Vector Field Visualization Research Articles

Streamline Uniform Placement Algorithm With Dynamic Seed Points

Streamline generation is an important technique for vector field visualization. Streamline uniform placement algorithm can make streamline distribution evenly and express vector information better. An effective streamline placement method should effectively express the characteristics of vector field, make the streamline distribution uniform, and allow the streamline length to be as long as possible. In this paper, a dynamic seed placement algorithm based on critical points and grid points is proposed. The algorithm firstly finds and retains the key points to ensure the key information of vector field, and then introduces uniform grids to control the streamline density of vector fieldso as to guarantee that the streamlines are evenly distributed. The experimental results show that the proposed algorithm can display the characteristic information of vector field well, makes the streamline distribution uniform, and allows the length of streamline to be long. As a result, there are almost no short streamlines.

Intelligent vector field visualization based on line integral convolution

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.

Efficient Local Statistical Analysis via Point-Wise Histograms in Tetrahedral Meshes and Curvilinear Grids

Local histograms (i.e., point-wise histograms computed from local regions of mesh vertices) have been used in many data analysis and visualization applications. Previous methods for computing local histograms mainly work for regular or rectilinear grids only. In this paper, we develop theory and novel algorithms for computing local histograms in tetrahedral meshes and curvilinear grids. Our algorithms are theoretically sound and efficient, and work effectively and fast in practice. Our main focus is on scalar fields, but the algorithms also work for vector fields as a by-product with small, easy modifications. Our methods can benefit information theoretic and other distribution-driven analysis. The experiments demonstrate the efficacy of our new techniques, including a utility case study on tetrahedral vector field visualization.

UIA: a uniform integrated advection algorithm for steady and unsteady piecewise linear flow field on structured and unstructured grids

Integration-based geometric method is widely used in vector field visualization. To improve the efficiency of integration advection-based visualization, we propose a uniform integrated advection (UIA) algorithm on steady and unsteady vector field according to common piecewise linear field data set analysis. UIA employs cell gradient-based interpolation along spatial and temporal direction, and transforms multi-step advection into single-step advection in association with fourth-order Runge–Kutta advection process. UIA can significantly reduce computational load, and is applicable on arbitrary grid type with cell-center/cell-vertex data structure. The experiments are performed on steady/unsteady vector fields with two-dimensional cell-center unstructured grids and three-dimensional cell-vertex grids, and also on unsteady field from fluid dynamics numerical simulation. The result shows that the proposed algorithm can significantly improve advection efficiency and reduce visualization computational time compared with fourth-order Runge–Kutta.

Functional Decomposition for Bundled Simplification of Trail Sets.

Bundling visually aggregates curves to reduce clutter and help finding important patterns in trail-sets or graph drawings. We propose a new approach to bundling based on functional decomposition of the underling dataset. We recover the functional nature of the curves by representing them as linear combinations of piecewise-polynomial basis functions with associated expansion coefficients. Next, we express all curves in a given cluster in terms of a centroid curve and a complementary term, via a set of so-called principal component functions. Based on the above, we propose a two-fold contribution: First, we use cluster centroids to design a new bundling method for 2D and 3D curve-sets. Secondly, we deform the cluster centroids and generate new curves along them, which enables us to modify the underlying data in a statistically-controlled way via its simplified (bundled) view. We demonstrate our method by applications on real-world 2D and 3D datasets for graph bundling, trajectory analysis, and vector field and tensor field visualization.

Enhanced vector field visualization via Lagrangian accumulation

In this paper, we revisit the Lagrangian accumulation process that aggregates the local attribute information along integral curves for vector field visualization. Similar to the previous work, we adopt the notation of the Lagrangian accumulation field or A field for the representation of the accumulation results. In contrast to the previous work, we provide a more in-depth discussion on the properties of A fields and the meaning of the patterns exhibiting in A fields. In particular, we revisit the discontinuity in the A fields and provide a thorough explanation of its relation to the flow structure and the additional information about the flow that it may reveal. In addition, other remaining questions about the A field, such as its sensitivity to the selection of integration time, are also addressed. Based on these new insights, we demonstrate a number of enhanced flow visualizations aided by the accumulation framework and the A fields, including a new A field guided ribbon placement, an A field guided stream surface seeding and the visualization of particle-based flow data. To further demonstrate the generality of the accumulation framework, we extend it to the non-integral geometric curves (i.e., streak lines), which enable us to reveal information about the flow behavior other than those revealed by the integral curves. Finally, we introduce the Eulerian accumulation, which can reveal different flow behaviors than those revealed by Lagrangian accumulation. In summary, we believe that Lagrangian accumulation and the resulting A fields offer a valuable means to investigate flow behavior complementary to the current state-of-the-art techniques.

Interactive 3D simulation for fluid–structure interactions using dual coupled GPUs

The scope of this work involves the integration of high-speed parallel computation with interactive, 3D visualization of the lattice-Boltzmann-based immersed boundary method for fluid–structure interaction. An NVIDIA Tesla K40c is used for the computations, while an NVIDIA Quadro K5000 is used for 3D vector field visualization. The simulation can be paused at any time step so that the vector field can be explored. The density and placement of streamlines and glyphs are adjustable by the user, while panning and zooming is controlled by the mouse. The simulation can then be resumed. Unlike most scientific applications in computational fluid dynamics where visualization is performed after the computations, our software allows for real-time visualizations of the flow fields while the computations take place. To the best of our knowledge, such a tool on GPUs for FSI does not exist. Our software can facilitate debugging, enable observation of detailed local fields of flow and deformation while computing, and expedite identification of ‘correct’ parameter combinations in parametric studies for new phenomenon. Therefore, our software is expected to shorten the ‘time to solution’ process and expedite the scientific discoveries via scientific computing.

Implementation methods and applications of flow visualization in a watershed simulation platform

Computer-based flow visualization, which is an important approach to examine both the dynamic flow process and to elucidate the laws of fluid movement, can greatly facilitate our understanding of the complicated hydrologic cycle and provide insights into regional water resources management. Nevertheless, at present, few software tools can efficiently perform different flow visualizations for watershed modeling. In this study, a virtual watershed platform was developed and various implementation methods of flow visualization were assessed, such as scalar field visualization, vector field visualization, and visual water effects. In the platform, spatially distributed flow model results and georeferenced datasets are visualized in a virtual 3D environment. End users can conveniently explore modeling results within that environment. Based on analysis of the varying requirements of the flow visualization methods applied to watershed simulation, overheads associated with a user-determined switch between different systems were reduced, and the level of comprehensive information management and analysis of large volumes of watershed data was improved. This study shows that application of the watershed platform can enhance flow visualization in the water resources research community, and makes related water modeling more practical in support of water resources management.

Flow-Induced Inertial Steady Vector Field Topology

Traditionally, vector field visualization is concerned with 2D and 3D flows. Yet, many concepts can be extended to general dynamical systems, including the higher-dimensional problem of modeling the motion of finite-sized objects in fluids. In the steady case, the trajectories of these so-called inertial particles appear as tangent curves of a 4D or 6D vector field. These higher-dimensional flows are difficult to map to lower-dimensional spaces, which makes their visualization a challenging problem. We focus on vector field topology, which allows scientists to study asymptotic particle behavior. As recent work on the 2D case has shown, both extraction and classification of isolated critical points depend on the underlying particle model. In this paper, we aim for a model-independent classification technique, which we apply to two different particle models in not only 2D, but also 3D cases. We show that the classification can be done by performing an eigenanalysis of the spatial derivatives' velocity subspace of the higher-dimensional 4D or 6D flow. We construct glyphs that depict not only the types of critical points, but also encode the directional information given by the eigenvectors. We show that the eigenvalues and eigenvectors of the inertial phase space have sufficient symmetries and structure so that they can be depicted in 2D or 3D, instead of 4D or 6D.

Mechanism of transition to turbulence in a circular cylinder wake in a channel

Transition to turbulence in the circular cylinder wake has been studied experimentally and numerically at growing Reynolds number. Good agreement of calculation results with the flow visualization and measurements of instantaneous vector fields of velocity and vorticity has been demonstrated. The growing Reynolds number is shown to make large-scale vortex generation onset move upstream. It also triggers the transition to 3D flow pattern in the cylinder wake. This process is accompanied by non-monotonous behavior of the profiles of velocity and its turbulent fluctuations at equal distances from the cylinder. Non-monotonous behavior of the cylinder drag has been revealed for the Reynolds numbers ranging from 120 to 300.

Hairy Slices: Evaluating the Perceptual Effectiveness of Cutting Plane Glyphs for 3D Vector Fields.

Three-dimensional vector fields are common datasets throughout the sciences. Visualizing these fields is inherently difficult due to issues such as visual clutter and self-occlusion. Cutting planes are often used to overcome these issues by presenting more manageable slices of data. The existing literature provides many techniques for visualizing the flow through these cutting planes; however, there is a lack of empirical studies focused on the underlying perceptual cues that make popular techniques successful. This paper presents a quantitative human factors study that evaluates static monoscopic depth and orientation cues in the context of cutting plane glyph designs for exploring and analyzing 3D flow fields. The goal of the study was to ascertain the relative effectiveness of various techniques for portraying the direction of flow through a cutting plane at a given point, and to identify the visual cues and combinations of cues involved, and how they contribute to accurate performance. It was found that increasing the dimensionality of line-based glyphs into tubular structures enhances their ability to convey orientation through shading, and that increasing their diameter intensifies this effect. These tube-based glyphs were also less sensitive to visual clutter issues at higher densities. Adding shadows to lines was also found to increase perception of flow direction. Implications of the experimental results are discussed and extrapolated into a number of guidelines for designing more perceptually effective glyphs for 3D vector field visualizations.

Topological Analysis of Inertial Dynamics.

Traditional vector field visualization has a close focus on velocity, and is typically constrained to the dynamics of massless particles. In this paper, we present a novel approach to the analysis of the force-induced dynamics of inertial particles. These forces can arise from acceleration fields such as gravitation, but also be dependent on the particle dynamics itself, as in the case of magnetism. Compared to massless particles, the velocity of an inertial particle is not determined solely by its position and time in a vector field. In contrast, its initial velocity can be arbitrary and impacts the dynamics over its entire lifetime. This leads to a four-dimensional problem for 2D setups, and a six-dimensional problem for the 3D case. Our approach avoids this increase in dimensionality and tackles the visualization by an integrated topological analysis approach. We demonstrate the utility of our approach using a synthetic time-dependent acceleration field, a system of magnetic dipoles, and N-body systems both in 2D and 3D.

User-defined feature comparison for vector field ensembles

Most of the existing approaches to visualize vector field ensembles are to reveal the uncertainty of individual variables, for example, statistics, variability, etc. However, a user-defined derived feature like vortex or air mass is also quite significant, since they make more sense to domain scientists. In this paper, we present a new framework to extract user-defined derived features from different simulation runs. Specially, we use a detail-to-overview searching scheme to help extract vortex with a user-defined shape. We further compute the geometry information including the size, the geo-spatial location of the extracted vortexes. We also design some linked views to compare them between different runs. At last, the temporal information such as the occurrence time of the feature is further estimated and compared. Results show that our method is capable of extracting the features across different runs and comparing them spatially and temporally.

An information model for managing multi-dimensional gridded data in a GIS

Earth observation agencies like NASA and NOAA produce huge volumes of historical, near real-time, and forecasting data representing terrestrial, atmospheric, and oceanic phenomena. The data drives climatological and meteorological studies, and underpins operations ranging from weather pattern prediction and forest fire monitoring to global vegetation analysis. These gridded data sets are distributed mostly as files in HDF, GRIB, or netCDF format and quantify variables like precipitation, soil moisture, or sea surface temperature, along one or more dimensions like time and depth. Although the data cube is a well-studied model for storing and analyzing multi-dimensional data, the GIS community remains in need of a solution that simplifies interactions with the data, and elegantly fits with existing database schemas and dissemination protocols. This paper presents an information model that enables Geographic Information Systems (GIS) to efficiently catalog very large heterogeneous collections of geospatially-referenced multi-dimensional rasters—towards providing unified access to the resulting multivariate hypercubes. We show how the implementation of the model encapsulates format-specific variations and provides unified access to data along any dimension. We discuss how this framework lends itself to familiar GIS concepts like image mosaics, vector field visualization, layer animation, distributed data access via web services, and scientific computing. Global data sources like MODIS from USGS and HYCOM from NOAA illustrate how one would employ this framework for cataloging, querying, and intuitively visualizing such hypercubes. ArcGIS—an established platform for processing, analyzing, and visualizing geospatial data—serves to demonstrate how this integration brings the full power of GIS to the scientific community.

Sistema volumétrico de coordenadas tridimensionales mediante el uso de Light-Emitting-Diodes (LED) y microcontroladores

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.

From numerics to combinatorics: a survey of topological methods for vector field visualization

Topological methods are important tools for data analysis, and recently receiving more and more attention in vector field visualization. In this paper, we give an introductory description to some important topological methods in vector field visualization. Besides traditional methods of vector field topology, space-time method and finite-time Lyapunov exponent, we also include in this survey Hodge decomposition, combinatorial vector field topology, Morse decomposition, and robustness, etc. In addition to familiar numerical techniques, more and more combinatorial tools emerge in vector field visualization. The numerical methods often rely on error-prone interpolations and interpolations, while combinatorial techniques produce robust but coarse features. In this survey, we clarify the relevant concepts and hope to guide future topological research in vector field visualization.

Interactive timeline for vector field visualization

Interactive timeline for vector field visualization

BIVARIATE QUANTILE INTERPOLATION FOR ENSEMBLE DERIVED PROBABILITY DENSITY ESTIMATES

Probability distribution functions (PDFs) may be estimated from members in an ensemble. For an ensemble of 2D vector fields, this results in a bivariate PDF at each location in the field. Vector field analysis and visualization, e.g., stream line calculation, require an interpolation to be defined over these 2D density estimates. Thus, a nonparametric PDF interpolation must advect features as opposed to cross-fading them, where arbitrary modalities in the distribution can be introduced. This is already achieved for 1D PDF interpolation via inverse cumulative distribution functions (CDFs). However, there is no closed-form extension to bivariate PDF. This paper presents one such direct extension of the 1D closed-form solution for bivariates. We show an example of physically coupled components (velocity) and correlated random variables. Our method does not require a complex implementation or expensive computation as does displacement interpolation Bonneel et al., ACM Trans. Graphics (TOG), 30(6):158, 2011. Additionally, our method does not suffer from ambiguous pair-wise linear interpolants, as does Gaussian Mixture Model Interpolation.

A View-Dependent and Physical Feature-Preservation Streamline Simplification Method for 3D Vector Field Visualization

The streamline is of great importance for the visualization of 3D vector field. In order to solve those problems of streamline occlusion and visual confusion caused by of excessive streamlines. Meanwhile the streamlines have to present the variation law and important features of vector field exactly. In this paper, a view-dependent and physical feature-preservation streamline simplification method for 3D vector field visualization is proposed. Firstly, streamline set of 3D vector field is generated by particle tracking. Secondly, view-dependent mapping of the streamline set is implemented. Finally, the streamline set is simplified effectively following an iterative feature-preservation computation and view-dependent computation. The experiment results show that the streamlines are visually enhanced meanwhile the physical features of vector field are effectively maintained.

Common Behaviors of Spinor-Type Instantons in 2D Thirring and 4D Gursey Fermionic Models

We investigate two examples of conformal invariant pure spinor fermionic models, which admit particle-like solutions of the classical field equations. For different dimensions and quantum spinor numbers, the vector field visualizations of the models are constructed to provide a better understanding of the spinor-type instanton dynamics in phase space. The hierarchical cluster analysis method investigations of the models are also presented. Finally, the autocorrelation and power spectrum graphs of models are constructed and frequencies of motions are defined.