三维破碎物体多尺度拼接技术

在分析三维物体碎片轮廓曲线的特征和表示的基础上,研究多尺度小波轮廓描述符的计算,提出了一种多尺度下轮廓曲线特征提取及基于多尺度分析的三维物体碎片拼接方法.轮廓曲线经多尺度小波变换平滑后,提取曲率和挠率构成特征矢量;在选择了基于小波轮廓描述符的三维曲线匹配起点后,比较2条轮廓曲线的特征矢量以判断轮廓的相似性,并将轮廓匹配的2块相邻物体碎片拼接,实现破碎物体复原.最后通过实验验证了该方法的有效性.     

基于矢量场的二维区域全自动四边网格生成

为了实现任意二维几何模型的高质量分块结构四边形网格自动生成,提出一种基于矢量场的二维区域全自动分解方法.首先利用边界元法求解拉普拉斯型控制方程,获取一个反映模型边界几何特征、覆盖整个问题域的矢量场;然后结合矢量与标架的映射关系,将计算得到的矢量场转化为标架场;最后通过分析标架场的奇异结构将问题域分解成多个四边子区域,并在每个子区域利用映射法生成高质量的结构四边形网格.通过复杂区域的网格生成实例,验证了该方法的有效性和可靠性.     

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。     

一种基于矢量场结构的等值面构造方法

为得到非结构矢量场中的等值面图像,给出了一种基于矢量场曲线结构的等值面构造新方法.算法利用矢量可视化映射过程中获得的曲线结构来组织数据并计算等值点,采取自适应聚类划分方法获得各个等值面包含的数据点集合后利用曲面重建算法来构造等值面.在计算等值点时,不但利用了数据场中各个数据点处的空间位置与场值大小,而且充分考虑了数据点处的矢量方向信息.实验表明,该方法能够稳定、有效地构造出非结构矢量数据场中的等值面.与基于体元的传统等值面构造方法相比,可以有效加快计算进程,得到更为准确的计算结果.     

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。     

一种非结构矢量场的线卷积积分方法

传统的结构化LIC方法不适用于非结构矢量场数据处理的主要原因有两个,一是矢量幅度的表现力不强,二是因分辨率等因素无法有效地应用于采样点位置随机的矢量场．为解决上述问题,可以采用如下方法：在DDA曲线的生成过程中,采用基于数值的计算方法替代结构化LIC中基于网格的计算方法,从而有效地保证了处理结果的分辨率;在DDA曲线的卷积积分（LIC）处理过程中,采用区域标记的策略替代快速LIC方法中的线标记策略,一方面,因为被标记的采样点不再作为以后各轮DAA曲线生成的起始点,从而可以有效地减少计算量;另一方面,区域标记方法能够使LIC处理的结果稀疏化,表现为矢量场中幅度大的区域矢量线密集,而幅度小的区域矢量线稀疏,从而有效地提高矢量场幅度、结构的表现力．     

基于Normalized cut的矢量场分割方法

基于Normalized cut的矢量场分割方法融合了格林函数和Normalized cut两种基本技术,即先用格林函数和初始矢量做卷积得到可保持其拓扑结构的标量场,再用Normalized cut方法对标量场进行分割,最后将分割好的标量场对应映射到初始矢量场中,以完成矢量场的分割.这种基于Normalized cut方法的特点就是分割时能综合考虑矢量场的整体特征和局部特征,由于利用矢量场潜在的拓扑结构可把在某一奇异点周围的矢量划分到同一个区域中,因此可达到最佳分割效果.     

矢量场可视化的研究现状与发展趋势

矢量场广泛存在于自然界并在科学计算和工程分析中扮演着重要的角色,试图为矢量场可视化研究领域提供一个清晰的概貌。阐述了矢量场可视化的基本流程,矢量场可视化的研究现状以及迄今为止的一些研究成果,并讨论了矢量场可视化的发展趋势及应重视的研究方向。     

二维LIC矢量场可视化算法的研究及改进

线积分卷积(LIC)是一种针对矢量场的可视化方法.针对二维空间上的LIC算法进行了研究并提出了改进.首先,针对某些二维矢量场在用户关注区域矢量大小比较接近的问题,采用非线性的颜色映射法进行处理,最终的可视化结果可以突出用户感兴趣区域的矢量场特征.其次,从原始LIC算法的串行计算任务中提取出4个可以并行计算的子模块,并依托NVIDIA的CUDA架构实现了颜色增强LIC法的硬件加速.结果表明,加速后算法的加速比随着输入矢量场分辨率的增加而增加.因此,该算法适用于高分辨率二维矢量场的交互式可视化,且没有特别高的硬件要求,通用性较好.总之,新的算法较原始算法在视觉效果和性能上都有所改进.     

基于时间延迟的矢量场可视化方法的应用研究

矢量场可视化是科学计算可视化中最具有挑战性的研究课题之一。该文提出了一种基于时间延迟逐步生成、绘制和显示流线的方法,从而把稳定的二维矢量场的拓扑结构、方向、速度等特征以动画的形式显示出来。实验证明此方法简单、直观、形象。     

An Approximate Parallel Vectors Operator for Multiple Vector Fields

The Parallel Vectors (PV) Operator extracts the locations of points where two vector fields are parallel. In general, these features are line structures. The PV operator has been used successfully for a variety of problems, which include finding vortex‐core lines or extremum lines. We present a new generic feature extraction method for multiple 3D vector fields: The Approximate Parallel Vectors (APV) Operator extracts lines where all fields are approximately parallel. The definition of the APV operator is based on the application of PV for two vector fields that are derived from the given set of fields. The APV operator enables the direct visualization of features of vector field ensembles without processing fields individually and without causing visual clutter. We give a theoretical analysis of the APV operator and demonstrate its utility for a number of ensemble data.     

Mesh-driven vector field clustering and visualization: an image-based approach

Vector field visualization techniques have evolved very rapidly over the last two decades, however, visualizing vector fields on complex boundary surfaces from computational flow dynamics (CFD) still remains a challenging task. In part, this is due to the large, unstructured, adaptive resolution characteristics of the meshes used in the modeling and simulation process. Out of the wide variety of existing flow field visualization techniques, vector field clustering algorithms offer the advantage of capturing a detailed picture of important areas of the domain while presenting a simplified view of areas of less importance. This paper presents a novel, robust, automatic vector field clustering algorithm that produces intuitive and insightful images of vector fields on large, unstructured, adaptive resolution boundary meshes from CFD. Our bottom-up, hierarchical approach is the first to combine the properties of the underlying vector field and mesh into a unified error-driven representation. The motivation behind the approach is the fact that CFD engineers may increase the resolution of model meshes according to importance. The algorithm has several advantages. Clusters are generated automatically, no surface parameterization is required, and large meshes are processed efficiently. The most suggestive and important information contained in the meshes and vector fields is preserved while less important areas are simplified in the visualization. Users can interactively control the level of detail by adjusting a range of clustering distance measure parameters. We describe two data structures to accelerate the clustering process. We also introduce novel visualizations of clusters inspired by statistical methods. We apply our method to a series of synthetic and complex, real-world CFD meshes to demonstrate the clustering algorithm results.     

Asymmetric Tensor Analysis for Flow Visualization

The gradient of a velocity vector field is an asymmetric tensor field which can provide critical insight that is difficult to infer from traditional trajectory-based vector field visualization techniques. We describe the structures in the eigenvalue and eigenvector fields of the gradient tensor and how these structures can be used to infer the behaviors of the velocity field. To illustrate the structures in asymmetric tensor fields, we introduce the notions of eigenvalue and eigenvector manifolds. These concepts afford a number of theoretical results that clarify the connections between symmetric and antisymmetric components in tensor fields. In addition, these manifolds naturally lead to partitions of tensor fields, which we use to design effective visualization strategies. Both eigenvalue manifold and eigenvector manifold are supported by a tensor reparameterization with physical meaning. This allows us to relate our tensor analysis to physical quantities such as rotation, angular deformation, and dilation, which provide physical interpretation of our tensor-driven vector field analysis in the context of fluid mechanics. To demonstrate the utility of our approach, we have applied our visualization techniques and interpretation to the study of the Sullivan Vortex as well as computational fluid dynamics simulation data.     

Direct Visualization of Deformation in Volumes

Deformation is a topic of interest in many disciplines. In particular in medical research, deformations of surfaces and even entire volumetric structures are of interest. Clear visualization of such deformations can lead to important insight into growth processes and progression of disease.
We present new techniques for direct focus+context visualization of deformation fields representing transformations between pairs of volumetric datasets. Typically, such fields are computed by performing a non-rigid registration between two data volumes. Our visualization is based on direct volume rendering and uses the GPU to compute and interactively visualize features of these deformation fields in real-time. We integrate visualization of the deformation field with visualization of the scalar volume affected by the deformations. Furthermore, we present a novel use of texturing in volume rendered visualizations to show additional properties of the vector field on surfaces in the volume.     

面向二维GIS矢量数据三维可视化的地形匹配技术研究

提出一种二维GIS矢量数据三维可视化过程中地物与地形的快速匹配方法.结合矢量所代表地物的特性,对基于矢量信息的三维地物进行了分类,综合采用了地物匹配地形和地形匹配地物两种方法.地物匹配地形算法通过实时调整地物的位置和姿态实现与地形的匹配,地形匹配地物算法以不同的距离度量为基础,对矢量约束域内地形进行变形操作实现匹配.本算法还讨论了原始地形数据分辨率较低以及多个地形匹配影响域相交等特殊情况的处理方法.试验结果表明,本方法能满足基于点、线、面矢量信息的三维地物与地形的匹配需求,实现地物与地形无缝结合及平滑过渡,从而达到改善视觉效果的目的.     

Stable Morse Decompositions for Piecewise Constant Vector Fields on Surfaces

Numerical simulations and experimental observations are inherently imprecise. Therefore, most vector fields of interest in scientific visualization are known only up to an error. In such cases, some topological features, especially those not stable enough, may be artifacts of the imprecision of the input. This paper introduces a technique to compute topological features of user‐prescribed stability with respect to perturbation of the input vector field. In order to make our approach simple and efficient, we develop our algorithms for the case of piecewise constant (PC) vector fields. Our approach is based on a super‐transition graph, a common graph representation of all PC vector fields whose vector value in a mesh triangle is contained in a convex set of vectors associated with that triangle. The graph is used to compute a Morse decomposition that is coarse enough to be correct for all vector fields satisfying the constraint. Apart from computing stable Morse decompositions, our technique can also be used to estimate the stability of Morse sets with respect to perturbation of the vector field or to compute topological features of continuous vector fields using the PC framework.     

使用Voronoi图对流场拓扑区域进行划分

特征可视化中的拓扑结构分析法,能够快速的显示流场的全局结构,在侧重于考虑流场的特殊结构时显示出了较大的优越性。但是在很多情况下,仅仅显示流场的结构还不够,还需要更详细的知道拓扑场中每个区域的作用范围。传统的方法都是根据特征矢量的虚部来判断拓扑区域的作用范围,这种方法太过于概括,区域大小只是相对的,没有考虑到附近临界点对周围流体运动的影响。为了能更真实的反映临界点对周围流运动的影响,论文提出使用Voronoi图来划分拓扑区域的作用范围,并将该方法应用于海洋流场。同时也与传统的特征矢量方法进行了对比,实验表明,取得了较好的效果。     

基于纹理合成的向量场可视化

在纹理合成过程中利用向量场作为指导,生成反映向量场大小和方向变化的合成结果.采用块纹理合成的流程,在对向量场合成块均匀划分的基础上,通过进一步的自适应分割,将向量场划分成为不同大小和不同形状的最终合成块,使之与向量场的变化趋势相吻合.对向量变化过于剧烈的区域,则采用点合成的方式进行纹理合成,以保证合成效果的平滑.实验表明,文中的方法可以实现快速而高质量的向量场可视化.     

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.