An Illustrative Visualization Framework for 3D Vector Fields

Most 3D vector field visualization techniques suffer from the problem of visual clutter, and it remains a challenging task to effectively convey both directional and structural information of 3D vector fields. In this paper, we present a novel visualization framework that combines the advantages of clustering methods and illustrative rendering techniques to generate a concise and informative depiction of complex flow structures. Given a 3D vector field, we first generate a number of streamlines covering the important regions based on an entropy measurement. Then we decompose the streamlines into different groups based on a categorization of vector information, wherein the streamline pattern in each group is ensured to be coherent or nearly coherent. For each group, we select a set of representative streamlines and render them in an illustrative fashion to enhance depth cues and succinctly show local flow characteristics. The results demonstrate that our approach can generate a visualization that is relatively free of visual clutter while facilitating perception of salient information of complex vector fields.     

基于信息熵的流线质量评估和布局算法

基于流线的矢量场可视化是科学可视化的重要分支,在许多领域都有重要应用。但是现有的可视化方法很难有效评估流线对矢量场信息的反映程度。为了解决这一问题,提出了一种基于信息熵的矢量场种子点评估和布局算法。首先,基于信息熵进行初始布点捕捉矢量场中的主要特征,并利用模板将这些特征加强显示。然后,基于生成的流线恢复中间矢量场,通过恢复的矢量场和输入矢量场的条件熵值量化评估现有流线对矢量场的信息反映程度。根据条件熵和重要性添加新种子点。重新评估流线质量,反复迭代直到条件熵收敛。实验表明,该方法可以用较少的流线反映出矢量场中较多的信息。     

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.     

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.     

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.     

基于非结构化三角网格的海洋流场可视化

针对二维流场可视化均是基于结构化网格流场数据的情况,提出一种基于非结构化三角网格的海洋流场可视化策略：使用流线表达流场,流线可视化的主要挑战是种子点放置问题,即流线的初始点,制定了非结构化三角网格下基于特征引导的种子点放置策略,合理放置流线初始点以利于表达流场特征;设计了基于网格密度的层次聚类算法,引入网格密度属性对流线进行聚类并基于聚类质心进行流线放置,在保留了FVCOM 模式数据的多密度性前提下提高了流线可视化效果。实验表明,该方法可以有效地保留流场特征,并且借助 FVCOM 模式的边界拟合性能在海湾、河道等地区取得良好的可视化效果;在此基础上,基于 Cesium引擎开发了基于流线聚类数据的动态流场可视化应用,其是 FVCOM 模式数据首次应用于动态粒子流场的一次尝试,并且具有较好的可视化效果。     

Pathline glyphs

Visualization of pathlines is common and highly relevant for the analysis of unsteady flow. However, pathlines can intersect, leading to visual clutter and perceptual issues. This makes it intrinsically difficult to provide expressive visualizations of the entire domain by an arrangement of multiple pathlines, in contrast to well‐established streamline placement techniques. We present an approach to reduce these problems. It is inspired by glyph‐based visualization and small multiples: we partition the domain into cells, each corresponding to a downscaled version of the entire domain. Inside these cells, a single downscaled pathline is drawn. On the overview scale, our pathline glyphs lead to emergent visual patterns that provide insight into time‐dependent flow behavior. Zooming‐in allows us to analyze individual pathlines in detail and compare neighboring lines. The overall approach is complemented with a context‐preserving zoom lens and interactive pathline‐based exploration. While we primarily target the visualization of 2D flow, we also address the extension to 3D. Our evaluation includes several examples, comparison to other flow visualization techniques, and a user study with domain experts.     

基于流线纹理合成的2D矢量场可视化

针对科学试验数据可视化问题,提出了一种2D矢量场可视化的方法－流线纹理合成方法,即通过将1D纹理映射到流线上,再利用流线纹理来合成可视化图象,因为移动1D纹理很容易形成矢量场动画。该方法是利用局部区域内流线的近似平行性,首先依据临界点来设定流线宽度,然后把流线绘制成多条平行流线,再分别将多条不同的1D纹理映射到流线上,从而能够加快计算。实际结果表明,由于流线纹理合成的纹理图象上清楚地显示了流线,因而反映了矢量场的方向信息,同时,该方法计算速度快,可以达到交互可视化的要求。     

基于微分的增强型三维矢量场可视化

为提高3D矢量场可视化效果,提出了一种基于微分滤波的流线增强方法。首先对三维纹理进行线性卷积运算,生成具有空间相关性的卷积纹理;其次对卷积纹理进行分数阶微分滤波,增强流线之间强度对比;最后采用纹理映射体绘制技术实现三维矢量场可视化,并通过设计体绘制的传输函数来显示矢量场的内部结构。实验结果表明,该方法有效地增强了流线间的对比,使绘制的流线更加平滑,同时也有效地消除了卷积数据过多引起的紊乱与相互遮挡。     

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。     

Visual Reconstructability as a Quality Metric for Flow Visualization

We present a novel approach for the evaluation of 2D flow visualizations based on the visual reconstructability of the input vector fields. According to this metric, a visualization has high quality if the underlying data can be reliably reconstructed from the image. This approach provides visualization creators with a cost‐effective means to assess the quality of visualization results objectively. We present a vision‐based reconstruction system for the three most commonly‐used visual representations of vector fields, namely streamlines, arrow glyphs, and line integral convolution. To demonstrate the use of visual reconstructability as a quality metric, we consider a selection of vector fields obtained from numerical simulations, containing typical flow features. We apply the three types of visualization to each dataset, and compare the visualization results based on their visual reconstructability of the original vector field.     

表意性方法在三维流线可视化中的应用综述

流线可视化是流场可视化的重要方法,其能直观地表达流场的结构和流动趋势。但在三维流场使用流线可视化时,不恰当地绘制方法、选择方法、呈现方式会导致可视化结果表达能力差,用户很难从中高效获取流动信息。重点对解决该类问题的表意性可视化方法进行了调研,为了全面反映表意性方法在三维流线可视化中的研究进展,对近十几年国内外具有代表性的论文进行了系统地阐述。首先介绍了表意性可视化方法的相关概念,然后将视觉感知增强类、可见性管理类和焦点+上下文等表意性方法在三维流线可视化中的应用进行分类阐述,并讨论了各种方法的优缺点。最后总结分析了表意性方法在三维流线可视化中面临的问题和挑战,并对未来的研究方向进行了展望。     

A Survey of Seed Placement and Streamline Selection Techniques

Streamlines are an extensively utilized flow visualization technique for understanding, verifying, and exploring computational fluid dynamics simulations. One of the major challenges associated with the technique is selecting which streamlines to display. Using a large number of streamlines results in dense, cluttered visualizations, often containing redundant information and occluding important regions, whereas using a small number of streamlines could result in missing key features of the flow. Many solutions to select a representative set of streamlines have been proposed by researchers over the past two decades. In this state-of-the-art report, we analyze and classify seed placement and streamline selection (SPSS) techniques used by the scientific flow visualization community. At a high-level, we classify techniques into automatic and manual techniques, and further divide automatic techniques into three strategies: density-based, feature-based, and similarity-based. Our analysis evaluates the identified strategy groups with respect to focus on regions of interest, minimization of redundancy, and overall computational performance. Finally, we consider the application contexts and tasks for which SPSS techniques are currently applied and have potential applications in the future.     

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.     

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。     

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.     

VR系统中的三维流场可视化

本文提出了一种将基于几何图元的三维流场可视化集成到VR系统的新方法。该方法的主要目标是把握流场中的基本特征，并提供较强的沉浸感显示。首先，流域中的临界点被抽取出来，分成不同的类别，并据此在临界点周围设置不同的种子点模板；其次，提出了一种根据原始流线创建流管的新方法；最后，将可视化结果集成到一个可交互的后处理单元。通过佩戴立体眼镜和头位跟踪器，用户可以清楚地把握流场中的主要特征。     

An advanced evenly-spaced streamline placement algorithm

This paper presents an advanced evenly-spaced streamline placement algorithm for fast, high-quality, and robust layout of flow lines. A fourth-order Runge-Kutta integrator with adaptive step size and error control is employed for rapid accurate streamline advection. Cubic Hermite polynomial interpolation with large sample-spacing is adopted to create fewer evenly-spaced samples along each streamline to reduce the amount of distance checking. We propose two methods to enhance placement quality. Double queues are used to prioritize topological seeding and to favor long streamlines to minimize discontinuities. Adaptive distance control based on the local flow variance is explored to reduce cavities. Furthermore, we propose a universal, effective, fast, and robust loop detection strategy to address closed and spiraling streamlines. Our algorithm is an order-of-magnitude faster than Jobard and Lefer's algorithm with better placement quality and over 5 times faster than Mebarki et al.'s algorithm with comparable placement quality, but with a more robust solution to loop detection.