基于形态学的任意三维物体变形的算法及实现

提出三维物体变形的形态学方法，给出了此方法的理论证明，用一个统一的数学模型来描述变形内插的关系，较好地解决任意形状物体的变形。实验表明这种方法是一种有效的变形方法，克服了现有方法的缺点，实现简单，并可推广至一般的造型系统中，为计算机图形学开辟了一种新途径。     

基于四面体坐标系的三维变形方法及应用

为了直观、精确地控制模型的形变,提出一种基于自定义四面体坐标系的三维变形计算方法.首先从几何上给出四面体坐标系的定义,阐述并证明了其关于几何变换的一些性质,使得拓扑变形易于实现,并可应用在三维变形技术中;然后描述了基于四面体坐标系的2种三维变形算法:嵌入式变形与基于特征的精确变形算法.通过多个变形实例结果证明,该方法能够有效地实现物体的变形以及物体间的渐变.     

一种基于调和函数的自由变形算法

为解决传统网格自由变形(FFD)结果往往不自然的问题,提出一种基于调和函数的变形算法.基于三维网格模型的拓扑信息,采用离散化的Laplace-Beltrami算子计算物体表面的调和函数,并以之引导物体进行自然形变.实验结果表明,借助于调和函数具有的光滑性和稳定性特点,该算法能够通过简洁的操作实现三维模型的自然变形,不仅...     

三维“变形”动画制作技术

一、引言变形是一门基于节点的造型技术，在应用程序内部是通过物体节点序列的普换矩阵来实现的。在3DS中实现变形的必要条件（也是唯一的条件）是变形源物体与目标物体的节点数必须相同。但要使变形的中间过程不致产主“混乱”，还应当使得源物体与目标物体的节点排序相同。用3DS实现变形一般可通过四种途径：（1）在ZDShaper中制作舅有相同8南数僵形状不同的平面图形，在3DLofter中用相同湖路径（Path）放样既不同形状的源物体和目标物体；（2）联合＊D＊bacer的平面图形和3Dno什er中的Defo厂mation工冥制作变形物体；（3）在3DEd比…     

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。     

嵌入参数空间的曲面控制自由变形方法

提出了一种新的通过控制参数曲面来实现物体的自由变形的方法，物体通过映射函数被嵌入到曲面的参数空间从而实现变形，同时映射函数的引入增加了变形的控制手段。实验表明该方法具有易于交互和控制的优点，适用于几何造型和计算机动画领域。     

支持异种材料体造型的特征布尔运算

针对传统CAD不能提供材料等非几何信息,且无法实现异种材料物体间的布尔运算,提出了一种可应用于构造异种材料物体的特征布尔运算,包含了由材料决定的布尔差和交运算及新的布尔复形并运算,由特征合并和特征抽取两步完成;并给出了该运算的几何实现、实现算法及实例．     

采用变形模型的图像序列可视外壳计算方法

针对基于图像序列变形模型三维重建中至关重要的初始模型计算问题,提出一种基于图像序列计算可视外壳的方法.该方法基于Snake活动轮廓变形模型,将真实物体可视外壳的计算问题转化为初始曲面通过内外力作用驱动收敛于目标物体的问题.以真实物体图像序列中提取的物体轮廓为输入,根据轮廓信息和光滑度信息计算内力及轮廓力大小,驱动球体初始曲面变形收敛于可视外壳;在变形过程中加入删除短边、分裂长边、对角线翻转等网格优化操作,以避免发生网格错乱.实验结果表明,文中方法有效地克服了传统的基于体元素细分产生网格算法网格质量不高的缺点,且参数可调,易于实现,占用内存少,生成的曲面更加光滑,细节恢复效果理想.     

3D Studio中的变形技术

变形是指将一种物体转变为另一种物体的一种技术实现手段,它广泛地用于广告传媒中,是一种很具创造性的表现手法。 设置一个变形的步骤,必须先创建一个初始物体,及相应要变形的目标物体。初始物体是需要真正渲染的,目标物体通常隐藏起来,仅仅作为初始物体变形行为的结果模板。作为变形实现的必须条件,就是要求源物体与目标物体应有相同数量的节点,并且要求第一节点匹配。在Shaper中,命令Modify/Segment/Refine便可以使节点数达到一致,     

二维物体变形技术现状与发展

二维物体变形技术在计算机动画、工业造型设计、科学计算可视化、电影特技等领域有着广泛的应用,具有十分重要的意义。近年来,有许多研究者提出了一些效果不错的算法,文中对这些算法进行了分析,对二维物体变形技术做了较全面的综述,探讨了现有二维物体变形技术中需要改进的关键问题,并给出了变形技术在未来的发展方向。     

多边形物体的精确B-样条自由变形*

在计算机动画与几何造型中,自由变形是一种重要的几何形状修改方法.该文从移位算子和函数复合的观点探讨一种方法,即当被变形物体用三角片表示、变形工具为B-样条参数体时,变形后的物体可以精确地表示为一组三角Bzier曲面片,其次数为B-样条参数体3个方向的次数之和.此方法的核心在于自由变形是作用在三角片上,而不是顶点上,所以解决了多边形物体B-样条自由变形的点采样问题.     

基于曲线和曲面控制的多边形物体变形反走样

基于参数曲线和曲面控制的空间变形是重要的几何外形编辑和柔性物体动画实现手段．当这两类变形方法的对象是多边形物体时,如何对变形物体进行重采样以得到高质量结果,是计算机动画和几何造型领域中的一个重要问题．该文针对B-样条曲线和曲面控制的空间变形方法,提出了面向多边形物体的空间变形反走样方法．在该方法中,利用等距技术将B-样条曲线或曲面所张成的变形空间近似表示为张量积B-样条参数体,结合作者提出的多边形物体精确B-样条自由变形方法,实现了参数曲线和曲面控制的多边形物体变形反走样．     

Geometric deformations based on 3D volume morphing

This paper presents a new geometric deformation method based on 3D volume morphing by using a new cocept called directinal polar coordinate.The user specifies the source control object and the destination control object which act as the embedded spaces.The source and the destination control objects deterine a 3D volume morphing which maps the space enclosed in the source control object to that of the destination cotrol object.By embedding the object to be deformed into the source control boject,the 3D volume morphing determines the deformed object automatically without the tiring moving of control points.Experiments show that this deformation model is efficient and intuitive ,and it can achieve some deformation effects which are difficult to achieve for traditional methods.     

Shape deformation with tunable stiffness

The paper presents a 2D or 3D shape deformation method which incorporates global and local stiffness controls. First, a geometric object is embedded into a regular lattice and then the deformation is conducted on the lattice; thus, the method is independent of the underlying object representation. The lattice cells are organized as overlapping local rigid regions, and the region width could be regarded as a means of the global lattice stiffness control. For each region, there is a local stiffness coefficient to control the lattice deformation locally. During the deformation a nonlinear objective function is optimized to achieve the natural lattice deformation with the prescribed global and local stiffnesses. Then, the lattice deformation is passed to the embedded object through bilinear or trilinear interpolation. In this way we can deform the object in a more physically plausible way with tunable stiffness. Experimental results show that the method is intuitive and flexible.     

Parametric Estimation of Affine Transformations: An Exact Linear Solution

We consider the problem of estimating the geometric deformation of an object, with respect to some reference observation on it. Existing solutions, set in the standard coordinate system imposed by the measurement system, lead to high-dimensional, non-convex optimization problems. We propose a novel framework that employs a set of non-linear functionals to replace this originally high dimensional problem by an equivalent problem that is linear in the unknown transformation parameters. The proposed solution includes the case where the deformation relating the observed signature of the object and the reference template is composed both of the geometric deformation due to the affine transformation of the coordinate system and a constant amplitude gain. The proposed solution is unique and exact and is applicable to any affine transformation regardless of its magnitude.     

Physically-based deformations: copy and paste

In contrast with purely geometric approaches, physically-based deformation techniques usually afford greater realism in the animation of soft objects and characters, due to the consideration of the inherent physical properties of the materials. In this paper, we present a novel physically-based technique allowing versatile deformation effects to be created using simple copy and paste operations. The copy process involves the extraction of the deformation behaviour from a source object, and the paste operation applies it to a different object (target), resulting in the target object being deformed in a physically plausible manner. Our technique defines the deformation of an object as a linear combination of a set of carefully chosen fundamental solutions from classic mechanics, which separates the deformation data from the geometry. The deformation of the source object can be computed using any existing physically-based technique. To copy the deformation from an object is to formulate the weighting coefficients to the fundamental solutions. To paste the deformation to another object is to apply our deformation model to the target object with the derived weighting coefficients. Repeated copy and paste operations allow various local and global deformation effects to be created. In addition to visual realism, the main advantages of our technique compared with other existing physically-based methods are its capability to reuse the deformation data, computational efficiency and friendliness to animators.     

改进的多边形物体精确自由变形

针对已有精确变形方法中的物体剖分和共面判断，提出了一种改进的精确自由变形方法，实验结果表明，新方法具有鲁棒性和快速交互的特点，并且变形结果的表示形式与工业标准STEP一致，易于集成入已有的计算机动画和几何造型系统。     

基于李代数的变形目标跟踪

动态几何变形是图像跟踪技术面临的突出难题之一. 本文提出基于李代数的变形目标跟踪方法, 用Gabor特征表征目标, 以仿射李群建立目标几何变形, 利用李代数和李群之间的指数映射将参数的最优化求解从欧氏空间转至光滑流形, 实现了对变形目标的稳定跟踪.从物理层面分析了目标跟踪过程中的参数几何变换的实质, 从理论上对在光滑流形上进行迭代求解的优点进行了详细分析, 并对其收敛性做出了证明.图像序列跟踪测试的对比实验表明, 本文方法较现有基于欧氏空间的算法在收敛速度、跟踪稳定性和精确性方面有显著提高.     

An autowave based methodology for deformable object simulation

This paper presents a new methodology for deformable object simulation by drawing an analogy between autowaves and elastic deformation. The potential energy stored in an elastic body as a result of a deformation caused by an external force is propagated among mass points by non-linear autowaves. The novelty of the methodology is that autowave techniques are established to describe the potential energy distribution of a deformation for extrapolating internal elastic forces, and non-linear material properties are modelled with non-linear autowaves other than geometric non-linearity. A haptic virtual reality system has been developed for deformation simulation with force feedback. The proposed methodology not only deals with large-range deformations, but also accommodates isotropic, anisotropic and inhomogeneous materials by simply modifying diffusion coefficients.     

基于区域面积比的几何不变量构造算法*

几何不变量是物体几何结构信息的抽象与概括,在识别中可解决由目标移动产生的旋转或变形等问题。针对现有的算法在提取几何不变量特征时,易造成误差增大和效率不高的问题,提出了一个基于区域面积比的几何不变量构造算法。该算法利用质心和伪质心构成的直线,对灰度图像的面积区域应用划分策略,构建几何不变量的矢量表示形式。在哥伦比亚大学的fish及coil-100数据集上的实验表明,算法得到的不变量特征满足仿射不变性,在物体图像受到一定范围内干扰(被擦除、涂抹及遮挡)下,提取出的不变量特征具有良好的区分辨别能力。