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     

Design and implementation of the 2D tied bone vector animation performances

It is a great challenge to use digital technology to inherit and reproduce Xinjiang Qiuci music and dance authentically.The thesis displays the cultural beauty of Qiuci music and dance through the change of vector images controlled by bones.The concrete methods are:first,get video images,do edge detection;then set up 2D character model based on anime studio,and build the skeleton according to the level,make key frames;finally use vector animation performance with the help of platform.Compared with Flash,this method is more flexible and natural.By setting up the skeleton libraries,it could lay the foundation for intellectualized design animation performance.     

Strategies for the visualization of multiple 2D vector fields

Strategies for effectively visualizing colocated 2D vector fields enable understanding of key physical structures of one vector field within the context of a related vector field. This article describes the range of effects possible by combining several existing flow visualization techniques for analyzing multiple vector fields. Our present efforts focus primarily on the investigation of methods for effectively visualizing multiple fields defined over a 2D domain; the problem of effectively visualizing multiple fields defined over a 3D domain is even more challenging, and an important area for future work.     

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。     

Computer generated display of 3D vector fields

A new method for displaying 3D vector fields has been devised. An arrow of fixed proportions is used to display the magnitude and direction of the field at each point it is known. The arrow head has thickness and the whole arrow is scaled in proportion to the magnitude of the field so that the orientation perpendicular to the plane of the paper or display screen is indicated by the body of the head and foreshortening of the image. Such an arrow is drawn using a computer program in the spacially correct position where the vector field is specified by three perpendicular components, having first scaled the arrow to the largest vector amplitude in the field. As an example, the method is used to display analytic values of the electric and magnetic fields inside a rectangular waveguide. It will have application in branches of engineering and science where calculations give numerical values of vector fields.     

Detecting singular patterns in 2D vector fields using weighted Laurent polynomial

In this paper, we propose a method for detecting patterns of interest in vector fields. Our method detects patterns in a scale- and rotation-invariant manner. It works by approximating the vector-field data locally using a Laurent polynomial weighted by radial basis functions. The proposed representation is able to model both analytic and non-analytic flow fields. Invariance to scale and rotation is achieved by combining the linearity properties of the model coefficients and a scale-space parameter of the radial basis functions. Promising detection results are obtained on a variety of fluid-flow sequences.     

Computation of localized flow for steady and unsteady vector fields and its applications

We present, extend, and apply a method to extract the contribution of a sub-region of a data set to the global flow. To isolate this contribution, we decompose the flow in the subregion into a potential flow that is induced by the original flow on the boundary and a localized flow. The localized flow is obtained by subtracting the potential flow from the original flow. Since the potential flow is free of both divergence and rotation, the localized flow retains the original features and captures the region-specific flow that contains the local contribution of the considered subdomain to the global flow. In the remainder of the paper, we describe an implementation on unstructured grids in both two and three dimensions for steady and unsteady flow fields. We discuss the application of some widely used feature extraction methods on the localized flow and describe applications like reverse-flow detection using the potential flow. Finally, we show that our algorithm is robust and scalable by applying it to various flow data sets and giving performance figures.     

基于表演的2维角色动画技术研究

鉴于基于表演的动画技术非常直观自然,因此特别适合新手以及非专业人员使用,已在近些年受到了重要关注。但是已有的基于表演的动画系统,或是需要特殊的交互设备,或是只适合于低自由度的物体的动画,比如刚体动画。针对这一问题,提出了一种新的基于表演的动画技术,并根据该技术开发了一个2维角色动画系统。它可使用笔作为道具,实时地把笔的运动映射到动画角色上,而角色的运动过程被录制下来即生成动画。评估结果表明,该系统降低了动画制作的门槛,让非专业人员也可以简单快速地创作角色动画。     

计算机二维动画中一种快速动画变形方法的研究*

提出了一种针对于同构三角网格图形的快速插值方法。在三角网格中,每个三角形均用三角形的质心和三个顶点连线表示的向量来代替这个三角形,在插值每个三角形时均对这三个向量进行插值;然后将所有插值产生的三角形按照预先定义好的规则组合成中间的插值图形。该算法简单、计算速度快,能够达到实时的要求。实验结果表明,该算法能够得到令人满意的变形效果,可以避免中间图形的扭曲和变形,适用于计算机动画、几何造型、CAD等领域。     

Topology preserving top-down compression of 2D vector fields using bintree and triangular quadtrees

We present a hierarchical top-down refinement algorithm for compressing 2D vector fields that preserves topology. Our approach is to reconstruct the data set using adaptive refinement that considers topology. The algorithms start with little data and subdivide regions that are most likely to reconstruct the original topology of the given data set. We use two different refinement techniques. The first technique uses bintree subdivision and linear interpolation. The second algorithm is driven by triangular quadtree subdivision with Coons patch quadratic interpolation. We employ local error metrics to measure the quality of compression and as a global metric we compute Earth Mover's Distance (EMD) to measure the deviation from the original topology. Experiments with both analytic and simulated data sets are presented. Results indicate that one can obtain significant compression with low errors without losing topological information. Advantages and disadvantages of different topology preserving compression algorithms are also discussed in the paper.     

Bit map transformations in computerized 2D animation

This paper introduces problems that professional animators have to solve before the computer can be used to assist them in the production of cartoons. Many animation effects rely on simple transformations such as zoom, pan and rotation. In scan-and-paint systems, most drawings that are to be animated are scanned in and manipulated as bit maps. However, when transformations apply to bit maps, the use of simple transformation matrices does not work and more sophisticated computations are required to achieve smoothness in the animation and prevent object distortion. The paper presents the details of the computations that smooth rotation requires. It does not show, however, how such computationally intensive transformations can be optimized so that production time can be minimized.     

Feature- and region-based auto painting for 2D animation

This paper presents a novel approach to automating the entire coloring process in traditional cel animation production. A feature-based region-matching algorithm is proposed. It first matches a set of master frames to construct correspondences between regions in the master frames and extract a stable topology. The first frame of each scene is then colored based on the set of master frames. With the painted first frame and established stable topology, each region in subsequent frames is matched with regions in the previous frames and colored. Compared with other algorithms, our approach is able to handle bigger changes between frames and automatically color the first frame of each sequence.     

Topological methods for 2D time-dependent vector fields based on stream lines and path lines

This paper describes approaches to topologically segmenting 2D time-dependent vector fields. For this class of vector fields, two important classes of lines exist: stream lines and path lines. Because of this, two segmentations are possible: either concerning the behavior of stream lines or of path lines. While topological features based on stream lines are well established, we introduce path line oriented topology as a new visualization approach in this paper. As a contribution to stream line oriented topology, we introduce new methods to detect global bifurcations like saddle connections and cyclic fold bifurcations as well as a method of tracking all isolated closed stream lines. To get the path line oriented topology, we segment the vector field into areas of attracting, repelling, and saddle-like behavior of the path lines. We compare both kinds of topologies and apply them to a number of test data sets.     

Visualization techniques for 3D vector fields: an application to electrostatic fields of molecules

In chemistry, computer graphics is now well established as a tool to interpret simulation results, since molecules are complicated in their structures and mutual interactions. As a probe to study such molecular interactions, electrostatic fields are considered to be useful. However, since they are given as 3D vector fields having cusps in the fields, conventional drawing techniques are not applicable. In this article, two new approaches are presented to visualize the electrostatic fields of molecules. One is an extension of topological skeletons, by which interactions between atoms having opposite charges are expressed, which is not shown with the conventional methods. The other is to define new functions called selective functions to select regions of interest only from the geometrical features of the fields. Furthermore, from the definition of the new functions, mathematical relations between the topological skeletons and selective functions are discussed. An example is presented in applications to chemical reactions to show how the scheme is used. Copyright © 2001 John Wiley & Sons, Ltd.     

平面动画版本控制系统的设计研究

针对平面动画工程设计了一套能够高效、科学地管理平面动画工程过程和过程文件的自动化管理系统.明确了系统的主要目标和主要功能,对系统的“部门与人员管理”、“项目管理”和“文件管理”三大功能模块进行分析设计,给出了每一功能模块的数据结构和数据操作设计方案,从而构建了一套比较通用的平面动画版本控制系统.     

Feature matching and affine transformation for 2D cell animation

This paper presents an application for feature matching and affine transformation in computer graphics. The study case considered is 2D cell animation, which is still a labor-intensive process in current cartoon film production. One key problem in automating 2D cell animation in inbetween frame generation. The objective of our work is to investigate how to automatically generate inbetweening from pairs of hand-drawn 2D key frames. Our technique first establishes the correspondence of feature points and then estimates the affine transformation between each pair of 2D key frames. The inbetween frames are then automatically generated by interpolation.     

Finding and classifying critical points of 2D vector fields: a cell-oriented approach using group theory

We present a novel approach to finding critical points in cell-wise barycentrically or bilinearly interpolated vector fields on surfaces. The Poincaré index of the critical points is determined by investigating the qualitative behavior of 0-level sets of the interpolants of the vector field components in parameter space using precomputed combinatorial results, thus avoiding the computation of the Jacobian of the vector field at the critical points in order to determine its index. The locations of the critical points within a cell are determined analytically to achieve accurate results. This approach leads to a correct treatment of cases with two first-order critical points or one second-order critical point of bilinearly interpolated vector fields within one cell, which would be missed by examining the linearized field only. We show that for the considered interpolation schemes determining the index of a critical point can be seen as a coloring problem of cell edges. A complete classification of all possible colorings in terms of the types and number of critical points yielded by each coloring is given using computational group theory. We present an efficient algorithm that makes use of these precomputed classifications in order to find and classify critical points in a cell-by-cell fashion. Issues of numerical stability, construction of the topological skeleton, topological simplification, and the statistics of the different types of critical points are also discussed.     

二维和三维矢量场的可视化

矢量场可视化用来帮助人们直观理解二维和三维矢量场。由于目前的矢量场可视化方法只能展示二维矢量场的方向而不能展示强度,并且对于三维矢量场可视化的效果不太令人满意,因此本文提出了用线积分卷积来实现二维平面矢量场可视化,以及三维空间矢量场可视化的方法。对于线积分卷积中的流线跟踪,利用扩展的Bresenham画线算法的思想,实现了二维平面和三维空间流线的跟踪,并且通过建立一个二维表和三维表来分别存储二维平面矢量场和三维空间矢量场中每个点在流线中的上一个点和下一点的位置,来避免传统流线跟踪方法的冗余计算,提高了效率。对于二维平面矢量场,把线积分卷积的结果和矢量的强度进行加权平均,从而利用输出图像的纹理和颜色,共同来表现矢量场的方向和强度。对于三维空间矢量场,利用体线积分卷积（Volume Line Integral Convolution, Volume LIC）的方法来得到输出体纹理,并且用光线投射的体渲染方法来展示三维空间矢量场。结果显示出本文的方法能够清晰直观的看到二维平面矢量场和三维空间矢量场。     

High-quality 2D mesh generation without obtuse and small angles

In this paper, we present an efficient method to eliminate the obtuse triangles for high quality 2D mesh generation. Given an initialization (e.g., from Centroidal Voronoi Tessellation—CVT), a limited number of point insertions and removals are performed to eliminate obtuse or small angle triangles. A mesh smoothing and optimization step is then applied. These steps are repeated till a desired good quality mesh is reached. We tested our algorithm on various 2D polygonal domains and verified that our algorithm always converges after inserting a few number of new points, and generates high quality triangulation with no obtuse triangles.