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．     

利用Maya创建局部变形特效

亮点推荐：造型动画（Blend Shape）主要用于角色动画的画部控制及一些变形特效中。被变形物体与目标物体之间通常来说都是一次性转化的，但在近两年的好莱坞特效电影，比如「X-Men」中，我们看到了一种新式的、激动人心的变形效果，也就是一个人从头到脚逐渐变为另外一个人的过程。通过Myay的内置工具来完成类似的局部变形特效，令你更进一步的了解到Maya的造型动画（Blend Shape）工具。[编者按]     

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。     

基于骨架的隐曲面造型技术

为实现光滑物体的参数化特征造型，对巳有的基于骨架的隐曲面造型技术做了两项改进：（1）提出一个不同于传统的欧几里得距离定义的点到一般凸集骨架距离定义，使得基于点到骨架距离定义的一般凸集骨架所张成的曲面保留了点骨架所张成曲面-球面的所有特性，特别是曲面的高度光滑性和曲面的骨架表示的高度抽象性；（2）提出一种骨架生成场的融合方法，即累乘各个骨架生成场，与传统的融合方法相比，这种融合方法具有更好的融合特性。     

有限元方法在变形曲线曲面造型中的应用

变形同线曲面造型方法是将ＣＡＧＤ中参数化几何描述方法与某些力学原理相结合，自动确定曲经曹面的各种控制参数，使满足给定的几何约束条件，克服忆部修改和整体光顺的矛盾，可用于构造具有复杂形状的物体，在曲线曲面插值，光顺和光滑拼接，以及Ｎ边域构造方面有优越性基于能量函数的变形模型是由能量函数，几何约束和外部载葆定义的变分问题，应用有限元技术求解可变形曲线曲面，本文对应用有限元方法时的一些关键技术，如有限元     

基于支持向量机与细节层次的三维地形识别与检索

提出对相似3D物体识别与检索的算法．该算法首先使用细节层次模型对3D物体进行三角面片数量的约减，然后提取3D物体的特征．由于所提取的特征维数很大，因此独立成分分析被用来进行3D特征约减．基于约减后的特征，使用支持向量机进行识别与检索．将该算法用于3D丘陵与山地的地形识别中，取得了良好效果。     

可变形物体间的精确碰撞检测方法研究

针对可变形物体,提出了一种基于粒子的精确碰撞检测算法。首先用LBG矢量量化技术将物体的表面划分成几个小区域,然后在每个区域中分别选择一个点作为检测粒子。当一个物体接近另一个物体时,找出两物体上靠得最近的粒子对。为了得到精确的碰撞位置坐标,进一步计算靠得最近的顶点的相关三角面片之间的最短距离。若此距离小于某个给定的阈值,则可认为两物体在相关三角面片上的最近点处发生了碰撞。仿真实验验证了该算法能有效处理虚拟力交互仿真中的可变形物体的碰撞检测。     

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。     

刚性关节链模型在保弧长曲线变形中的应用

采用刚性关节链模型解决了保弧长的曲线变形问题．基于逆向运动学，进一步解决了中间关节点目标约束的问题，避免了单纯的逆向运动学重构关节链的繁复工作．定义一个关节角限制意义上的势函数作为目标函数，用求解约束优化问题的方法把动力学引入到逆向运动学方法中，体现了变形物体的物理属性，因而可以实现较逼真的动画效果．该方法适用于计算机角色动画、布料仿真、机器人任务规划等应用领域。     

以复形为基础的非流型造型与基于物理的造型相结合的物 …

提出了一个新的表示物体的框架，通过非流形造型与基于物理的造型相结合，从拓扑结构和几何信息两个方面扩大了模型的表示范围，以代数拓扑中的复形为基础的非流形造型的作用是生成物体的拓扑框架，既可以表示ＣＡＤ的物体，更适合表示具有复杂拓扑的自然物体，基于物理的造型的作用是在拓扑框架上生成最终的几可信息，二者的给提供了一种新的几何造型手段。     

Deformation by examples: a density flow approach

In this article, a shape transformation technique is introduced for deforming objects based on a given deformation example. The example consists of two reference shapes representing two different states of an object. The reference shapes are assumed to morph from one state to the other. The evolution between the two reference shapes determines the shape transformation function. Any given objects can then be deformed by the same transformation. A continuous 4D Radial Basis Function is used to construct a density flow field (an extension of the optical flow in computer vision) representing the shape transformation of the example in 3‐space. Objects embedded in the density flow field are deformed by moving vertices of the objects along the density flow vectors. Additional parameters are introduced to control the process of the deformation. This provides explicit control on the shape of the object obtained in the deformation process. Copyright © 2007 John Wiley & Sons, Ltd.     

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.     

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.     

Free-form deformation of constructive shell models

Free-form deformation (FFD) is known to be a powerful technique for deforming an object independent of its representation. A point on a solid is deformed by specifying the point relative to a coordinate system defined with a lattice of control points. Adjusting the control points of the lattice deforms the object. The deformed object can be visualized by sampling points on the object surfaces, or by approximating the object with a polyhedral model. However, a conversion of the polyhedral model to the underlining solid representation is required if further solid operations (e.g. Boolean operation) is to be applied. This paper presents a technique for applying FFD on constructive shell models (CSR). A CSR object is constructed by subtracting a set of depression (negative) trunctets from the union of a set of outer (positive) trunctets and a polyhedron core. FFD is applied to the polyhedron core and the trunctets of the model. A trunctet is deformed by applying FFD to a set of selected surface points on the trunctet. The deformed trunctet is obtained by interpolating a surface through the deformed surface points. In the deformation of a trunctet, an outer trunctet may become a depression trunctet (or vice versa). By using the concept of mating trunctet, and an approach for classifying the shape of a trunctet, shape changes of a trunctet in a deformation can be determined. Deformation of a trunctet may also result in an invalid trunctet that bulges out of its enclosing tetrahedron. Besides, the degree of the algebraic surface used determines the size of a trunctet relative to the distance between adjacent lattice control points. A subdivision of a trunctet may have to be performed to maintain the validity of a deformation.     

基于形变模型由立体序列图象恢复物体的3D形状

结合立体视觉和形变模型提出了一种新的物体3D形状的恢复方法。采用立体视觉方法导出物体表面的3D坐标;利用光流模型估计物体的3D运动,根据此运动移动形变模型,使其对准物体的表面块;由形变模型将由各幅图象得到的离散的3D点融为一起,得到物体的表面形状。实验结果表明该方法能用于形状复杂的物体恢复。     

Layered deformation of solid model using conformal mapping

In this paper, we present a solid model deformation method based on layered conformal mapping. For a solid model represented by base patch and height field, the shape of the model can be deformed by interactive means, such as changing the base patch by conformal mappings and adjusting the height field by a pre-defined function. In our method, the deformation is predictable and the transformation function of the deformation can be expressed analytically by Schwarz–Christoffel formula. To perform a deformation of a cylinder to a desired solid of rotation hierarchically, a generalized Schwarz–Christoffel formula is also introduced. Numerical examples show that the proposed method is convenient and efficient to deform solid models, especially to solids with genus zero.     

Elastic Tubes: Modeling Elastic Deformation of Hollow Tubes

The Cosserat theory of elastic rods has been used in a wide range of application domains to model and simulate the elastic deformation of thin rods. It is physically accurate and its implementations are efficient for interactive simulation. However, one requirement of using Cosserat rod theory is that the tubular object must have rigid cross‐sections that are small compared to its length. This requirement make it difficult for the approach to model elastic deformation of rods with large, non‐rigid cross‐sections that can change shape during rod deformation, in particular, hollow tubes. Our approach achieves this task using a hybrid model that binds a mesh elastically to a reference Cosserat rod. The mesh represents the surface of the hollow tube while the reference rod models bending, twisting, shearing and stretching of the tube. The cross‐sections of the tube may take on any arbitrary shape. The binding is established by a mapping between mesh vertices and the rod's directors. Deformation of the elastic tube is accomplished in two phases. First, the reference rod is deformed according to Cosserat theory. Next, the mesh is deformed using Laplacian deformation according to its mapping to the rod and its surface elastic energy. This hybrid approach allows the tube to deform in a physically correct manner in relation to the bending, twisting, shearing, and stretching of the reference rod. It also allows the surface to deform realistically and efficiently according to surface elastic energy and the shape of the reference rod. In this way, the deformation of elastic hollow tubes with large, non‐rigid cross‐sections can be simulated accurately and efficiently.     

一种应用参数曲面的动态自由变形方法

本文提出了一种动态自由变形方法，被变形物体首先附在两张参数曲面上，当参数曲面的形状发生变化时，物体会随之变形。这两张参数曲面分别被称为形状曲面和高度曲面，其中形状曲面用于控制变形物体的形状，高度曲面用于控制物体沿着形状曲面法向的高度。     

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.