apply the proposed techniques to flow simulation data and demonstrate their usefulness for the purpose of studying recirculation and separation phenomena.

Ronald Peikert, Filip Sadlo

Scale-Space Tracking of Critical Points in 3D Vector Fields

Summary

Scale-space techniques are very popular in image processing since they allow for the integrated analysis of image structure. The multi-scale approach enables one to distinguish between important features such as edges and small-scale features such as numerical artifacts or noise. In general, the same properties hold for vector fields such as flow data. Many flow features, e.g. vortices, can be observed on multiple scales of the data and also many features that can be detected are essentially artifacts of the employed interpolation scheme or originate from noise in the data. In this paper, we investigate an approach based on scale-space hierarchies of threedimensional vector fields. Our main interest concerns how vector field singularities can be tracked over multiple spatial scales in order to assess the importance of a critical point to the overall behavior of the underlying flow field.

Thomas Klein, Thomas Ertl

Feature Flow Fields in Out-of-Core Settings

Summary

Feature Flow Fields (FFF) are an approach to tracking features in a time-dependent vector field v. The main idea is to introduce an appropriate vector field f in space-time, such that a feature tracking in v corresponds to a stream line integration in f. The original approach of feature tracking using FFF requested that the complete vector field v is kept in main memory. Especially for 3D vector fields this may be a serious restriction, since the size of time-dependent vector fields can exceed the main memory of even high-end workstations. We present a modification of the FFF-based tracking approach which works in an out-of-core manner. For an important subclass of all possible FFF-based tracking algorithms we ensure to analyze the data in one sweep while holding only two consecutive time steps in main memory at once. Similar to the original approach, the new modification guarantees the complete feature skeleton to be found. We apply the approach to tracking of critical points in 2D and 3D time-dependent vector fields.

Tino Weinkauf, Holger Theisel, Hans-Christian Hege, Hans-Peter Seidel

Streamline Predicates as Flow Topology Generalization

Summary

Streamline predicates are simply boolean functions on the set of all streamlines in a flow field. A characteristic set of a streamline predicate is the set of all streamlines fulfilling the predicate. If streamline predicates are defined based on asymptotic behavior, the characteristic sets become α- or ω-basins. Using boolean algebra on the streamline predicates, we obtain the usual flow topology. We show that these considerations allow us to generalize flow topology to flow structure definitions. These flow structure definitions can be flexibly adapted to typical analysis tasks arising in flow studies and taylored to the users' needs

Tobias Salzbrunn, Gerik Scheuermann

Topology-based versus Feature-based Flow Analysis – Challenges and an Application

Summary

This paper is the result of research and contemplation on the actual usefulness of topology-based methods in real-world applications. We recapitulate commonly used arguments in favor of topology-based approaches first to realign our expectations with respect to the utilization of topology extraction in the context of concrete applications. To illustrate some of our considerations, we take a closer look at one specific example, i.e., the visual analysis of flow through a cooling jacket and we report our respective experiences. After discussing the topology-based analysis of the cooling jacket case, we contrast topology-based flow visualization with an alternative approach, i.e., the interactive feature extraction for feature-based visualization. Without generalizing just from the one concrete example scenario, we still are able to conclude with some broader experiences which we have made in the past and which seem to align well with the opinion of others in our field.

Helwig Hauser, Robert S. Laramee, Helmut Doleisch

Topology Based Flow Analysis and Superposition Effects

Summary

Using topology for feature analysis in flow fields faces several problems. First of all, not all features can be detected using topology based methods. Second, while in flow feature analysis the user is interested in a quantification of feature parameters like position, size, shape, radial velocity and other parameters of feature models, many of these parameters can not be determined using topology based methods alone. Additionally, in some applications it is advantageous to regard the vector field as a superposition of several, possibly simple, features. As topology based methods are quite sensitive to superposition effects, their precision and usability is limited in these cases. In this paper, topology based analysis and visualization of flow fields is estimated and compared to other feature based approaches demonstrating these problems.

Julia Ebling, Alexander Wiebel, Christoph Garth, Gerik Scheuermann

On the Applicability of Topological Methods for Complex Flow Data

Summary

In this paper we study the applicability of topological methods for creating expressive, feature revealing visualizations of 3D vector fields. 3D vector fields can become very complex by having a high number of critical points and separatrices. Moreover, they may have a very sparse topology due to a small number of critical points or their total absence. We show that classical topological methods based on the extraction of separation surfaces are poorly suited for creating expressive visualizations of topologically complex fields. We show this fact by pointing out that the number of sectors of different flow behavior grows quadratically with the number of critical points - contrary to 2D vector fields. Although this limits the applicability of topological methods to a certain degree, we demonstrate the extensibility of this limit by using further simplifying methods like saddle connectors. For 3D vector fields with a very sparse topology, topological visualizations may fail to reveal the features inherent to the field. We show how to overcome this problem for a certain class of flow fields by removing the ambient part of the flow.

Holger Theisel, Tino Weinkauf, Hans-Christian Hege, Hans-Peter Seidel

Extraction and Visualization of Swirl and Tumble Motion from Engine Simulation Data

Summary

An optimal combustion process within an engine block is central to the performance of many motorized vehicles. Associated with this process are two important patterns of flow: swirl and tumble motion, which optimize the mixing of fluid within each of an engine's cylinders. The simulation data associated with in-cylinder tumble motion within a gas engine, given on an unstructured, timevarying and adaptive resolution CFD grid, demands robust visualization methods that apply to unsteady flow. Good visualizations are necessary to analyze the simulation data of these in-cylinder flows. We present a range of methods including integral, feature-based, and image-based schemes with the goal of extracting and visualizing these two important patterns of motion. We place a strong emphasis on automatic and semi-automatic methods, including topological analysis, that require little or no user input.We make effective use of animation to visualize the time-dependent simulation data. We also describe the challenges and implementation measures necessary in order to apply the presented methods to time-varying, volumetric grids.

Christoph Garth, Robert S. Laramee, Xavier Tricoche, Jürgen Schneider, Hans Hagen

Simulation Methods for Advanced Design Engineering

Summary

Since the time numerical simulation tools have been introduced in design engineering the requirements on their capabilities have increased steadily. Computer resources and people's expectations on the simulation itself have reached a high level over the years. More powerful computers are used to process meshes with several million cells. 3-d time accurate calculations with moving or deforming meshes are manageable as well as large eddy and direct numerical simulations. Advanced visualization techniques are used to extract more information leading to a deeper understanding of complex flow phenomena. Using examples of ongoing and recently finished projects the use of flow simulation methods and visualization tools will be presented. The use of commercial tools for cfd and post processing and their adaptation for simulation of human comfort as well as for particle transport simulations will be presented and potentials for topology based visualization methods will be pointed out.

Markus Trenker, Wolfgang Payer, Matthias Haigis

A Practical Approach to Two-Dimensional Scalar Topology

Summary

Computing and analyzing the topology of scalar fields has proven to be a powerful tool in a wide variety of applications. In recent years the field has evolved from computing contour trees of two-dimensional functions to Reeb graphs of general two-manifolds, analyzing the topology of time-dependent volumes, and finally to creating Morse-Smale complexes of two and three dimensional functions. However, apart from theoretical advances practical applications depend on the development of robust and easy to implement algorithms. The progression from initial to practical algorithms is evident, for example, in the contour tree computation where the latest algorithms consist of no more than a couple of dozens lines of pseudo-code. In this paper we describe a similarly simple approach to compute progressive Morse-Smale complexes of functions over two-manifolds. We discuss compact and transparent data-structures used to compute and store Morse-Smale complexes and demonstrate how they can be used to implement interactive topology based simplification. In particular, we show how special cases arising, for example, from manifolds with boundaries or highly quantized functions are handled effectively. Overall the new algorithm is easier to implement and more efficient both run-time and storage wise than previous approaches by avoiding to refine a given triangulation.

Peer-Timo Bremer, Valerio Pascucci

On the Role of Topology in Focus+Context Visualization

Summary

In this paper three types of visualization scenarios are discussed, where topology improves the readability of particular visualization results. The first type combines topology information represented by simple graphical primitives with other forms of visual representations. The second type uses the topology information to define the relevance of objects within the data. The relevance is reflected in the visualization by applying the cut-away concept. The third type of visualizations is based on the change of topology of the underlying data to increase visibility of the most interesting information. Every type handles topology in a different way. This illustrates various roles of topology in scientific visualization.

Ivan Viola, Eduard Gröller

N-dimensional Data-Dependent Reconstruction Using Topological Changes

Summary

We introduce a new concept for a geometrically based feature preserving reconstruction technique of n-dimensional scattered data. Our goal is to generate an n-dimensional triangulation, which preserves the high frequency regions via local topology changes. It is the generalization of a 2D reconstruction approach based on data-dependent triangulation and Lawson's optimization procedure. The definition of the mathematic optimum of the reconstruction is given. We discuss an original cost function and a generalization of known functions for the n-dimensional case.

Zsolt Tóth, Ivan Viola, Andrej Ferko, Eduard Gröller

Backmatter

Titel: Topology-based Methods in Visualization
herausgegeben von: Helwig Hauser
Hans Hagen
Holger Theisel
Verlag: Springer Berlin Heidelberg
Electronic ISBN: 978-3-540-70823-0
Print ISBN: 978-3-540-70822-3
DOI: https://doi.org/10.1007/978-3-540-70823-0