Vector Field Visualization Research Articles

Animation of Orthogonal Texture Patterns for Vector Field Visualization

This paper introduces orthogonal vector field visualization on 2D manifolds: a representation by lines that are perpendicular to the input vector field. Line patterns are generated by line integral convolution (LIC). This visualization is combined with animation based on motion along the vector field. This decoupling of the line direction from the direction of animation allows us to choose the spatial frequencies along the direction of motion independently from the length scales along the LIC line patterns. Vision research indicates that local motion detectors are tuned to certain spatial frequencies of textures, and the above decoupling enables us to generate spatial frequencies optimized for motion perception. Furthermore, we introduce a combined visualization that employs orthogonal LIC patterns together with conventional, tangential streamline LIC patterns in order to benefit from the advantages of these two visualization approaches. In addition, a filtering process is described to achieve a consistent and temporally coherent animation of orthogonal vector field visualization. Different filter kernels and filter methods are compared and discussed in terms of visualization quality and speed. We present respective visualization algorithms for 2D planar vector fields and tangential vector fields on curved surfaces, and demonstrate that those algorithms lend themselves to efficient and interactive GPU implementations.

Vector Field Editing and Periodic Orbit Extraction Using Morse Decomposition

Design and control of vector fields is critical for many visualization and graphics tasks such as vector field visualization, fluid simulation, and texture synthesis. The fundamental qualitative structures associated with vector fields are fixed points, periodic orbits, and separatrices. In this paper, we provide a new technique that allows for the systematic creation and cancellation of fixed points and periodic orbits. This technique enables vector field design and editing on the plane and surfaces with desired qualitative properties. The technique is based on Conley theory, which provides a unified framework that supports the cancellation of fixed points and periodic orbits. We also introduce a novel periodic orbit extraction and visualization algorithm that detects, for the first time, periodic orbits on surfaces. Furthermore, we describe the application of our periodic orbit detection and vector field simplification algorithms to engine simulation data demonstrating the utility of the approach. We apply our design system to vector field visualization by creating data sets containing periodic orbits. This helps us understand the effectiveness of existing visualization techniques. Finally, we propose a new streamline-based technique that allows vector field topology to be easily identified.

Representing Higher-Order Singularities in Vector Fields on Piecewise Linear Surfaces

Accurately representing higher-order singularities of vector fields defined on piecewise linear surfaces is a non-trivial problem. In this work, we introduce a concise yet complete interpolation scheme of vector fields on arbitrary triangulated surfaces. The scheme enables arbitrary singularities to be represented at vertices. The representation can be considered as a facet-based "encoding" of vector fields on piecewise linear surfaces. The vector field is described in polar coordinates over each facet, with a facet edge being chosen as the reference to define the angle. An integer called the period jump is associated to each edge of the triangulation to remove the ambiguity when interpolating the direction of the vector field between two facets that share an edge. To interpolate the vector field, we first linearly interpolate the angle of rotation of the vectors along the edges of the facet graph. Then. we use a variant of Nielson's side-vertex scheme to interpolate the vector field over the entire surface. With our representation, we remove the bound imposed on the complexity of singularities that a vertex can represent by its connectivity. This bound is a limitation generally exists in vertex-based linear schemes. Furthermore, using our data structure, the index of a vertex of a vector field can be combinatorily determined. We show the simplicity of the interpolation scheme with a GPU-accelerated algorithm for a LIC-based visualization of the so-defined vector fields, operating in image space. We demonstrate the algorithm applied to various vector fields on curved surfaces.

Dense texture-based visualization of unsteady and multi-variate vector fields

We propose a novel technique that allows producing dense smooth visualization of unsteady vector fields. The suggested algorithm is texture-based: the field, which may depend on various quantities, such as time, determines how a chosen basic pattern of a texture has to be transformed and adapted to locally represent the features and variation of the field. Texture synthesis methods that aim at generating globally smooth textures yield dense visualizations of the vector field. Extending this synthesis in time leads to texture-based animations with frame-to-frame coherence. This approach is general and produces unsteady field visualizations in an intuitive and straightforward way. Additional degrees of freedom offer ways for user intervention (e.g. filtering and blending) or taking into consideration perception issues. This also makes this methodology useful and adaptable for a broad range of applications.

Coarse-Grid Processing Based Load Balancing for Maximizing the Performance of Parallel 3D LIC for Large Vector Field Visualization

Despite its proven usefulness for vector field visualization, LIC requires large amounts of processing power and memory. Parallel processing is an effective approach for computational intensive problems, however in the case of LIC it can suffer from workload imbalance depending on the distribution and orientation of the vectors elements in a given vector field. Specifically, elements of the boundary and singularity regions have the potential to cause workload imbalance, therefore affecting the parallel processing performance. In this paper, we propose and evaluate a coarse-grid pre-processing based load balancing method for minimizing this undesirable performance loss. By utilizing the same LIC algorithm in both pre-processing and final LIC computation stages, we can avoid redundant computations and minimize the impact of the pre-processing stage on the total LIC computation time. Since this method does not influence the original LIC algorithm, it is expected to work along with other enhancements proposed for LIC. We verified the effectiveness of the proposed method for maximizing the performance of parallel 3D LIC.

A LIC Method for Visualization of Unstructured Vector Field

A LIC Method for Visualization of Unstructured Vector Field

Interactive exploration of tensor fields in geosciences using volume rendering

Volume rendering methods enable the user to explore interactively scalar data on regularly spaced three-dimensional grids. This article discusses how to use this method to explore and analyse three-dimensional tensor fields. The proposed visualization makes use of the programmability of modern graphics hardware and of “Line Integral Convolution”, a texture-based technique for the visualization of vector fields. While an example from geomechanics is used for presentation purposes, the rendering methods introduced are generic and would suit other application areas that involve volumetric data with several attributes equally well.

Visualization of blast waves created by exploding bridge wires

Blast waves created by small exploding bridge wires are used as a test bed for the development of a particle image velocimetry (PIV) technique that uses polymers, seeded with scattering particles, as dynamic witness plates. Combined with pulsed, incoherent schlieren photography, the PIV method permits visualization of the instantaneous velocity vector field in a plane cutting through the blast wave.

Visualization of vector fields using seed LIC and volume rendering

Line Integral Convolution (LIC) is a powerful texture-based technique for visualizing vector fields. Due to the high computational expense of generating the 3D textures and the difficulties of effectively displaying the result, LIC has most commonly been used to depict vector fields in 2D or over a surface in 3D. Here, we propose new methods for more effective volume visualization of three-dimensional vector fields using LIC: 1) We present a fast method for computing volume LIC textures that exploits the sparsity of the input texture. 2) We propose the use of a shading technique, called limb darkening, to reveal the depth relations among the field lines. The shading effect is obtained simply by using appropriate transfer functions and, therefore, avoids using expensive shading techniques. 3) We demonstrate how two-field visualization techniques can be used to enhance the visual information describing a vector field. The volume LIC textures are rendered using texture-based rendering techniques, which allows interactive exploration of a vector field.

ISA and IBFVS: image space-based visualization of flow on surfaces

We present a side-by-side analysis of two recent image space approaches for the visualization of vector fields on surfaces. The two methods, Image Space Advection (ISA) and Image-Based Flow Visualization for Curved Surfaces (IBFVS) generate dense representations of time-dependent vector fields with high spatio-temporal correlation. While the 3D vector fields are associated with arbitrary surfaces represented by triangular meshes, the generation and advection of texture properties is confined to image space. Fast frame rates are achieved by exploiting frame-to-frame coherency and graphics hardware. In our comparison of ISA and IBFVS, we point out the strengths and weaknesses of each approach and give recommendations as to when and where they are best applied.

Topological Construction and Visualization of Higher Order 3D Vector Fields

Abstract We present the first algorithm for constructing 3D vector fields based on their topological skeleton. The skeleton itself is modeled by interactively moving a number of control polygons. Then a piecewise linear vector field is automatically constructed which has the same topological skeleton as modeled before. This approach is based on a complete segmentation of the areas around critical points into sectors of different flow behavior. Based on this, we present the first approach to visualizing higher order critical points of 3D vector fields. Categories and Subject Descriptors (according to ACM CCS): I.3.3 [Computer Graphics]: Line and Curve Generation I.3.7 [Computer Graphics]: Three‐Dimensional Graphics and Realism

Interactive visualization of three-dimensional vector fields with flexible appearance control

In this paper, we present an interactive texture-based algorithm for visualizing three-dimensional steady and unsteady vector fields. The goal of the algorithm is to provide a general volume rendering framework allowing the user to compute three-dimensional flow textures interactively and to modify the appearance of the visualization on the fly. To achieve our goal, we decouple the visualization pipeline into two disjoint stages. First, flow lines are generated from the 3D vector data. Various geometric properties of the flow paths are extracted and converted into a volumetric form using a hardware-assisted slice sweeping algorithm. In the second phase of the algorithm, the attributes stored in the volume are used as texture coordinates to look up an appearance texture to generate both informative and aesthetic representations of the vector field. Our algorithm allows the user to interactively navigate through different regions of interest in the underlying field and experiment with various appearance textures. With our algorithm, visualizations with enhanced structural perception using various visual cues can be rendered in real time. A myriad of existing geometry-based and texture-based visualization techniques can also be emulated.

Visualization techniques in plasma numerical simulations

Numerical simulations of plasma processes usually yield a huge amount of raw numerical data. Information about electric and magnetic fields and particle positions and velocities can be typically obtained. There are two major ways of elaborating these data. First of them is calledplasma diagnostics. We can calculate average values, variances, correlations of variables, etc. These results may be directly comparable with experiments and serve as the typical quantitative output of plasma simulations. The second possibility is theplasma visualization. The results are qualitative only, but serve as vivid display of phenomena in the plasma followed-up. An experience with visualizing electric and magnetic fields via Line Integral Convolution method is described in the first part of the paper. The LIC method serves for visualization of vector fields in two dimensional section of the three dimensional plasma. The field values can be known only in grid points of three-dimensional grid. The second part of the paper is devoted to the visualization techniques of the charged particle motion. The colour tint can be used for particle’s temperature representation. The motion can be visualized by a trace fading away with the distance from the particle. In this manner the impressive animations of the particle motion can be achieved.

B208 3次元磁界ベクトル可視化の一方法

Visualization of the magnetic field distributions radiated from various electronic/electrical devices makes it possible to evaluate the magnetic field sources, i.e. current distributions. The magnetic field sources distributions reveal to the soundness of the electrical/electronic devices. According this methodology, it may be possible to work out a fully automatic inspection system of the electrical/electronic devices in a factory line. However, in order to realize this system, we have to solve to various serious difficult problems. One of the most basic and important problems is the visualizing methodology of magnetic fields, i.e. how to visualize the vector fields as the color images.In the present paper, we propose a deterministic method, which enable us to the unique visualize vector field images as the color images. Applying our color image cognition methodology to these vector field images suggests that our vector field visualization method has various possibilities for the study of physical vector fields not only the magnetic fields.

FIRST: a flexible and interactive resampling tool for CFD simulation data

We introduce a flexible, variable resolution tool for interactive resampling of computational fluid dynamics (CFD) simulation data on versatile grids. The tool and coupled algorithm afford users precise control of glyph placement during vector field visualization via six interactive degrees of freedom. Other important characteristics of this method include: (1) an algorithm that resamples any unstructured grid onto any structured grid, (2) handles changes to underlying topology and geometry, (3) handles unstructured grids with holes and discontinuities, (4) does not rely on any pre-processing of the data, and (5) processes large numbers of unstructured grid cells efficiently. We believe this tool to be a valuable asset in the engineer's pursuit of understanding and visualizing the underlying flow field in CFD simulation results.

A wavelet decomposition scheme and compression method for streamline-based vector field visualizations

Flow visualization has been an active research field for several years and streamlines have proved to be an effective representation of two-dimensional steady vector fields. Online simulation of complex dynamic systems, computed on remote powerful computers are becoming more common. Efficient steering of the computational process requires the analysis of simulation results in real time. Visualization offers the possibility of at-a-glance analysis of the data but requires being able to download visualizations efficiently. Here we propose a wavelet model and compression scheme for streamline-based images of 2D steady vector fields. This method allows us to decrease the size of the data by a factor of 2.5 for a visualization quality comparable to the original image, and the compression factor increases to 10 if we accept small deformations.

Hardware Accelerated Interactive Vector Field Visualization: A level of detail approach

Hardware Accelerated Interactive Vector Field Visualization: A level of detail approach

Hardware Accelerated Interactive Vector Field Visualization: A level of detail approach

This paper presents an interactive global visualization technique for dense vector fields using levels of detail. We introduce a novel scheme which combines an error-controlled hierarchical approach and hardware acceleration to produce high resolution visualizations at interactive rates. Users can control the trade-off between computation time and image quality, producing visualizations amenable for situations ranging from high frame-rate previewing to accurate analysis. Use of hardware texture mapping allows the user to interactively zoom in and explore the data, and also to configure various texture parameters to change the look and feel of the visualization. We are able to achieve sub-second rates for dense LIC-like visualizations with resolutions in the order of a million pixels for data of similar dimensions.

Visualizing vector fields: the thick oriented stream-line algorithm (TOSL)

The visualization of dense vector fields has important applications for scientific purposes. Beyond the standard methods, such as arrows and particle tracing, texture-based methods are able to show almost all the details of a field. This paper presents the Thick Oriented Stream-Line (TOSL) algorithm, which can show direction, orientation and local flow speed even for dense vector fields by simulating the convolution process. A practical comparison of the performances of TOSL vs. other visualizations algorithms (LIC and fastLIC) shows that the proposed algorithm can provide output textures faster than the other considered techniques.

Unsteady Flow Visualization by Animating Evenly‐Spaced Streamlines

In recent years the work on vector field visualization has been concentrated on LIC‐based methods. In this paper we propose an alternative solution for the visualization of unsteady flow fields. Our approach is based on the computation of temporal series of correlated images. While other methods are based on pathlines and try to correlate successive images at the pixel level, our approach consists in correlating instantaneous visualizations of the vector field at the streamline level. For each frame a feed forward algorithm computes a set of evenly‐spaced streamlines as a function of the streamlines generated for the previous frame. This is achieved by establishing a correspondence between streamlines at successive time steps. A cyclical texture is mapped onto every streamline and textures of corresponding streamlines at different time steps are correlated together so that, during the animation, they move along the streamlines, giving the illusion that the flow is moving in the direction defined by the streamline. Our method gives full control on the image density so that we are able to produce smooth animations of arbitrary density, covering the field of representations from sparse, that is classical streamline‐based images, to dense, that is texture‐like images.