复杂向量场数据可视化技术研究与实现

本文结合实际应用背景 ,对向量场数据可视化进行了广泛的研究和探索。纹理方法是有效的二维向量场数据全局可视化技术 ,文中通过分析纹理方法的频率含义 ,指出现有方法的不足 ,并提出纹理流线方法。该方法的频率含义更为明确 ,实现更为简洁 ,并可以通过纹理的伸缩来实现一幅图象中的多频纹理 ,直接表现出向量的大小。对于非定常数据 ,好的可视化算法不仅应能描绘出每个时间步的物理状态 ,还应能通过对连续时间步的顺序显示反映出物理过程的时间变化情况。对来自爆轰、爆炸等复杂物理过程模拟产生的二维非定常网格向量数据 ,可视化尤为困难。…     

基于多频稀疏噪声的流场运动方向可视化算法

针对现有流场可视化算法存在的矢量场运动指向二义性以及缺乏对矢量场速率区分等问题进行了研究,提出了一种基于多频稀疏噪声纹理的改进线积分卷积算法,用来提高流场可视化后的信息表达效果。该方法首先根据矢量场速率量级的大小划分频率不同的噪声群,并合成适用于该向量场的特定多频噪声纹理;然后使用斜坡卷积核根据向量场流线对噪声纹理进行卷积;最后生成一幅同时具有矢量场运动方向和运动速率信息的彩色图像。实验结果表明,该方法可以增强用户对流场流量大小和矢量场方向的感知效果,在大规模风场数据可视化的验证实验上取得了良好的可视化效果。     

平面时变向量场Hopf分岔的精确定位与可视化

分岔是指动力系统在演化过程中定性行为发生质变的现象．分岔研究对揭示复杂流场的不稳定过程有重要意义．文中提出一个平面时变向量场Hopf分岔的榆出、定位与可视化算法．通过精密跟踪场内全体临界点的变化以及用一个颜色模型图画般地记述这些变化的演化路径，新算法不仅实现了对平面时变向量场中全部Hopf分岔点的检出和定位，还能详尽显示分岔的发展过程，文中方法原则上也适用于其它局部分岔类型的检出，为用数据可视化技术观察和研究分岔现象开辟了新的途径。     

基于两级采样的非结构化网格流场多激波特征可视化方法

激波特征可视化是流场可视化的重要内容.目前主流的激波特征提取方法是先采用正则马赫数检测激波,再设计过滤算法去除噪声.已有方法在计算正则马赫数时,并未区分压力梯度和密度梯度;在过滤噪声时,有效性依赖于数据集本身,适应性和准确性差.当流场中存在强度不同的多激波特征时,往往在过滤噪声的同时也滤掉了"弱激波",且即便对于单激波特征,也常出现激波面不连通甚至断裂现象.论述了基于压力梯度计算正则马赫数的必要性;利用激波物理特性,结合光线投射算法优势,提出了一种基于两级采样的多激波特征可视化方法;并针对拓扑复杂的3D非结构化网格数据,在GPU上设计实现了算法.实验表明,该方法能自动识别并过滤噪声,即便对包含多激波特征的复杂流场,也具有很好的适应性和准确性,过滤效果明显优于已有方法,且对较大规模非结构化网格数据,绘制性能可满足实时交互.     

一种基于网格框架下改进的多密度SNN聚类算法

针对数据集中数据分布密度不均匀以及存在噪声点,噪声点容易导致样本聚类时产生较大的偏差问题,提出一种基于网络框架下改进的多密度SNN聚类算法。网格化递归划分数据空间成密度不同的网格,对高密度网格单元作为类簇中心,利用网格相对密度差检测出在簇边界网格中包含噪声点;使用改进的SNN聚类算法计算边界网格内样本数据点的局部密度,通过数据密度特征分布对噪声点进行类簇分配,从而提高聚类算法的鲁棒性。在UCI高维的数据集上的实验结果表明,与传统的算法相比,该算法通过网格划分数据空间和局部密度峰值进行样本类簇分配,有效地平衡聚类效果和时间性能。     

与物理特征相关的平面向量场的拓扑简化及压缩

针对现有拓扑简化方法忽略物理特征保持的缺陷,提出一种对物理特征敏感的平面向量场拓扑简化算法,其中心思想是使用为应用定制的物理判据分类向量场区域,将向量场的特征检出与拓扑简化关联起来.通过合并次要物理特征所在区域上的网格及在新网格布局下重新提取向量场拓扑,该算法不仅能完好地保持场内的重要特征,还能同时实现向量场的数据压缩.实验结果表明,该算法在复杂流场的特征提取方面可发挥重要的作用.     

基于屏幕空间的海洋仿真的研究与实现

针对海洋模拟仿真中真实性和实时性难以均衡的难题,提出一种基于频谱统计模型和Perlin噪声模型对海浪建模,应用快速傅里叶变换(FFT)生成高度场并与Perlin噪声高度场线性混合的方法。把在屏幕空间生成的高度场网格点通过算法投射到世界空间生成合适的网格,利用统一计算设备架构(CUDA)高效的并行计算能力把复杂的模型数据转移到图形处理器(GPU)中进行处理。实验结果表明,该方法在保持场景真实性的同时,有效降低了计算复杂度,提高了绘制实时性。     

Catmull-Clark细分网格数据点拾取

针对将OpenGL选择拾取机制直接作用于Catmull-Clark细分网格数据点的拾取,可能会因细分网格数据量过大而导致名字堆栈溢出的问题,借鉴细分曲面求交的思想,提出一种新的细分网格数据点拾取方法.该方法通过提取拾取对象的邻域网格并进行局部细分,将对细分任意层次上网格数据点的拾取转化为对初始控制网格以及在达到细分层次要求以前每一次局部细分网格点、边、面的拾取和对最后一次局部细分网格数据点的拾取.采用多个拾取算例进行对比分析实验,当细分网格顶点数量较多时,所给拾取方法的拾取命名对象总量和拾取时间都远小于传统OpenGL选择拾取方法.实验结果表明,所给拾取方法能快速准确实现细分网格数据点的拾取,尤其适用于数据量较大的复杂细分模型,可有效避免因拾取名字堆栈溢出而导致的拾取错误.     

基于相似度的网格聚类算法

提出了一种基于相似度的网格聚类算法（SGCA）。该算法主要利用网格技术去除数据集中的部分孤立点或噪声,使用边界点阈值函数提取类的边界点,最后利用相似度方法进行聚类。SGCA算法只要求对数据集进行一遍扫描。实验表明,该算法可扩展性好,能处理任意形状和大小的聚类,能够很好的识别出孤立点或噪声,它不仅适用于综合数据集,而且对高维数据集也具有较好的聚类结果。本文中还引进了网格核技术,进一步改善了SGCA算法的时间复杂度。     

三维地形生成及其可视化处理研究

针对在三维地形处理领域中存在的地形数据获取困难,可视化处理过程复杂真实感效果不强的问题.文中提出了一种三维地形生成和可视化处理的方法,该方法采用分形算法生成虚拟地形数据,然后将其存储为地理信息系统中通用的数字高程数据格式,最后将数据导入三维建模软件Multigen Creator 3.0中,结合网格生成、三维投影和纹理映射等,进行可视化处理.仿真试验表明:该方法能快速获取有效的地形高程数据,经过处理后得到了直观的,真实感较强的三维显示效果图.该文为三维地形生成和可视化处理问题提供了一种有效的、可实现的处理方法.     

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.     

Feature Driven Combination of Animated Vector Field Visualizations

Animated visualizations are one of the methods for finding and understanding complex structures of time-dependent vector fields. Many visualization designs can be used to this end, such as streamlines, vector glyphs, and image-based techniques. While all such designs can depict any vector field, their effectiveness in highlighting particular field aspects has not been fully explored. To fill this gap, we compare three animated vector field visualization techniques, OLIC, IBFV, and particles, for a critical point detection-and-classification task through a user study. Our results show that the effectiveness of the studied techniques depends on the nature of the critical points. We use these results to design a new flow visualization technique that combines all studied techniques in a single view by locally using the most effective technique for the patterns present in the flow data at that location. A second user study shows that our technique is more efficient and less error prone than the three other techniques used individually for the critical point detection task.     

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。     

Robust Reference Frame Extraction from Unsteady 2D Vector Fields with Convolutional Neural Networks

Robust feature extraction is an integral part of scientific visualization. In unsteady vector field analysis, researchers recently directed their attention towards the computation of near‐steady reference frames for vortex extraction, which is a numerically challenging endeavor. In this paper, we utilize a convolutional neural network to combine two steps of the visualization pipeline in an end‐to‐end manner: the filtering and the feature extraction. We use neural networks for the extraction of a steady reference frame for a given unsteady 2D vector field. By conditioning the neural network to noisy inputs and resampling artifacts, we obtain numerically stabler results than existing optimization‐based approaches. Supervised deep learning typically requires a large amount of training data. Thus, our second contribution is the creation of a vector field benchmark data set, which is generally useful for any local deep learning‐based feature extraction. Based on Vatistas velocity profile, we formulate a parametric vector field mixture model that we parameterize based on numerically‐computed example vector fields in near‐steady reference frames. Given the parametric model, we can efficiently synthesize thousands of vector fields that serve as input to our deep learning architecture. The proposed network is evaluated on an unseen numerical fluid flow simulation.     

High-quality and interactive animations of 3D time-varying vector fields

In this paper, we present an interactive texture-based method for visualizing three-dimensional unsteady vector fields. The visualization method uses a sparse and global representation of the flow, such that it does not suffer from the same perceptual issues as is the case for visualizing dense representations. The animation is made by injecting a collection of particles evenly distributed throughout the physical domain. These particles are then tracked along their path lines. At each time step, these particles are used as seed points to generate field lines using any vector field such as the velocity field or vorticity field. In this way, the animation shows the advection of particles while each frame in the animation shows the instantaneous vector field. In order to maintain a coherent particle density and to avoid clustering as time passes, we have developed a novel particle advection strategy which produces approximately evenly-spaced field lines at each time step. To improve rendering performance, we decouple the rendering stage from the preceding stages of the visualization method. This allows interactive exploration of multiple fields simultaneously, which sets the stage for a more complete analysis of the flow field. The final display is rendered using texture-based direct volume rendering     

Using line integral convolution for flow visualization: curvilineargrids, variable-speed animation, and unsteady flows

Line integral convolution (LIC), introduced by Cabral and Leedom (1993) is a powerful technique for imaging and animating vector fields. We extend the LIC technique in three ways. Firstly the existing algorithm is limited to vector fields over a regular Cartesian grid. We extend the algorithm and the animation techniques possible with it to vector fields over curvilinear surfaces, such as those found in computational fluid dynamics simulations. Secondly we introduce a technique to visualize vector magnitude as well as vector direction, i.e., variable-speed flow animation. Thirdly we show how to modify LIC to visualize unsteady (time dependent) flows. Our implementation utilizes texture-mapping hardware to run in real time, which allows our algorithms to be included in interactive applications     

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.     

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 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. 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.