Detection and visualization of closed streamlines in planar flows

The analysis and visualization of flows is a central problem in visualization. Topology-based methods have gained increasing interest in recent years. This article describes a method for the detection of closed streamlines in flows. It is based on a special treatment of cases where a streamline reenters a cell to prevent infinite cycling during streamline calculation. The algorithm checks for possible exits of a loop of crossed edges and detects structurally stable closed streamlines. These global features are not detected by conventional topology and feature detection algorithms     

Hierarchical streamline bundles

Effective 3D streamline placement and visualization play an essential role in many science and engineering disciplines. The main challenge for effective streamline visualization lies in seed placement, i.e., where to drop seeds and how many seeds should be placed. Seeding too many or too few streamlines may not reveal flow features and patterns either because it easily leads to visual clutter in rendering or it conveys little information about the flow field. Not only does the number of streamlines placed matter, their spatial relationships also play a key role in understanding the flow field. Therefore, effective flow visualization requires the streamlines to be placed in the right place and in the right amount. This paper introduces hierarchical streamline bundles, a novel approach to simplifying and visualizing 3D flow fields defined on regular grids. By placing seeds and generating streamlines according to flow saliency, we produce a set of streamlines that captures important flow features near critical points without enforcing the dense seeding condition. We group spatially neighboring and geometrically similar streamlines to construct a hierarchy from which we extract streamline bundles at different levels of detail. Streamline bundles highlight multiscale flow features and patterns through clustered yet not cluttered display. This selective visualization strategy effectively reduces visual clutter while accentuating visual foci, and therefore is able to convey the desired insight into the flow data.     

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.     

On Perception of Semi‐Transparent Streamlines for Three‐Dimensional Flow Visualization

One of the standard techniques to visualize three‐dimensional flow is to use geometry primitives. This solution, when opaque primitives are used, results in high levels of occlusion, especially with dense streamline seeding. Using semi‐transparent geometry primitives can alleviate the problem of occlusion. However, with semi‐transparency some parts of the data set become too vague and blurry, while others are still heavily occluded. We conducted a user study that provided us with results on perceptual limits of using semi‐transparent geometry primitives for flow visualization. Texture models for semi‐transparent streamlines were introduced. Test subjects were shown multiple overlaying layers of streamlines and recorded how many different flow directions they were able to perceive. The user study allowed us to identify a set of top scoring textures. We discuss the results of the user study, provide guidelines on using semi‐transparency for three‐dimensional flow visualization and show how varying textures for different streamlines can further enhance the perception of dense streamlines. We also discuss the strategies for dealing with very high levels of occlusion. The strategies are per‐pixel filtering of flow directions, when only some of the streamlines are rendered at a particular pixel, and opacity normalization, a way of altering the opacity of overlapping streamlines with the same direction. We illustrate our results with a variety of visualizations.     

基于拓扑法的与时间相关二维矢量场的可视化

分析与时间相关二维矢量场可视化的拓扑法，并针对其在检测封闭流线时依赖网格以及不能对封闭流线精确定位的问题，进行改进。通过运用特征流场对临界点跟踪以及鞍状连接符对流面积分，提出一种检测封闭流线的方法。该方法不依赖于网格，解决了封闭流线精确定位的问题。实验结果表明本文提出的算法为与参数相关二维矢量场可视化提供一个基本框架。     

Stability of Dissipation Elements: A Case Study in Combustion

Recently, dissipation elements have been gaining popularity as a mechanism for measurement of fundamental properties of turbulent flow, such as turbulence length scales and zonal partitioning. Dissipation elements segment a domain according to the source and destination of streamlines in the gradient flow field of a scalar function f : → ?. They have traditionally been computed by numerically integrating streamlines from the center of each voxel in the positive and negative gradient directions, and grouping those voxels whose streamlines terminate at the same extremal pair. We show that the same structures map well to combinatorial topology concepts developed recently in the visualization community. Namely, dissipation elements correspond to sets of cells of the Morse‐Smale complex. The topology‐based formulation enables a more exploratory analysis of the nature of dissipation elements, in particular, in understanding their stability with respect to small scale variations. We present two examples from combustion science that raise significant questions about the role of small scale perturbation and indeed the definition of dissipation elements themselves.     

窄方腔软湍流热对流中角涡的三维发卡状 流动结构

通过直接数值模拟（Direct Numerical Simulation,DNS）求解三维窄方腔湍流Rayleigh Bénard（RB）热对流流场,讨论尺度比为1/4的三维窄方腔中的流动.三维方腔流场的流线图和速度场与二维流场一致,都反映出大尺度环流和角涡的软湍流流动特征.进一步观察三维流线图发现,在近底板附近流线的走向并不是沿着大尺度环流的方向.转换三维流线图的观察角度,可明显看到近底板附近流线是螺旋状的,并与角涡相连.分析整个流场的涡旋特征发现,在窄方腔热对流中沿底板棱边区域产生涡对与角涡连接形成三维发卡涡流动的结构.     

渗流场流线构造方法研究

流线是分析渗流场流体流动特性的一个非常重要的工具,其构造方法的研究已受到油藏工程师们的普遍关注。给出了基于约束Delaunay三角网格的等值线和流线生成算法。提出了一种新的计算渗流场压力梯度的方法,借助于“翼边”数据结构,设计了“指南针”算法加速流线的跟踪过程。实例表明,算法具有良好的时空效率,结果能够较为直观地反映出油藏流体在注采井间的运动轨迹。     

A mass conservative flow field visualization method

This paper introduces a new technique for computer visualization of three-dimensional flow fields. The most powerful feature of this technique is that the streamlines and stream surface are generated by mass conservative interpolation schemes. Interpolation is an important topic in flow visualization because CFD velocity fields are defined at a discrete location in space. Interpolation errors are more significant than those arising from numerical integration. The main draw-back of conventional trilinear interpolation of velocity is that it is not mass conservative. Failure to conserve mass can produce errors which can not be eliminated by reducing the integration step. A significant feature of the relationship between the velocity field and the stream functions is that it implies conservation of mass. So a mass conservative interpolation scheme is developed using a stream function, which is obtained by solving the partial differential equation in the local cell and approximated by a cluster of stream surfaces. Then the streamline can be traced using numerical techniques with mass conservative interpolation and the stream surface is directly calculated by slicing the stream function. The result is more accurate because we replace the polygoned tiling of streamlines by mass conservative stream surface generation. Results presented here compare the performance of the new method to the trilinear interpolation scheme and demonstrate its effectiveness.     

一种新的平面矢量场可视化方法

矢量场可视化是科学计算可视化的重要组成部分。提出了一种新的平面矢量场可视化方法，该方法利用局部区域内流线的近似平行性，将种子点的影响范围扩大，使一条流线能够覆盖与其平行的相邻的几条流线上的点，同时对流线之间进行调和，使流线间比较平滑。由于该方法一条流线上覆盖了更多的点，提高了计算速度，可达到交互可视化的要求。并将几种方法的结果图象进行了比较。     

Visualizing unstructured flow data using dual stream functions

One of the most important ways of visualizing fluid flow is the construction of streamlines, which are lines that are everywhere tangential to the local fluid velocity. Stream surfaces are defined as surfaces through which no fluid penetrates. Streamlines can therefore be computed from the intersection of two nonparallel stream surfaces. This paper presents new algorithms for the computation of dual stream functions from computational fluid dynamics data that is defined on an unstructured tetrahedral mesh. These algorithms are compared with standard numerical routines for computing streamlines, and are shown to be quicker and more accurate than techniques involving numerical integration along the streamline     

Efficient Parallel Vectors Feature Extraction from Higher‐Order Data

The parallel vectors (PV) operator is a feature extraction approach for defining line‐type features such as creases (ridges and valleys) in scalar fields, as well as separation, attachment, and vortex core lines in vector fields. In this work, we extend PV feature extraction to higher‐order data represented by piecewise analytical functions defined over grid cells. The extraction uses PV in two distinct stages. First, seed points on the feature lines are placed by evaluating the inclusion form of the PV criterion with reduced affine arithmetic. Second, a feature flow field is derived from the higher‐order PV expression where the features can be extracted as streamlines starting at the seeds. Our approach allows for guaranteed bounds regarding accuracy with respect to existence, position, and topology of the features obtained. The method is suitable for parallel implementation and we present results obtained with our GPU‐based prototype. We apply our method to higher‐order data obtained from discontinuous Galerkin fluid simulations.     

两种气象应用分析技术的软件算法研究与实现

以气象水文信息显示系统软件开发为背景,针对风场流线分析与显示和温度对数压力图绘制功能的实现,提出了流线分析算法和温度对数压力图的不稳定能量区分析算法.流线分析算法从流线的基本概念出发,结合其物理连续分布的特征,基于风场格点u/v分量数据直接"跟踪"获得流线,并对过密、过短等情况进行了处理.温度对数压力图的不稳定能量区分析算法利用温压曲线与状态曲线的单调性,分段处理温压曲线与状态曲线的位置关系进行不稳定能量区分析.实际使用结果表明,2种算法均具有良好的显示效果和较高的处理效率.     

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.     

Isidd: An interactive system for inductive database design

When designing a deductive database, the designer has to decide for each predicate (or relation) whether it should be defined extensionally or intensionally and what the definition should look like. An intelligent interactive system is presented to assist the designer in this task. It starts from an example state ofa database in which all predicates are defined extensionally. It can then compact the database by transforming extensionally defined predicates into intensionally defined ones. These predicates can be chosen by the user or by the system itself. Further compaction is possible by inventing new predicates; this invention is controlled by user-specified templates. The systemalso proposes semantic integrity constraints to the user. These do not lead to extra compaction but can be used to make the database more robust. The intelligent system employs techniques from the area of inductive logic programming.     

An information-theoretic framework for flow visualization

The process of visualization can be seen as a visual communication channel where the input to the channel is the raw data, and the output is the result of a visualization algorithm. From this point of view, we can evaluate the effectiveness of visualization by measuring how much information in the original data is being communicated through the visual communication channel. In this paper, we present an information-theoretic framework for flow visualization with a special focus on streamline generation. In our framework, a vector field is modeled as a distribution of directions from which Shannon's entropy is used to measure the information content in the field. The effectiveness of the streamlines displayed in visualization can be measured by first constructing a new distribution of vectors derived from the existing streamlines, and then comparing this distribution with that of the original data set using the conditional entropy. The conditional entropy between these two distributions indicates how much information in the original data remains hidden after the selected streamlines are displayed. The quality of the visualization can be improved by progressively introducing new streamlines until the conditional entropy converges to a small value. We describe the key components of our framework with detailed analysis, and show that the framework can effectively visualize 2D and 3D flow data.     

Streamline embedding for 3D vector field exploration

We propose a new technique for visual exploration of streamlines in 3D vector fields. We construct a map from the space of all streamlines to points in IR(n) based on the preservation of the Hausdorff metric in streamline space. The image of a vector field under this map is a set of 2-manifolds in IR(n) with characteristic geometry and topology. Then standard clustering methods applied to the point sets in IR(n) yield a segmentation of the original vector field. Our approach provides a global analysis of 3D vector fields which incorporates the topological segmentation but yields additional information. In addition to a pure segmentation, the established map provides a natural "parametrization” visualized by the manifolds. We test our approach on a number of synthetic and real-world data sets.     

Image-based streamline generation and rendering

Seeding streamlines in 3D flow fields without considering their projections in screen space can produce visually cluttered rendering results. Streamlines will overlap or intersect with each other in the output image, which makes it difficult for the user to perceive the underlying flow structure. This paper presents a method to control the seeding and generation of streamlines in image space to avoid visual cluttering and allow a more flexible exploration of flow fields. In our algorithm, 2D images with depth maps generated by a variety of visualization techniques can be used as input from which seeds are placed and streamlines are generated. The density and rendering styles of streamlines can be flexibly controlled based on various criteria to improve visual clarity. With our image space approach, it is straightforward to implement the level of detail rendering, depth peeling, and stylized rendering of streamlines to allow for more effective visualization of 3D flow fields.