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The visualization of numerical fluid flow datasets is essential to the engineering processes that motivate their computational simulation. To address the need for visual representations that convey meaningful relations and enable a deep understanding of flow structures, the discipline of Flow Visualization has produced many methods and schemes that are tailored to a variety of visualization tasks. The ever increasing complexity of modern flow simulations, however, puts an enormous demand on these methods. The study of vortex breakdown, for example, which is a highly transient and inherently three-dimensional flow pattern with substantial impact wherever it appears, has driven current techniques to their limits. In this thesis, we propose several novel visualization methods that significantly advance the state of the art in the visualization of complex flow structures. First, we propose a novel scheme for the construction of stream surfaces from the trajectories of particles embedded in a flow. These surfaces are extremely useful since they naturally exploit coherence between neighboring trajectories and are highly illustrative in nature. We overcome the limitations of existing stream surface algorithms that yield poor results in complex flows, and show how the resulting surfaces can be used a building blocks for advanced flow visualization techniques. Moreover, we present a visualization method that is based on moving section planes that travel through a dataset and sample the flow. By considering the changes to the flow topology on the plane as it moves, we obtain a method of visualizing topological structures in three-dimensional flows that are not accessible by conventional topological methods. On the same algorithmic basis, we construct an algorithm for the tracking of critical points in such flows, thereby enabling the treatment of time-dependent datasets. Last, we address some problems with the recently introduced Lagrangian techniques. While conceptually elegant and generally applicable, they suffer from an enormous computational cost that we significantly use by developing an adaptive approximation algorithm. This allows the application of such methods on very large and complex numerical simulations. Throughout this thesis, we will be concerned with flow visualization aspect of general practical significance but we will particularly emphasize the remarkably challenging visualization of the vortex breakdown phenomenon.
Sound surrounds us all the time and in every place in our daily life, may it be pleasant music in a concert hall or disturbing noise emanating from a busy street in front of our home. The basic properties are the same for both kinds of sound, namely sound waves propagating from a source, but we perceive it in different ways depending on our current mood or if the sound is wanted or not. In this thesis both pleasant sound as well as disturbing noise is examined by means of simulating the sound and visualizing the results thereof. However, although the basic properties of music and traffic noise are the same, one is interested in different features. For example, in a concert hall, the reverberation time is an important quality measure, but if noise is considered only the resulting sound level, for example on ones balcony, is of interest. Such differences are reflected in different methods of simulation and required visualizations, therefore this thesis is divided into two parts. The first part about room acoustics deals with the simulation and novel visualizations for indoor sound and acoustic quality measures, such as definition (original "Deutlichkeit") and clarity index (original "Klarheitsmaß"). For the simulation two different methods, a geometric (phonon tracing) and a wave based (FEM) approach, are applied and compared. The visualization techniques give insight into the sound behaviour and the acoustic quality of a room from a global as well as a listener based viewpoint. Furthermore, an acoustic rendering equation is presented, which is used to render interference effects for different frequencies. Last but not least a novel visualization approach for low frequency sound is presented, which enables the topological analysis of pressure fields based on room eigenfrequencies. The second part about environmental noise is concerned with the simulation and visualization of outdoor sound with a focus on traffic noise. The simulation instruction prescribed by national regulations is discussed in detail, and an approach for the computation of noise volumes, as well as an extension to the simulation, allowing interactive noise calculation, are presented. Novel visualization and interaction techniques for the calculated noise data, incorporated in an interactive three dimensional environment, enabling the easy comprehension of noise problems, are presented. Furthermore additional information can be integrated into the framework to enhance the visualization of noise and the usability of the framework for different usages.
Feature Based Visualization
(2007)
In this thesis we apply powerful mathematical tools such as interval arithmetic for applications in computational geometry, visualization and computer graphics, leading to robust, general and efficient algorithms. We present a completely novel approach for computing the arrangement of arbitrary implicit planar curves and perform ray casting of arbitrary implicit functions by jointly achieving, for the first time, robustness, efficiency and flexibility. Indeed we are able to render even the most difficult implicits in real-time with guaranteed topology and at high resolution. We use subdivision and interval arithmetic as key-ingredients to guarantee robustness. The presented framework is also well-suited for applications to large and unstructured data sets due to the inherent adaptivity of the techniques that are used. We also approach the topic of tensors by collaborating with mechanical engineers on comparative tensor visualization and provide them with helpful visualization paradigms to interpret the data.
Adaptive Extraction and Representation of Geometric Structures from Unorganized 3D Point Sets
(2009)
The primary emphasis of this thesis concerns the extraction and representation of intrinsic properties of three-dimensional (3D) unorganized point clouds. The points establishing a point cloud as it mainly emerges from LiDaR (Light Detection and Ranging) scan devices or by reconstruction from two-dimensional (2D) image series represent discrete samples of real world objects. Depending on the type of scenery the data is generated from the resulting point cloud may exhibit a variety of different structures. Especially, in the case of environmental LiDaR scans the complexity of the corresponding point clouds is relatively high. Hence, finding new techniques allowing the efficient extraction and representation of the underlying structural entities becomes an important research issue of recent interest. This thesis introduces new methods regarding the extraction and visualization of structural features like surfaces and curves (e.g. ridge-lines, creases) from 3D (environmental) point clouds. One main part concerns the extraction of curve-like features from environmental point data sets. It provides a new method supporting a stable feature extraction by incorporating a probability-based point classification scheme that characterizes individual points regarding their affiliation to surface-, curve- and volume-like structures. Another part is concerned with the surface reconstruction from (environmental) point clouds exhibiting objects that are more or less complex. A new method providing multi-resolutional surface representations from regular point clouds is discussed. Following the applied principles of this approach a volumetric surface reconstruction method based on the proposed classification scheme is introduced. It allows the reconstruction of surfaces from highly unstructured and noisy point data sets. Furthermore, contributions in the field of reconstructing 3D point clouds from 2D image series are provided. In addition, a discussion concerning the most important properties of (environmental) point clouds with respect to feature extraction is presented.
Computer-based simulation and visualization of acoustics of a virtual scene can aid during the design process of concert halls, lecture rooms, theaters, or living rooms. Because, not only the visual aspect of the room is important, but also its acoustics. In factory floors noise reduction is important since noise is hazardous to health. Despite the obvious dissimilarity between our aural and visual senses, many techniques required for the visualization of photo-realistic images and for the auralization of acoustic environments are quite similar. Both applications can be served by geometric methods such as particle- and ray tracing if we neglect a number of less important effects. By means of the simulation of room acoustics we want to predict the acoustic properties of a virtual model. For auralization, a pulse response filter needs to be assembled for each pair of source and listener positions. The convolution of this filter with an anechoic source signal provides the signal received at the listener position. Hence, the pulse response filter must contain all reverberations (echos) of a unit pulse, including their frequency decompositions due to absorption at different surface materials. For the room acoustic simulation a method named phonon tracing, since it is based on particles, is developed. The approach computes the energy or pressure decomposition for each particle (phonon) sent out from a sound source and uses this in a second pass (phonon collection) to construct the response filters for different listeners. This step can be performed in different precision levels. During the tracing step particle paths and additional information are stored in a so called phonon map. Using this map several sound visualization approaches were developed. From the visualization, the effect of different materials on the spectral energy / pressure distribution can be observed. The first few reflections already show whether certain frequency bands are rapidly absorbed. The absorbing materials can be identified and replaced in the virtual model, improving the overall acoustic quality of the simulated room. Furthermore an insight into the pressure / energy received at the listener position is possible. The phonon tracing algorithm as well as several sound visualization approaches are integrated into a common system utilizing Virtual Reality technologies in order to facilitate the immersion into the virtual scene. The system is a prototype developed within a project at the University of Kaiserslautern and is still a subject of further improvements. It consists of a stereoscopic back-projection system for visual rendering as well as professional audio equipment for auralization purposes.