计算机二维动画的算法实现

本文基于关键帧控制的动画原理，提出了一种基于多形描述目标，并通过多边形对主顶点插补中间帧的计算机二维动画算法。     

一种3维动画中间帧非线性插值算法

关键帧动画是3维动画制作的常用模式，中间帧插值又是关键帧动画中最为繁琐的环节。提出了一种针对无骨架3维网格模型的非线性插值算法，用于对网格模型的关键帧姿态进行插补，自动生成中间帧动画序列。该算法首先计算动画角色的网格模型各三角片在相邻关键帧中的仿射变换，并据此生成变形梯度向量，作为3维网格模型的形变信息，这种表示形式体现了变形过程中网格顶点之间的局部互相关关系。随后将各仿射变换分解为旋转成分与拉伸缩放成分，对拉伸缩放成分进行线性插值，而对旋转成分采用四元数插值算法进行非线性插值，合成中间帧姿态的变形梯度向量，并据此计算出中间帧网格模型。当相邻关键帧姿态存在较大差异时，该算法也能快速生成平稳而生动的中间帧动画，可有效减少关键帧的数量，提高动画制作效率。     

单位化建模衰减变形新方法

针对软组织自由变形中调整控制顶点难以准确控制物体变形的问题,提出了一种基于单位化建模的衰减变形算法。该算法利用三角网格进行单位化建模,将变形软组织碰撞点的三维世界坐标转换为三角网格二维顶点坐标,通过确定以碰撞点所在顶点为中心的自适应变形区域,控制区域内顶点偏移量发生衰减变化,从而直接作用于物体顶点进行形变,同时通过设计合适的衰减函数使偏移量呈抛物线衰减。通过实验证明该算法所建模型具有通用性,变形在局部区域内可取得准确的抛物线衰减效果。     

基于边折叠和质点-弹簧模型的网格简化优化算法

通过边折叠实现网格曲面简化，提出了保持曲面特征的边折叠基本规则，引入边折叠顺序控制因子λ，给出了折叠点坐标获取方法，简化过程中网格边长度趋于均匀．在曲面简化基础上，利用质点-弹簧模型优化网格形状．将网格顶点邻域参数化到二维域上，在质点-弹簧模型中引入约束弹簧，约束调整网格顶点，并逆映射到三维原始曲面上，局部优化网格顶点的相邻网格；调整曲面上所有网格顶点，在全局上优化网格形状．在曲面简化优化过程中，建立原始模型曲面和简化优化后曲面之间的双向映射关系；曲面的网格顶点始终在原始模型表面上滑动，并以双向Hausdorff距离衡量、控制曲面间的形状误差．应用实例表明：文中算法稳定、高效，适合于任意复杂的二维流形网格．     

求图中顶点之间所有最短路径的一种实用算法

提出了求一个顶点到另一个顶点的所有最短路径的一个算法，此算法中设计了一些独特的数据结构。在算法运行的整个过程中，求一个有效顶点（后面定义）到终点的所有最短路径的过程（入栈、出栈等操作）实际只进行一遍，用C语言编制的相应程序验证了这个算法的可靠性和实用性。     

双域单向水平倾角最小化圈绕凸壳新算法

本文依据同构化凸壳构造基本定理，提出了效率更高的双域单向水平倾角最小化圈绕二维点集凸壳新算法，实现了对卷包裹凸壳算法、单域单向水平倾角最小化圈绕凸壳算法的改进与创新。本新算法的同构化特点是：1）“初始顶点与双域生成”处理：找出给定二维点集S的最低点和最高点，即Y轴坐标值最小点（若有多个最小点，则只取最左的最小点）和Y轴坐标值最大点（若有多个最大点，则只取最右的最大点），作为凸壳逆时针圈绕的初始顶点；并以这两个初始顶点为端点的线段，把原二维点集划分为两个独立的子点集S右、S左。2）进行单向“圈绕寻找下一新顶点”：A）在S右内，过逆向次新顶点作X轴正向射线，并找出当前子点集内对该逆向次新顶点正向射线（为始边的）倾角最小的点，此最小点即为S右逆向最新顶点；B）在S左内，过次新顶点作X轴负向射线，并找出当前子点集内对该逆向次新顶点负向射线（为终边的）倾角最小的点，此最小点即为S左逆向最新顶点。3）删除对已得各项点所构成的子凸壳各内点。4）仅当所剩当前点集非空时才从“2）”继续作逐边双域单向圈绕。     

网格分割的3维网格模型非盲水印算法

目的 信息技术的发展使得面向3维模型版权保护的问题越来越突出,提出一种新的基于网格分割的3维网格模型非盲水印算法。方法 首先使用基于形状直径函数的网格分割算法对3维网格模型进行有意义的网格分割,然后计算每个分块的鲁棒重心并以此为中心将模型由直角坐标系转换到球面坐标系,最后通过调制每个顶点范数的分布来嵌入水印,在水印检测阶段使用非盲检测的方法提取水印。结果 针对目前基于网格分块的水印算法的网格分割不一致以及对分割边界依赖性过强等问题,引入基于形状直径函数的网格分割算法并在重对齐、重采样过程中加入待检测模型与原始模型分块匹配过程以保证网格分割的一致性,并且选取分块的顶点范数的分布作为水印嵌入基元,使得算法能够有效地减弱对分割边界的依赖性。结论 实验结果表明,该算法可以有效抵抗平移、旋转、缩放、噪声、细分、简化、剪切等常见的攻击以及多种攻击的联合攻击。     

一种求受顶点数限制的最短路径的新算法

提出了一种基于逆邻接表求受顶点数限制的最短路径的新算法，其时间复杂度为O(m-2)^*w)(m是受限制的顶点数，w是有向图中弧的条数)，优于同类算法。采用逆邻接表作为图的存储结构，该算法很容易实现。     

基于粒子系统和形状匹配的实时无网格变形仿真

介绍了一种基于粒子系统和形状匹配的无网格变形算法。该算法将模型的每个顶点当成一个粒子,一个模型对应一个粒子系统,通过粒子系统控制物体外形。同时,每个粒子都对应一个目标位置,粒子与其目标位置之间存在弹力,能将粒子拉向目标位置,使得变形后的物体能够恢复原来的形状。目标位置可以通过粒子系统未变形时的静止状态与当前变形状态之间的形状匹配来计算。该算法简单,易于实现,且不需要复杂的数据结构。实验结果表明该算法稳定,具有实时性,可以有效地应用于三维游戏中。     

一种鲁棒的矢量地图数字水印算法

通过仔细分析MQUAD算法的缺陷，提出一种双重嵌入的鲁棒矢量地图数字水印算法．该算法按地图内所含对象特征把矢量地图分为两层，对不同的图层采用不同算法调制水印信息到各顶点；分别计算两个图层中代表水印信息的位移量，在阈值的控制下，选择有效的顶点并计算顶点坐标平均值即得到水印信息位序列．实验结果表明，文中算法对随机噪声、扭曲变形和各种剪切具有很强的鲁棒性．     

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.     

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.     

2D shape morphing via automatic feature matching and hierarchical interpolation

The paper presents a new method to interpolate a pair of 2D shapes that are represented by piecewise linear curves. The method addresses two key problems in 2D shape morphing process: feature correspondence and path interpolation. First, a robust feature metric is defined to measure the similarity of a pair of 2D shapes in terms of visual appearance, orientation and relative size. Based on the metric, an optimal problem is defined and solved to associate the features on the source shape with the corresponding ones on the target shape. Then, a two-level hierarchical approach is proposed to solve the corresponding features interpolation trajectory problem. The algorithm decomposes the input shapes into a pair of corresponding coarse polygons and several pairs of corresponding features. Then the corresponding coarse polygons are interpolated in an as-rigid-as-possible plausible way; meanwhile the corresponding features are interpolated using the intrinsic method. Thus interior distortions of the intermediate shapes could be avoided and the feature details on the input shapes could be well preserved. Experimental results show that the method can generate smooth, natural and visually pleasing 2D shape morphing effects.     

自主非玩家角色面部行为的实现

为了用自主非玩家角色（ANPC）来实现游戏里的人工智能，提出了一种“模型．视图．控制器（VC），的设计模式来实现此类ANPC，该模式将AI从游戏引擎中分离出来。用一种混合变形顶点着色（BMVS）技术实现ANPC的面部行为，该技术可以把各个行为动画，如眨眼、微笑、视位（visemes），混合形成整个面部行为动画。采用顶点着色技术，不用锁定顶点缓存和新建混合后形成的网格（mesh），因而能提高动画渲染效率。     

基于简化多边形类正切空间表示的图形渐变算法

采用多边形简化的方法提取出包含源图形主要特征点的多边形.在简化多边形的类正切空间表示下,利用图形对应边在渐变过程中所掠过面积总和最小这一特征构造相似度量函数,由动态规划算法求解实现初始和目标简化多边形之间的顶点对应,再进一步建立源图形顶点之间的整体对应,最后通过插值边和角的方法实现图形渐变.实验结果表明:该算法简单有效,对应效果自然、合理.     

Interactive 3D Morphing

A new 3D morphing algorithm for polyhedral objects with the same genus is presented in the paper. Our main contribution is an efficient and general algorithm for setting up the vertex correspondence between the polyhedra. The proposed algorithm first interactively partitions the two original polyhedra into the same number of polygonal patches, the patch correspondence is also established during partitioning. Each pair of corresponding patches is then parametrized and resampled by using the harmonic maps. A feature polyhedron is finally constructed for each original polyhedron, and the vertex correspondence between each original polyhedron and its feature polyhedron is automatically established following a cluster scheme. The shape transition between the original polyhedral models is accomplished by composing three successive transformations using their feature polyhedra as the bridges. Experimental results demonstrate that our algorithm is very robust, and can deal with very general cases (non-zero genus polyhedral cases).     

Feature-based 3D morphing based on geometrically constrained spherical parameterization

Current trends in free form editing motivate the development of a novel editing paradigm for CAD models beyond traditional CAD editing of mechanical parts. To this end, we need robust and efficient 3D mesh deformation techniques such as 3D structural morphing.In this paper, we present a feature-based approach to 3D morphing of arbitrary genus-0 polyhedral objects that is appropriate for CAD editing. The technique is based on a sphere parameterization process built on an optimization technique that uses a target function to maintain the correspondence between the initial polygons and the mapped ones, while preserving topology and connectivity through a system of geometric constraints. Finally, we introduce a fully automated feature-based technique that matches surface areas (feature regions) with similar topological characteristics between the two morphed objects and performs morphing according to this feature correspondence list. Alignment is obtained without user intervention based on pattern matching between the feature graphs of the two morphed objects.     

DMorph [image metamorphosis]

Image morphing is an artist-driven process. A creative human being looks at the images (or sequences) to be bridged and determines a way to make the changes that will be pleasing to the viewer and harmonious with the piece. To help these artists, I've developed a technique for automatically and smoothly turning one convex 3D shape into another. Like any automatic morph method, this technique should be viewed as a tool and not a self-guided process. DMorph has pros and cons. On the pro side, it is satisfyingly simple and robust and easy to program. It doesn't place any constraints on the two objects being interpolated except that they're convex. One object can be a 200-sided cone where 200 polygons all share a single vertex, and the other object a baseball, and the algorithm doesn't care. There's no feature matching, automatic or otherwise. The transformations are smooth, and the blending looks nice. On the con side, the program is limited to convex objects.     

三角形渐变动画

介绍了目前常用的三角形渐变动画方法,并根据三角形运动变化的物理原理提出了一种三角形混合方法——物理模型法,为了衡量三角形渐变动画的效果,提出了三角形相似度与法向变化率两个新参数．实验结果表明,与其他现有方法相比,本文方法生成的渐变动画效果在保形性和法向光滑性方面都比较令人满意,并已应用于实际动画制作中。     

Volume-based three-dimensional metamorphosis using sphere-guided region correspondence

surface metamorphosis extends this paradigm by interpolating between discrete volume representations of the surfaces. The insensitivity of the established techniques to the surface topology enables morphing between completely different surfaces: however it can also lead to intermediate surfaces which have different topology from the originals. We present a method which improves on this situation by ensuring that no part of each surface remains disconnected during the morph. The morph is guided by region correspondence, derived automatically from a sphere representation of each surface: this can be combined with manual correspondence to retain user control over the morph. What emerges is a fast and flexible method for morphing surfaces, as demonstrated on several examples. Published online: 19 July 2001