改进的基于mean value重心坐标的多边形变形

对平面多边形的变形,为了避免变形过程中边界的退化和自交现象,目前主要采用将初始多边形与目标多边形分别嵌入到具有凸边界的同构三角网格中去,转化成三角网格的变形问题。但该方法在进行同构三角剖分时,增加的额外点数目较多,复杂度高,且不能实现刚性变形。论文提出一种基于多边形星形分解的同构三角网格剖分算法,使用较少的额外点,降低了算法复杂度。此外,文中选择正多边形作为三角网格的边界,并采用刚体变形技术以保持初始多边形和目标多边形尽可能刚性地变形,取得了较好的变形效果。     

优化变形能的平面多边形同构剖分

平面多边形间的同构三角剖分是平面形状渐进过渡与插值的基础,降低对应三角形的变形程度是获得高质量应用的关键.文中提出一种基于变形能优化的2个平面多边形的同构剖分算法,其中包含同构剖分生成和变形能最小化2个模块.首先根据用户指定的对应特征点对多边形进行顶点重采样,得到顶点一一对应的2个多边形;然后利用带约束的Delaunay剖分对其中的一个多边形进行三角化,得到源网格;再用重心坐标将源网格的内部顶点嵌入到另一个多边形得到同构剖分(目标网格);最后逐一检查三角形的变形能,对源网格中变形能超过阈值的三角形进行细分,用同构剖分模块生成新的目标网格.实验及数据统计分析表明,该算法可以得到较好的同构三角剖分,提升网格质量,并能很好地避免纹理细节失真.     

一种基于小波的多边形变形算法

文章提出了一种基于小波分解算法和相应的重构算法的变形方法。先用小波分解算法作用于平面多边形,得到平面多边形的轮廓和细节。然后分别对多边形的轮廓和细节进行变形,得到从初始图形变换到目标图形的中间图形的轮廓和细节。最后用重构算法重构出中间图形。该文算法可以处理任意顶点数的多边形,减少同构三角剖分的计算量,并且能够得到很好的变形结果。     

同构平面三角网格的保凸变形方法

对于具有不同凸边界的同构平面三角网格的变形,提出了一种简单、有效的方法．该方法结合了两种已有的算法．能够保证网格边界在变形过程中始终保持凸性,且任意时刻的中间网格与初末网格同构,即不产生自交现象;同时文中方法实现了两个凸多边形的保凸变形。     

保内部相似性的平面形状混合算法

为了在计算机动画中可以得到较好的图形过渡效果,提出了一保持平面多边形内部相似性的形状混合算法,从而有效地避免了中间多边形发生局部萎缩或者膨胀的现象.此方法从源和目标多边形的同构三角剖分出发,对同构三角网格每一个夹角处表示边角关系的几何量线性插值得到相对应的中间几何量,通过这些中间几何量以及它们与顶点坐标之间的关系来建立线性方程组,给定初始条件后用现成的程序库快速求解来得到中间三角网格(其边界即为中间多边形).还通过引入特征多边形来保持混合多边形的全局视觉特征.该算法计算量小、运行效率高,对形状复杂的多边形仍然可以得到满意的结果,适合于实际应用中实时的要求.     

可控制的同构平面三角网格的保凸变形

对于具有不同凸边界的同构平面三角网格的变形,提出了一种简单易行且允许人工参与的算法。算法在保证网格边界在变形过程中始终保持凸性,且中间网格与初末网格同构的基础上,提供了可调参数,从而在一定程度上实现了用户对变形过程的人为控制。     

多边形中心点向量的二次插值变形算法

多不动点约束下的网格变形算法需要用户确定不动点和操作点,针对该问题,提出多边形中心点向量的二次插值变形算法。该算法根据源、目标多边形中心点向量间旋转经过的面积与2个向量间的差值建立相似度函数,在变形过程中采用二次贝塞尔插值方法,在对应过程中利用改进的动态规划算法。实验结果表明,该算法可减少变形过程中多边形内部扭曲的程度,且计算量小、对应时间短、变形效果自然。     

基于三角基的平面多边形变形

本文讲解在VC 6.0环境下解通过对初始多边形和目标多边形进行Delaunay三角剖分,给出描述三角形网格各顶点空间位置的内在结构矩阵,然后插值相应的三角网格结构矩阵,实现多边形之间的形状变化。     

基于网格优化的隐式曲面自适应多边形化

隐式曲面多边形化是隐式曲面绘制的一种常用算法.基于网格优化的隐式曲面快速自适应多边形化算法,首先用多边形化算法生成一个粗糙的初始网格,再利用网格优化方法从网格顶点位置、规则性和网格法向三个方面对粗糙网格进行调整,最后根据网格的局部曲率用多边形细分策略细分优化后的网格.实验结果表明,该算法在网格生成速度和网格规则性上都胜于Marching Cubes的多边形化算法,恢复的隐式曲面能较好地反映形状特征.     

基于三角基的平面多边形变形

本文讲解在VC＋＋6．0环境下解通过对初始多边形和目标多边形进行Delaunay三角剖分,给出描述三角形网格各顶点空间位置的内在结构矩阵,然后插值相应的三角网格结构矩阵,实现多边形之间的形状变化。     

CR-Morph: Controllable Rigid Morphing for 2D Animation

This paper presents a rigidity-preserving morphing technique that blends a pair of 2D shapes in a controllable manner. The morphing is controllable in two aspects:1) motion dynamics in the interpolation sequences can be effectively enhanced through an intuitive skeleton control and 2) not only the boundaries but also the interior features of the source and target shapes are precisely aligned during the morphing. We introduce a new compatible triangulation algorithm to decompose the source and target shapes into isomorphic triangles. Moreover, a robust and motion-controllable rigiditypreserving transformation scheme is proposed to blend the compatible triangulations, ultimately leading to a morphing sequence which is appearance-preserving and with the desired motion dynamics. Our approach constitutes a powerful and easy-to-use morphing tool for two-dimensional animation. We demonstrate its versatility, effectiveness and visual accuracy through a variety of examples and comparisons to prior work.     

圆弧路径法，一种新的多边形变形方法

二维形状变形技术在二维角色动画、模式匹配、几何造型、虚拟现实、工业模拟、科学计算可视化等领域有着重要的应用。本文提出了一种顶点路径圆弧法的二维形状变形新方法。该算法通过控制关键帧多边形顶点按照一条特殊的圆弧曲线路径进行运动，实现二维形状变形。通过许多实例的测试表明，该算法效果良好：不仅可以保持首末关键帧形状的共同特征，而且中间插值形状变化自然平滑。同时，我们的方法易于用户交互控制；容易推广到高维情形；计算量较小、能达到系统实时的要求。     

Homotopic Morphing of Planar Curves

This paper presents an algorithm for morphing between closed, planar piecewise‐C¹ curves. The morph is guaranteed to be a regular homotopy, meaning that pinching will not occur in the intermediate curves. The algorithm is based on a novel convex characterization of the space of regular closed curves and a suitable symmetric length‐deviation energy. The intermediate curves constructed by the morphing algorithm are guaranteed to be regular due to the convexity and feasibility of the problem. We show that our method compares favorably with standard curve morphing techniques, and that these methods sometimes fail to produce a regular homotopy, and as a result produce an undesirable morph. We explore several applications and extensions of our approach, including morphing networks of curves with simple connectivity, morphing of curves with different turning numbers with minimal pinching, convex combination of several curves, and homotopic morphing of b‐spline curves via their control polygon.     

An intuitive polygon morphing

We present a new algorithm for morphing simple polygons that is inspired by growing forms in nature. While previous algorithms require user-assisted definition of complicated correspondences between the morphing objects, our algorithm defines the correspondence by overlapping the input polygons. Once the morphing of one object into another is defined, very little or no user interaction is necessary to achieve intuitive results. Our algorithm is suitable namely for growth-like morphing. We present the basic algorithm and its three variations. One of them is suitable mainly for convex polygons, the other two are for more complex polygons, such as curved or spiral polygonal forms.     

Light field morphing using 2D features

We present a 2D feature-based technique for morphing 3D objects represented by light fields. Existing light field morphing methods require the user to specify corresponding 3D feature elements to guide morph computation. Since slight errors in 3D specification can lead to significant morphing artifacts, we propose a scheme based on 2D feature elements that is less sensitive to imprecise marking of features. First, 2D features are specified by the user in a number of key views in the source and target light fields. Then the two light fields are warped view by view as guided by the corresponding 2D features. Finally, the two warped light fields are blended together to yield the desired light field morph. Two key issues in light field morphing are feature specification and warping of light field rays. For feature specification, we introduce a user interface for delineating 2D features in key views of a light field, which are automatically interpolated to other views. For ray warping, we describe a 2D technique that accounts for visibility changes and present a comparison to the ideal morphing of light fields. Light field morphing based on 2D features makes it simple to incorporate previous image morphing techniques such as nonuniform blending, as well as to morph between an image and a light field.     

Polygonal Shape Blending with Topological Evolutions

This paper presents a new general approach to blend 2D shapes with different topologies. All possible topological evolutions are classified into three types by attaching three different topological cells. This formalism is resulted from Morse theory on the behavior of the 3D surface around a non-degenerate critical point. Also we incorporate degenerate topological evolutions into our framework which produce more attractive morphing effects. The user controls the morph by specifying the types of topological evolutions as well as the feature correspondences between the source and target shapes. Some techniques are also provided to control the vertex path during the morphing process. The amount of user input required to produce a morph is directly proportional to the amount of control the user wishes to impose on the process. The user may allow the system to automatically generate the morph as well. Our approaches are totally geometric based and are easy and fast enough in fully interactive time. Many experimental results show the applicability and flexibility of our approaches.