Interactive visualization of three-dimensional vector fields with flexible appearance control

In this paper, we present an interactive texture-based algorithm for visualizing three-dimensional steady and unsteady vector fields. The goal of the algorithm is to provide a general volume rendering framework allowing the user to compute three-dimensional flow textures interactively and to modify the appearance of the visualization on the fly. To achieve our goal, we decouple the visualization pipeline into two disjoint stages. First, flow lines are generated from the 3D vector data. Various geometric properties of the flow paths are extracted and converted into a volumetric form using a hardware-assisted slice sweeping algorithm. In the second phase of the algorithm, the attributes stored in the volume are used as texture coordinates to look up an appearance texture to generate both informative and aesthetic representations of the vector field. Our algorithm allows the user to interactively navigate through different regions of interest in the underlying field and experiment with various appearance textures. With our algorithm, visualizations with enhanced structural perception using various visual cues can be rendered in real time. A myriad of existing geometry-based and texture-based visualization techniques can also be emulated.     

Parallel line integral convolution

Line integral convolution (LIC) is a powerful method for computing directional textures from vector data. LIC textures can be animated, yielding the effect of flowing motion. Both, static images and animation sequences are of great significance in scientific visualization. Although an efficient algorithm for computing static LIC textures is known, the generation of animation sequences still requires a considerable amount of computing time. In this paper we propose an algorithm for computing animation sequences on a massively parallel distributed memory computer. With this technique it becomes possible to utilise animated LIC for interactive vector field visualization. To take advantage of the strong temporal coherence between different frames, parallelization is performed in image space rather than in time. Image space coherence is exploited using a flexible update and communication scheme. In addition algorithmic improvements on LIC are proposed that can be applied to parallel and sequential algorithms as well.     

Animation of orthogonal texture patterns for vector field visualization

This paper introduces orthogonal vector field visualization on 2D manifolds: a representation by lines that are perpendicular to the input vector field. Line patterns are generated by line integral convolution (LIC). This visualization is combined with animation based on motion along the vector field. This decoupling of the line direction from the direction of animation allows us to choose the spatial frequencies along the direction of motion independently from the length scales along the LIC line patterns. Vision research indicates that local motion detectors are tuned to certain spatial frequencies of textures, and the above decoupling enables us to generate spatial frequencies optimized for motion perception. Furthermore, we introduce a combined visualization that employs orthogonal LIC patterns together with conventional, tangential streamline LIC patterns in order to benefit from the advantages of these two visualization approaches. In addition, a filtering process is described to achieve a consistent and temporally coherent animation of orthogonal vector field visualization. Different filter kernels and filter methods are compared and discussed in terms of visualization quality and speed. We present respective visualization algorithms for 2D planar vector fields and tangential vector fields on curved surfaces, and demonstrate that those algorithms lend themselves to efficient and interactive GPU implementations.     

Output-sensitive 3D line integral convolution

We propose an output-sensitive visualization method for 3D line integral convolution (LIC) whose rendering speed is largely independent of the data set size and mostly governed by the complexity of the output on the image plane. Our approach of view-dependent visualization tightly links the LIC generation with the volume rendering of the LIC result in order to avoid the computation of unnecessary LIC points: early-ray termination and empty-space leaping techniques are used to skip the computation of the LIC integral in a lazy-evaluation approach; both ray casting and texture slicing can be used as volume-rendering techniques. The input noise is modeled in object space to allow for temporal coherence under object and camera motion. Different noise models are discussed, covering dense representations based on filtered white noise all the way to sparse representations similar to oriented LIC. Aliasing artifacts are avoided by frequency control over the 3D noise and by employing a 3D variant of MIPmapping. A range of illumination models is applied to the LIC streamlines: different codimension-2 lighting models and a novel gradient-based illumination model that relies on precomputed gradients and does not require any direct calculation of gradients after the LIC integral is evaluated. We discuss the issue of proper sampling of the LIC and volume-rendering integrals by employing a frequency-space analysis of the noise model and the precomputed gradients. Finally, we demonstrate that our visualization approach lends itself to a fast graphics processing unit (GPU) implementation that supports both steady and unsteady flow. Therefore, this 3D LIC method allows users to interactively explore 3D flow by means of high-quality, view-dependent, and adaptive LIC volume visualization. Applications to flow visualization in combination with feature extraction and focus-and-context visualization are described, a comparison to previous methods is provided, and a detailed performance analysis is included.     

Texture-based visualization of unsteady 3D flow by real-time advection and volumetric illumination

This paper presents an interactive technique for the dense texture-based visualization of unsteady 3D flow, taking into account issues of computational efficiency and visual perception. High efficiency is achieved by a 3D graphics processing unit (GPU)-based texture advection mechanism that implements logical 3D grid structures by physical memory in the form of 2D textures. This approach results in fast read and write access to physical memory, independent of GPU architecture. Slice-based direct volume rendering is used for the final display. We investigate two alternative methods for the volumetric illumination of the result of texture advection: First, gradient-based illumination that employs a real-time computation of gradients, and, second, line-based lighting based on illumination in codimension 2. In addition to the Phong model, perception-guided rendering methods are considered, such as cool/warm shading, halo rendering, or color-based depth cueing. The problems of clutter and occlusion are addressed by supporting a volumetric importance function that enhances features of the flow and reduces visual complexity in less interesting regions. GPU implementation aspects, performance measurements, and a discussion of results are included to demonstrate our visualization approach.     

基于纹理的增强型3D流场绘制

提出一种基于纹理的增强型3D矢量场可视化算法,可显著地改善传统纹理法的绘制质量.首先通过对3D纹理的线性卷积运算生成具有空间相关性的卷积纹理;然后对卷积纹理进行高通滤波,以增加流面内流线之间强度的对比;最后通过体绘制方式展示3D卷积纹理.借助权重区域,该算法可以显示用户感兴趣区域或特征区域,避免卷积数据过多引起的紊乱及相互遮挡.     

飞行器表面矢量场数据动态纹理可视化方法

面向飞行器表面流场数据可视化的应用需求,提出一种基于线性卷积（LIC）及纹理平流（IBFVS）相结合的动态纹理可视化方法。算法通过将IBFVS方法的背景随机噪声替换为LIC纹理方式,结合了LIC纹理结果对比度高及IBFVS方法生成速度快的优势;针对LIC绘制速度慢的不足,利用GPU对曲面矢量场投影并插值,生成规则矢量数据场;用GPU对LIC部分进行并行加速,有效提高了LIC纹理图像产生速度;将LIC结果图像加入到IBFVS进行平流,生成纹理图像,最后加入颜色映射,丰富流场信息。实验结果表明,该方法生成的飞行器表面动态纹理图像对比度高,清晰度强,实时绘制性能好。     

A 2D flow visualization user study using explicit flow synthesis and implicit task design

This paper presents a 2D flow visualization user study that we conducted using new methodologies to increase the objectiveness. We evaluated grid-based variable-size arrows, evenly spaced streamlines, and line integral convolution (LIC) variants (basic, oriented, and enhanced versions) coupled with a colorwheel and/or rainbow color map, which are representative of many geometry-based and texture-based techniques. To reduce data-related bias, template-based explicit flow synthesis was used to create a wide variety of symmetric flows with similar topological complexity. To suppress task-related bias, pattern-based implicit task design was employed, addressing critical point recognition, critical point classification, and symmetric pattern categorization. In addition, variable-duration and fixed-duration measurement schemes were utilized for lightweight precision-critical and heavyweight judgment intensive flow analysis tasks, respectively, to record visualization effectiveness. We eliminated outliers and used the Ryan REGWQ post-hoc homogeneous subset tests in statistical analysis to obtain reliable findings. Our study shows that a texture-based dense representation with accentuated flow streaks, such as enhanced LIC, enables intuitive perception of the flow, while a geometry-based integral representation with uniform density control, such as evenly spaced streamlines, may exploit visual interpolation to facilitate mental reconstruction of the flow. It is also shown that inappropriate color mapping (e.g., colorwheel) may add distractions to a flow representation.     

Tabu search algorithm combined with global perturbation for packing arbitrary sized circles into a circular container

It is important for the rapid visualization of large scale forest scene to dynamically simplify and recombine model data. In order to preserve the geometric features and visual perception of tree model, this paper presents a real-time information recombination method of complex 3D tree model based on visual perception. This method adopts visual attention model and the visual characteristic of tree structures, and then uses geometry-based and image-based methods to simplify tree models and construct a hybrid representation model. The hybrid representation model reflects the visual perception features of 3D tree models that can embody topological semantics in dynamic simulation. In addition, this method automatically extracts the representation information of 3D tree model based on visual perception, and recombines model information in real time according to the dynamic viewpoint of virtual scene. Finally, this method is applied in the simplification of different tree models, and it is compared with the existing tree model simplification methods. Experimental results show that this method can not only preserve better visual perception for 3D tree models, but also effectively decrease the geometric data of forest scene, and improve the rendering efficiency of forest scene.     

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     

High-quality animation of 2D steady vector fields

Simulators for dynamic systems are now widely used in various application areas and raise the need for effective and accurate flow visualization techniques. Animation allows us to depict direction, orientation, and velocity of a vector field accurately. We extend a former proposal for a new approach to produce perfectly cyclic and variable-speed animations for 2D steady vector fields [B. Jobard, et al., (1997)] and [C. Chedot, et al., (1998)]. A complete animation of an arbitrary number of frames is encoded in a single image. The animation can be played using the color table animation technique, which is very effective even on low-end workstations. A cyclic set of textures can be produced as well and then encoded in a common animation format or used for texture mapping on 3D objects. As compared to other approaches, the method presented produces smoother animations and is more effective, both in memory requirements to store the animation, and in computation time.     

A new line integral convolution algorithm for visualizingtime-varying flow fields

New challenges on vector field visualization emerge as time dependent numerical simulations become ubiquitous in the field of computational fluid dynamics (CFD). To visualize data generated from these simulations, traditional techniques, such as displaying particle traces, can only reveal flow phenomena in preselected local regions and thus, are unable to track the evolution of global flow features over time. The paper presents an algorithm, called UFLIC (Unsteady Flow LIC), to visualize vector data in unsteady flow fields. Our algorithm extends a texture synthesis technique, called Line Integral Convolution (LIC), by devising a new convolution algorithm that uses a time-accurate value scattering scheme to model the texture advection. In addition, our algorithm maintains the coherence of the flow animation by successively updating the convolution results over time. Furthermore, we propose a parallel UFLIC algorithm that can achieve high load balancing for multiprocessor computers with shared memory architecture. We demonstrate the effectiveness of our new algorithm by presenting image snapshots from several CFD case studies     

Interactive clipping techniques for texture-based volume visualization and volume shading

We propose clipping methods that are capable of using complex geometries for volume clipping. The clipping tests exploit per-fragment operations on the graphics hardware to achieve high frame rates. In combination with texture-based volume rendering, these techniques enable the user to interactively select and explore regions of the data set. We present depth-based clipping techniques that analyze the depth structure of the boundary representation of the clip geometry to decide which parts of the volume have to be clipped. In another approach, a voxelized clip object is used to identify the clipped regions. Furthermore, the combination of volume clipping and volume shading is considered. An optical model is introduced to merge aspects of surface-based and volume-based illumination in order to achieve a consistent shading of the clipping surface. It is demonstrated how this model can be efficiently incorporated in the aforementioned clipping techniques.     

Direct volume editing

In this work we present basic methodology for interactive volume editing on GPUs, and we demonstrate the use of these methods to achieve a number of different effects. We present fast techniques to modify the appearance and structure of volumetric scalar fields given on Cartesian grids. Similar to 2D circular brushes as used in surface painting we present 3D spherical brushes for intuitive coloring of particular structures in such fields. This paint metaphor is extended to allow the user to change the data itself, and the use of this functionality for interactive structure isolation, hole filling, and artefact removal is demonstrated. Building on previous work in the field we introduce high-resolution selection volumes, which can be seen as a resolution-based focus+context metaphor. By utilizing such volumes we present a novel approach to interactive volume editing at sub-voxel accuracy. Finally, we introduce a fast technique to paste textures onto iso-surfaces in a 3D scalar field. Since the texture resolution is independent of the volume resolution, this technique allows structure-aligned textures containing appearance properties or textual information to be used for volume augmentation and annotation.     

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     

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。     

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.     

Texture-based feature tracking for effective time-varying data visualization

Analyzing, visualizing, and illustrating changes within time-varying volumetric data is challenging due to the dynamic changes occurring between timesteps. The changes and variations in computational fluid dynamic volumes and atmospheric 3D datasets do not follow any particular transformation. Features within the data move at different speeds and directions making the tracking and visualization of these features a difficult task. We introduce a texture-based feature tracking technique to overcome some of the current limitations found in the illustration and visualization of dynamic changes within time-varying volumetric data. Our texture-based technique tracks various features individually and then uses the tracked objects to better visualize structural changes. We show the effectiveness of our texture-based tracking technique with both synthetic and real world time-varying data. Furthermore, we highlight the specific visualization, annotation, registration, and feature isolation benefits of our technique. For instance, we show how our texture-based tracking can lead to insightful visualizations of time-varying data. Such visualizations, more than traditional visualization techniques, can assist domain scientists to explore and understand dynamic changes.     

基于线积分卷积算法的并行实现方法

线积分卷积（LIC）是矢量场可视化中一个强有力的工具。但其计算量过大、耗时过多,影响了它的应用。根据LIC算法的特点,提出了LIC算法的并行实现方法。由于流线跟踪和卷积计算的独立性,只需把输出图像以像素点为单位平均分配给各处理器节点进行计算。从进程之间没有通信,仅当从进程开始计算前和计算结束后,在主进程与从进程之间有数据传递,通信开销很小。最后应用MPI在Linux集群环境下实现了该算法,实验结果表明,该方法具有较高的并行度和加速比。