One-sided smoothness-increasing accuracy-conserving filtering for enhanced streamline integration through discontinuous fields

The discontinuous Galerkin (DG) method continues to maintain heightened levels of interest within the simulation community because of the discretization flexibility it provides. One of the fundamental properties of the DG methodology and arguably its most powerful property is the ability to combine high-order discretizations on an inter-element level while allowing discontinuities between elements. This flexibility, however, generates a plethora of difficulties when one attempts to use DG fields for feature extraction and visualization, as most post-processing schemes are not designed for handling explicitly discontinuous fields. This work introduces a new method of applying smoothness-increasing, accuracy-conserving filtering on discontinuous Galerkin vector fields for the purpose of enhancing streamline integration. The filtering discussed in this paper enhances the smoothness of the field and eliminates the discontinuity between elements, thus resulting in more accurate streamlines. Furthermore, as a means of minimizing the computational cost of the method, the filtering is done in a one-dimensional manner along the streamline.United States. Army Research Office (Grant no. W911NF-05-1-0395)National Science Foundation (U.S.) (Career Award NSF-CCF0347791

RENDERING PRINCIPAL DIRECTION CONTOUR LINES WITH ORIENTED TEXTURES

In this paper we explore the use of contour lines in computer graphics as a means of conveying shape to the end-user. Contour lines provide an alternative to traditional realistic rendering styles and may even provide a more appropriate visualization for certain situations. For our images, contour line orientation is established in accordance with principal curvature directions. We present a method for rendering a texture, oriented in the principal curvature direction, across a traditionally-modeled geometric surface that effectively forms suggestive contour lines to enhance the visualization of that surface. We further extend the method to create animated contour textures, wherein lines move across a surface to suggest its shape. We demonstrate how the animation can be made more intuitive and easier to follow through a meaningful generalization of the generated vector space

The perceptual optimization of two-dimensional flow visualizations using human-in-the-loop local hill climbing

Flow visualization is the graphical representation of vector fields or fluids that enables an observer to visually perceive the forces or motions involved. The fields being displayed are typically dynamic and complex, with a vector direction and magnitude at every point in the field, and often with additional underlying data that is also of interest to the observer. Distilling this mass of data into a static, two-dimensional image that captures the essential patterns and features in a way that is intuitively understandable can be a daunting task. Historically, there have been many different techniques and algorithms to generate visualizations of a flow field. These methods differ widely in implementation, but conceptually they involve the association of significant aspects of the data field (e.g., direction, velocity, temperature, vorticity) to certain visual parameters used in the graphic representation (e.g., size and orientation of lines or arrows, foreground and background color, density/sparsity of graphical elements). For example, the velocity of a field could be mapped to color, line width, line length, arrow head or glyph size, etc. There are many such potential parameter mappings within each technique, and many value ranges that can be used to constrain each parameter within a given mapping, resulting in a virtually limitless number of possible permutations for visually representing a flow field. So, how does one optimize the output? How can one determine which mappings and what values within each mapping produce the best results? Such optimization requires the ability to rapidly generate high-quality visualizations across a wide variety of parameter mappings and settings. We address this need by providing a highly-configurable interactive software system that allows rapid, human-in-the-loop optimization of two-dimensional flow visualization. This software is then used in a study to generate quality visual solutions to a two-dimensional ocean current flow plus surface temperature over a variety of parameter mappings. The results of this study are used to identify relevant rules and patterns governing the efficacy of each combination of parameters, and to draw some general conclusions concerning 2D flow visualization parameter mapping and values

Dynamic line integral convolution for visualizing electromagnetic phenomena

Thesis (M.Eng. and S.B.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science; and, (S.B.)--Massachusetts Institute of Technology, Dept. of Physics, 2001.Includes bibliographical references (leaves 62-63).This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Vector field visualization is a useful tool in science and engineering, giving us a powerful way of understanding the structure and evolution of the field. A fairly recent technique called Line Integral Convolution (LIC) has improved the level of detail that can be visualized by convolving a random input texture along the streamlines in the vector field. This thesis extends the technique to time-varying vector fields, where the motion of the field lines is specified explicitly via another vector field. The sequence of images generated is temporally coherent, clearly showing the evolution of the fields over time, while at the same time each individual image retains the characteristics of the LIC technique. This thesis describes the new technique, entitled Dynamic Line Integral Convolution, and explores its application to experiments in electromagnetism.by Andreas Sundquist.S.B.M.Eng.and S.B

Visualization and analysis of diffusion tensor fields

technical reportThe power of medical imaging modalities to measure and characterize biological tissue is amplified by visualization and analysis methods that help researchers to see and understand the structures within their data. Diffusion tensor magnetic resonance imaging can measure microstructural properties of biological tissue, such as the coherent linear organization of white matter of the central nervous system, or the fibrous texture of muscle tissue. This dissertation describes new methods for visualizing and analyzing the salient structure of diffusion tensor datasets. Glyphs from superquadric surfaces and textures from reactiondiffusion systems facilitate inspection of data properties and trends. Fiber tractography based on vector-tensor multiplication allows major white matter pathways to be visualized. The generalization of direct volume rendering to tensor data allows large-scale structures to be shaded and rendered. Finally, a mathematical framework for analyzing the derivatives of tensor values, in terms of shape and orientation change, enables analytical shading in volume renderings, and a method of feature detection important for feature-preserving filtering of tensor fields. Together, the combination of methods enhances the ability of diffusion tensor imaging to provide insight into the local and global structure of biological tissue

Scientific visualization of stress tensor information with applications to stress determination by X-ray and neutron diffraction

Includes bibliographical references (leaves 232-249).The visual analysis of mechanical stress facilitates physical understanding of the tensor quantity which is concealed in scalar and vector methods. In this study, the principles and techniques of scientific visualization are used to develop a visual analysis of mechanical stresses. Scientific visualization is not only applied to the final tensorial quantity obtained from the diffraction measurements, but the visual methods are developed from, and integrated into current residual stress analysis practices by relating the newly developed visual techniques to the conventional techniques, highlighting its advantages. This study consists of the mathematical analysis of the tensor character of mechanical stresses, discussion of the principles and techniques of scientific visualization (visual data analysis) in physical research, and tensor determination, visual analysis and presentation of residual stresses obtained from diffraction measurements

Doctor of Philosophy

dissertationIn this dissertation, we advance the theory and practice of verifying visualization algorithms. We present techniques to assess visualization correctness through testing of important mathematical properties. Where applicable, these techniques allow us to distinguish whether anomalies in visualization features can be attributed to the underlying physical process or to artifacts from the implementation under verification. Such scientific scrutiny is at the heart of verifiable visualization - subjecting visualization algorithms to the same verification process that is used in other components of the scientific pipeline. The contributions of this dissertation are manifold. We derive the mathematical framework for the expected behavior of several visualization algorithms, and compare them to experimentally observed results in the selected codes. In the Computational Science & Engineering community CS&E, this technique is know as the Method of Manufactured Solution (MMS). We apply MMS to the verification of geometrical and topological properties of isosurface extraction algorithms, and direct volume rendering. We derive the convergence of geometrical properties of isosurface extraction techniques, such as function value and normals. For the verification of topological properties, we use stratified Morse theory and digital topology to design algorithms that verify topological invariants. In the case of volume rendering algorithms, we provide the expected discretization errors for three different error sources. The results of applying the MMS is another important contribution of this dissertation. We report unexpected behavior for almost all implementations tested. In some cases, we were able to find and fix bugs that prevented the correctness of the visualization algorithm. In particular, we address an almost 2 0 -year-old bug with the core disambiguation procedure of Marching Cubes 33, one of the first algorithms intended to preserve the topology of the trilinear interpolant. Finally, an important by-product of this work is a range of responses practitioners can expect to encounter with the visualization technique under verification

Simulação numérica e visualização 3D interativa de objetos sob fluxos irrotacionais em tempo Quase-Real

Resumo: De uma maneira geral, qualquer fluxo irrotacional e incompressível é governado pela equação de Laplace. Esta não possui resolução analítica para problemas reais de engenharia, os quais possuem domínios e condições de contorno complexas, exceto para poucos casos particulares. A Dinâmica dos Fluidos Computacional (DFC) é um método utilizado para resolver numericamente a equação de Laplace, satisfazendo condições iniciais e de contorno. Porém, ao se refinar ou estender um domínio calculado, a quantidade de dados numéricos resultantes aumentará proporcionalmente e a análise destes valores pode se tornar complexa e onerosa. Complementariamente, para a compreensão dos resultados, é importante uma representação visual. A resolução numérica da equação de Laplace está descrita neste trabalho, com um algoritmo de solução inédito para as condições de contorno que atende qualquer forma geométrica em três dimensões. Desenvolveu-se um simulador que possibilita alterações geométricas de objetos 3D, calcula e visualiza interativamente velocidades, linhas de fluxo e força de sustentação para fluxos irrotacionais e incompressíveis em tempo quase-real. O sistema utiliza o método das diferenças finitas para a solução das equações. A interface gráfica foi desenvolvida utilizando, deste modo ineditamente para a DFC, a linguagem C++ e o VTK (Visualization Tool Kit). A quantidade, a origem das linhas de fluxo, a seleção do campo de velocidades, o cálculo da força de sustentação e a visualização estereoscópica são parâmetros que podem ser ajustados e selecionados para a visualização. O algoritmo passou por validações mostrando a capacidade de resolução em três dimensões. Assim, o simulador desenvolvido resolve, ao contrário dos softwares já existentes, o problema do cálculo e visualização interativa imediata ao se fazer modificações em objetos 3D. Este procedimento permitirá que se façam comparações entre formas geométricas imediatamente alteradas para que se possa escolher, entre elas, a que se adequar melhor às necessidades de um projeto

Interactive visualization of computational fluid dynamics data.

This thesis describes a literature study and a practical research in the area of flow visualization, with special emphasis on the interactive visualization of Computational Fluid Dynamics (CFD) datasets. Given the four main categories of flow visualization methodology; direct, geometric, texture-based and feature-based flow visualization, the research focus of our thesis is on the direct, geometric and feature-based techniques. And the feature-based flow visualization is highlighted in this thesis. After we present an overview of the state-of-the-art of the recent developments in the flow visualization in higher spatial dimensions (2.5D, 3D and 4D), we propose a fast, simple, and interactive glyph placement algorithm for investigating and visualizing boundary flow data based on unstructured, adaptive resolution boundary meshes from CFD dataset. Afterward, we propose a novel, automatic mesh-driven vector field clustering algorithm which couples the properties of the vector field and resolution of underlying mesh into a unified distance measure for producing high-level, intuitive and suggestive visualization of large, unstructured, adaptive resolution boundary CFD meshes based vector fields. Next we present a novel application with multiple-coordinated views for interactive information-assisted visualization of multidimensional marine turbine CFD data. Information visualization techniques are combined with user interaction to exploit our cognitive ability for intuitive extraction of flow features from CFD datasets. Later, we discuss the design and implementation of each visualization technique used in our interactive flow visualization framework, such as glyphs, streamlines, parallel coordinate plots, etc. In this thesis, we focus on the interactive visualization of the real-world CFD datasets, and present a number of new methods or algorithms to address several related challenges in flow visualization. We strongly believe that the user interaction is a crucial part of an effective data analysis and visualization of large and complex datasets such as CFD datasets we use in this thesis. In order to demonstrate the use of the proposed techniques in this thesis, CFD domain experts reviews are also provided