Two-dimensional unsteady flow visualization by animating evenly-spaced streamlets

Flow visualization has been widely used to display and discover patterns and features in vector fields. Common applications include the representation of ocean currents and weather model data. In this thesis, a flexible method for animating vector fields is developed, based on a generalization of a Poisson disc sampling method. The algorithm has two stages; in the first streamlets are drawn into an image buffer, larger than their intended size. Before they are drawn they are tested to see if they impact on already drawn areas; if they do, they are rejected. In the second stage the ones that pass the test are drawn normal size. The concept of a 3D streamlet object, which groups consecutive time step streamlets as a primitive rendering object, is introduced as part of a method for animating streamlets so that they have minimal overlap and show frame-to-frame coherence providing visual continuity when animating time varying vector fields. Acceptance schemes that allow for occasional overlap between streamlets are explored and found to improve both the speed and the overall quality. Both model data and real weather data are used to evaluate the method. The results show that the method produces good results and is flexible, allows for variable size and density of streamlets, and produces good results

Similarity-Guided Streamline Placement with Error Evaluation

Most streamline generation algorithms either provide a particular density of streamlines across the domain or explicitly detect features, such as critical points, and follow customized rules to emphasize those features. However, the former generally includes many redundant streamlines, and the latter requires Boolean decisions on which points are features (and may thus suffer from robustness problems for real-world data). We take a new approach to adaptive streamline placement for steady vector fields in 2D and 3D. We define a metric for local similarity among streamlines and use this metric to grow streamlines from a dense set of candidate seed points. The metric considers not only Euclidean distance, but also a simple statistical measure of shape and directional similarity. Without explicit feature detection, our method produces streamlines that naturally accentuate regions of geometric interest. In conjunction with this method, we also propose a quantitative error metric for evaluating a streamline representation based on how well it preserves the information from the original vector field. This error metric reconstructs a vector field from points on the streamline representation and computes a difference of the reconstruction from the original vector field

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

Détermination d'indicateurs géomorphologiques à partir de données altimétriques laser

Dans le domaine de l'analyse et la gestion du territoire, les modèles numériques d'altitude (MNA) sont utilisés depuis longtemps. Cependant, l'apparition de MNA laser (haute précision et rpsolution) a permis d'élargir les applications des modèles de terrain. C'est dans ce concept que s'inscrit cette étude

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

Multiresolution flow visualization

Flow visualization has been an active research field for several years and various techniques have been proposed to visualize vector fields, streamlines and textures being the most effective and popular ones. While streamlines are suitable to get rough information on the behavior of the flow, textures depict the flow properties at the pixel level. Depending on the situation the suitable representation could be streamlines or texture. This paper presents a method to compute a sequence of streamline-based images of a vector field with different densities, ranging from sparse to texturelike representations. It is based on an effective streamline placement algorithm and a production scheme that recalls those used in the multiresolution theory. Indeed a streamline defined at level J of the hierarchy is defined for all levels J’>J. A viewer allows us to interactively select the desired density while zooming in and out in a vector field. The density of streamlines in the image can also be automatically computed as a function of a derived quantity, such as velocity or vorticity

MULTIRESOLUTION FLOW VISUALIZATION

Vector field data are produced by scientific experimentations and numerical simulations, which are now widely used to study complex dynami