An Efficient Algorithm for Streamline Visualization in Unstructured Steady Vector Field

The analysis of data that consists of multiple vector fields can be greatly facilitated by the simultaneous visualization of the vector fields. An effective visualization must accurately reflect the key physical structures of the fields in a way that does not allow for an unintended bias toward one distribution. While there are several effective techniques to visualize a single vector field through equally spaced streamlines, applying these techniques to individual vector fields and combining them in a single image yields undesirable artifacts. In this paper, we present strategies for the effective visualization of two vector fields through the use of streamlines.

A new method for the simplification and the visualization of vector fields is presented based on the notion of centroidal Voronoi tessellations (CVT's). A CVT is a special Voronoi tessellation for which the generators of the Voronoi regions in the tessellation are also the centers of mass (or means) with respect to a prescribed density. A distance function in both the spatial and vector spaces is introduced to measure the similarity of the spatially distributed vector fields. Based on such a distance, vector fields are naturally clustered and their simplified representations are obtained. Our method combines simple geometric intuitions with the rigorously established optimality properties of the CVTs. It is simple to describe, easy to understand and implement. Numerical examples are also provided to illustrate the effectiveness and competitiveness of the CVT-based vector simplification and visualization methodology.

This paper describes an approach for interactive visualization of mixed scalar and vector fields, in which vector icons are generated from pre-voxelized icon templates and volume-rendered together with the volumetric scalar data. This approach displays simultaneously the global structure of the scalar field and the detailed features of the vector field. Interactive visualization is achieved with incremental image update, by re-rendering only a small portion of the image wherever and whenever a change occurs. This technique supports a set of interactive visualization tools, including change of vector field visualization parameters, real-time animation of vector icons advected within the scalar field, a zooming lens, and a local probe. Subject Terms: data visualisation; interactive systems; graphical user interfaces; rendering (computer graphics); interactive visualization; scalar fields; vector fields; vector icons; pre-voxelized icon templates; volume-rendered; volumetric scalar data; incremental image update; real-time animation; zooming lens; local probe

One major discipline of Scientific Visualization is the display of vector field data. We address the problem of visualizing vector fields containing critical points of higher order Poincare-Index. We use polynomial pieces so that the degree is high enough to get the right Poincare-Index at the location of the critical points. This is an essential improvement because nearly all visualization of vector fields up to now used piecewise linear interpolation and therefore can not show this kind of critical points. A description of vector fields in Clifford algebra opens the way to a better understanding of some plane polynomial vector fields. This is used to choose the polynomial approximations needed for the visualization.

We present the design of a scalable parallel pathline construction method for visualizing large time-varying 3D vector fields. A 4D (i.e., time and the 3D spatial domain) representation of the vector field is introduced to make a time-accurate depiction of the flow field. This representation also allows us to obtain pathlines through streamline tracing in the 4D space. Furthermore, a hierarchical representation of the 4D vector field, constructed by clustering the 4D field, makes possible interactive visualization of the flow field at different levels of abstraction. Based on this hierarchical representation, a data partitioning scheme is designed to achieve high parallel efficiency. We demonstrate the performance of parallel pathline visualization using data sets obtained from terascale flow simulations. This new capability will enable scientists to study their time-varying vector fields at the resolution and interactivity previously unavailable to them.

In flow visualization, the streamline has always been used to display the vector fields, but only using streamlines cannot reveal the nature of flowing intuitively. The dynamic glyphs technology is an important method to show flowing 3D vector fields. However, existing methods of dynamic glyphs are hard to convey the global patterns and local entities at the same time. In this paper, we present a practical method for dynamic visualization of 3D vector fields which combine dynamic glyphs and streamlines, which are rendered respectively according to the information of 3D vector fields. Our method integrates virtues of these two usual techniques, and provides high performance visualization of flowing 3D vector fields directly. Experiments with practical datasets certify that our method could not only depict the local and the global patterns, but more importantly reveal the dynamic nature of flowing 3D vector data.

Vector field visualization techniques have evolved very rapidly over the last two decades, however, visualizing vector fields on complex boundary surfaces from computational flow dynamics (CFD) still remains a challenging task. In part, this is due to the large, unstructured, adaptive resolution characteristics of the meshes used in the modeling and simulation process. Out of the wide variety of existing flow field visualization techniques, vector field clustering algorithms offer the advantage of capturing a detailed picture of important areas of the domain while presenting a simplified view of areas of less importance. This paper presents a novel, robust, automatic vector field clustering algorithm that produces intuitive and insightful images of vector fields on large, unstructured, adaptive resolution boundary meshes from CFD. Our bottom-up, hierarchical approach is the first to combine the properties of the underlying vector field and mesh into a unified error-driven representation. The motivation behind the approach is the fact that CFD engineers may increase the resolution of model meshes according to importance. The algorithm has several advantages. Clusters are generated automatically, no surface parameterization is required, and large meshes are processed efficiently. The most suggestive and important information contained in the meshes and vector fields is preserved while less important areas are simplified in the visualization. Users can interactively control the level of detail by adjusting a range of clustering distance measure parameters. We describe two data structures to accelerate the clustering process. We also introduce novel visualizations of clusters inspired by statistical methods. We apply our method to a series of synthetic and complex, real-world CFD meshes to demonstrate the clustering algorithm results.

Feature-aware streamline generation of planar vector fields via topological methods

In order to reflect the internal motion characteristics of entire vector fields, texture visualization methods based on line integral convolution are usually adopted. However, the visualization results obtained in this way have low image quality. To solve this problem, this paper suggests using line integral convolution to optimize two specific aspects - texture enhancement and color enhancement – to provide an enhanced vector field visualization model. Existing texture enhancement algorithms can create texture aliasing. Based on an analysis of the relationship between vector angles, sampling distance and texture aliasing, the paper puts forward a texture enhancement algorithm that uses the vector angle to adjust the sampling distance of a high-pass filter. This greatly reduces the presence of texture aliasing. For color enhancement, a linear algorithm is usually used that adds vector size information to the vector field. However, the resulting image has a problem of color concentration. In view of this, the distribution characteristics of the vector field are analyzed using a histogram and a dynamic nonlinear color enhancement algorithm is proposed. This noticeably improves the color distribution of the resulting image and improves the overall visual quality of the result.

The paper discusses CAVEvis and a related set of tools for the interactive visualization and exploration of large sets of time-varying scalar and vector fields using the CAVE virtual reality environment. Since visualization of large data sets can be very time-consuming in both computation and rendering time, the task is distributed over multiple machines, each of which is specialized for some aspect of the visualization process. All modules must run asynchronously to maintain the highest level of interactivity. A model of distributed visualization is introduced that addresses important issues related to the management of time-dependent data, module synchronization, and interactivity bottlenecks.

We propose a new technique to visualize dense vector fields associated with unsteady fluid flows. This technique is based on a Lagrangian-Eulerian Advection (LEA) scheme, and it enables animations with high spatio-temporal correlation at interactive rates. We demonstrate the efficiency and efficacy of the technique in applications to numerical simulation of a shock interacting with a longitudinal vortex, and of ocean circulation in the Gulf of Mexico. The simplicity of the data structures and the facility of implementation suggest that LEA could become a useful component of any scientific visualization toolkit concerned with the display of unsteady flows.

In this paper, we present a high-quality texture-based enhanced approach for the visualization of unsteady vector fields. It adopts a scheme of streamline enhancement by applying a ID high-pass filter to flow textures along the orthogonal flow direction to enhance the intensity contrast among streamlines and improve the image quality of flow textures. A scheme of boundary supplement is also used to modulate the characteristic of particles flow. Using the color mapping of some scalar properties, such as magnitude, orientation and curvature, it is capable of displaying many properties of vector field which are helpful to analyze the features and topological flow patterns. It is capable of achieving a real-time rendering performance on a personal computer by using current graphics hardware.

It is a challenging task to visualize the behavior of time-dependent 3D vector fields. Most of the time an overview of unsteady fields is provided via animations, but, unfortunately, animations provide only transient impressions of momentary flow. In this paper we present two approaches to visualize time varying fields with fixed geometry. Path lines and streak lines represent such a steady visualization of unsteady vector fields, but because of occlusion and visual clutter it is useless to draw them all over the spatial domain. A selection is needed. We show how bundles of streak lines and path lines, running at different times through one point in space, like through an eyelet, yield an insightful visualization of flow structure (eyelet lines). To provide a more intuitive and appealing visualization we also explain how to construct a surface from these lines. As second approach, we use a simple measurement of local changes of a field over time to determine regions with strong changes. We visualize these regions with isosurfaces to give an overview of the activity in the dataset. Finally we use the regions as a guide for placing eyelets.

espanolLa visualizacion de funciones con multiples variables de campos y funciones vectoriales, generalmente, requiere de tres dimensiones para analizar fenomenos quimicos, fisicos y matematicos. Por ello, es de gran importancia contar con un sistema de coordenadas tridimensionales para lograr visualizar adecuadamente las funciones de interes. En este reporte se presenta la construccion de un sistema de coordenadas volumetrico que cuenta con una resolucion de 1000 voxeles para la visualizacion de funciones tridimensionales. El control se realiza de manera optima mediante un par de microcontroladores ATMEGA2560 sincronizados por una comunicacion I2C simple. EnglishThe visualization of multiple variable functions, vector fields and vector functions, usually requires three dimensions in order to be able to analyze chemical, physical and mathematic phenomena. This is why it is very important to count with a three dimensional coordinate system, in order to properly display the functions being analyzed. This report presents the construction of a volumetric coordinate system consisting of 1000 voxels for the visualization of three-dimensional functions. The control is done by two ATMEGA2560 microcontrollers which communicate through a simple I2C connection.

Personal computer-based visualization of three-dimensional scalar and vector fields: An application to molecular graphics