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。     

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．     

沿参数曲面的均匀变形方法

基于参数曲面控制的物体自由变形是一项实用的技术，在已有的方法中，待变形物体被直接主控制曲面的参数空间，由于映射的非线性，导致物体变形同扭曲现象，本提出了一种基于参数曲面控制的均匀变形方法，新方法中，变形控制曲面首先以等距或局部等怕方式展开为平面，然后经由平面的线性映射，将待为形物体嵌入控制曲面的参数空间中，从而产生符合控制曲面形状的局部均匀变形，实验结果表明，本方法所产生的结果是令人满意的。     

骨架驱动的作物叶片变形模拟

针对作物器官的变形问题,将骨架驱动物体变形的方法应用于作物器官的局部变形,提出了一种骨架驱动的叶片变形方法：生成叶片骨架模型,驱动骨架模型发生变形,并根据变形后的叶片骨架将变形操作应用到叶片曲面上,进而实现叶片曲面变形。应用该方法,分别对小麦叶片曲面进行弯曲和扭曲变形模拟。实验结果表明,基于骨架驱动的作物叶片形变方法能灵活控制叶片弯曲和扭曲程度,从而获得自然的叶片曲面变形效果。     

基于细分曲面的多分辨率空间变形

在几何造型和计算机动画中，空间变形是一种重要的几何外形编辑和柔性物体动画生成技术．提出一种基于细分曲面控制的多分辨率空间变形方法，解决了变形控制手段的复杂性和变形效率之间的矛盾．对采用多种细分规则的变形结果进行了比较和分析，得出了选择适当的细分规则和细分深度的经验性原则．在算法效率方面，通过采用空间剖分技术加速了参数化过程，并且利用细分的局部性缩短了变形的响应时间，从而达到了实时交互的目的．最后，在上述算法的基础上实现了一个完整的空间变形系统，提供了多种交互手段用以生成控制网格，并实现了具有多分辨率性质的变形控制．     

基于三幅图像的曲面造型及纹理提取

利用标准的参数曲面来表示真实的三维曲面物体，并将物体正面、侧面及背面拍摄图像的侧影轮廓线作为约束，通过最小化线性约束下的二次目标函数实现曲面造型。将曲面重新投影到物体的正面、背面及侧面图像上，利用基于重心坐标的加权纹理提取方法提取纹理图像。利用真实图像实现了逼真的曲面造型，验证了该方法的可行性和正确性。     

基于两步法的交互式纹理映射研究

两步纹理映射方法将映射过程分解为S映射与O映射两步进行.针对两步纹理映射方法研究中复杂物体表面纹理映射时出现的变形问题,采用B样条曲面代替简单的中间映射媒介,用它近似地包裹在三维物体的外表面,将纹理通过某种方式映射到曲面上实现参数化.基于两步映射方法提出了一种交互式纹理映射的算法.该算法允许用户交互选择贴图范围,通过控制B样条曲面实现对映射效果的调整.实验结果表明,该算法可显著提高纹理映射质量,纹理贴图效果良好.     

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.     

基于NURBS权因子调整的FFD直接操作

FFD（Free-Form Deformation）是计算机动画和变形中最重要的方法之一。FFD的直接操作为变形提供了更直观更方便的控制手段。该文用约束优化方法，通过调整张量积网格控制点对应的权因子，解决基于NURBS的FFD直接操作问题，给出了变形物体在单点约束下FFD直接操作的解，使变形后的物体通过给定的目标点。该方法计算简便，易于实现。文中给出的变形实例也表明，变形结果比较自然。     

三维形体的形态运算及应用

本文首先讨论了边界表示的物体的形态学运算问题，文中讨论了任意形状的物体，包括凸物体和非凸物体，引入了负形体的概念，并提出了2D和3D连续物体的Minkowski运算的统一算法。利用这一算法，提出了3D任意形体间的变形新算法，把边界表示的物体的形态学运算的概念扩展到任意曲线和任意曲面上，并且介绍了3D物空间中曲线的概念和3D硪空间双参数曲面的概念。文中任意形体的3D变形算法能很好地解决具有不同拓扑结构的3D边界表示的物体之间的变形问题。     

Approximate development of trimmed patches for surface tessellation

This paper presents a method for constructing an auxiliary planar domain of triangulation for tessellating trimmed parametric surface patches. By minimizing a mapping error function, an approximate locally isometric mapping between a given trimmed parametric surface patch and its triangulation domain is constructed. In this way the shape of triangular elements on the triangulation domain is approximately preserved when mapped into three-dimensional space. We also provide an efficient method to achieve a good initial guess for the minimization of the mapping error function. Furthermore, our proposed method guarantees a homeomorphism between a triangulation domain and parametric space/given surface patch by robustly removing the possibility of self-intersection on the developed surface net. Practical application of the proposed algorithm can include the formation of ship hulls, ducts, shoes, clothing and automobile parts as well as the surface meshing procedure.     

Turbine blade temperature transfer using the load surface method

Temperature transfer is important to MDA (multidisciplinary analysis) of turbine blades, for the separation of aerodynamics and structure analysis codes. To re-couple these codes, a load surface method is provided here to transfer temperature across the interface of arbitrarily meshed CFD (Computational Fluid Dynamics) and CSM (Computational Structural Mechanics) models. The idea of the method is to transfer temperature by a Bi-cubic B-spline surface, fitted from the CFD temperature results of interfaces in parametric space. The temperature of the CSM nodes of the interface is calculated from the load surface in the same parametric space. An important step in this transfer method is to map the CFD and CSM nodes into the same parametric space. The mapping surface method is detailed for this purpose. In the mapping method, the nodes are mapped onto a structured quad mesh, called a mapping surface, which is additionally generated on the interface surface. Then, the nodes are mapped into the parametric space, which is defined by a parameterization of the mapping surface. To evaluate the accuracy of the method, the temperature of a turbine blade is transferred experimentally. The result indicates that the method is accurate even for coarse meshes.     

基于整数维约束的分维形状映射生成方法

把整数维图形研究方法与分数维图形研究方法相结合，提出一种基于整数维规则几何形状的约束的分维形状映射生成方法，有于描述自然界和工程中出现的且具有特定基本形状趋势的随机现象和随机过程，首先，任意选取一个具有调配函数的自由形状构造一个有序参数空间，确定有序参数的取值规律和区域，把有序参数空间与自适应神经网络，随机性相结合，构造一个随机离散参数空间，并建立起有序参数与随机离散参数之间的参数对应关系，最后，通过有序与无序的参数对应关系，建立一个独立于任意规则几何形状的统一的分形映射关系，对相应整数维的任意规则参数几何形状分形映射，生成宏观形态趋势可预见和可控制的分维形状，该提出的方法适有于任意参数几何形状的分形映射，生成分形图形，且方法简明，易于实现。     

Simultaneous aligning and smoothing of surface triangulations

In this work we develop a procedure to deform a given surface triangulation to obtain its alignment with interior curves. These curves are defined by splines in a parametric space and, subsequently, mapped to the surface triangulation. We have restricted our study to orthogonal mapping, so we require the curves to be included in a patch of the surface that can be orthogonally projected onto a plane (our parametric space). For example, the curves can represent interfaces between different materials or boundary conditions, internal boundaries or feature lines. Another setting in which this procedure can be used is the adaption of a reference mesh to changing curves in the course of an evolutionary process. Specifically, we propose a new method that moves the nodes of the mesh, maintaining its topology, in order to achieve two objectives simultaneously: the piecewise approximation of the curves by edges of the surface triangulation and the optimization of the resulting mesh. We will designate this procedure as projecting/smoothing method and it is based on the smoothing technique that we have introduced for surface triangulations in previous works. The mesh quality improvement is obtained by an iterative process where each free node is moved to a new position that minimizes a certain objective function. The minimization process is done on the parametric plane attending to the surface piece-wise approximation and to an algebraic quality measure (mean ratio) of the set of triangles that are connected to the free node. So, the 3-D local projecting/smoothing problem is reduced to a 2-D optimization problem. Several applications of this method are presented.     

2D structured grid generation method producing a mesh with prescribed properties near boundary

A variational method of generating a structured mesh on a two-dimensional domain is considered. To this end, a quasiconformal mapping of the parametric domain with a given Cartesian mesh onto the underlying physical domain is used. The functions implementing the mapping are sought by solving the Dirichlet problem for the system of elliptic second-order partial differential equations. An additional control for the cell shape is executed by introducing a local mapping which induces a control metric. In some particular cases, instead of an additional local mapping, a global mapping of the parametric domain onto the intermediate domain is used, where the curvilinear mesh is produced, and next this domain is mapped onto the underlying physical domain. The control metric allows to obtain a mesh with required properties: grid line orthogonality and prescribed mesh point clustering near the domain boundary. Examples of mesh in the annulus and near airfoil are presented.     

采用向量化运算进行图像融合的真实感纹理映射

提出一种基于向量运算体现纹理形变要求的映射对应点获取方法,根据场景表面纹理走势特点划分表面形变控制网格,以网格边界为形变控制向量,通过对控制向量的合成取得映射点;同时,根据对应点亮度进行图像融合达到纹理真实感融入．对于场景表面纹理走势细节性变化给出了网格调整方法,进一步使用三次参数样条曲线拟合映射区域,基于曲率半径进行边界多边形化以实现对映射区域的精确判断．该方法能产生高度真实感的虚拟实景效果．     

体参数化模型离散调和映射生成

目的 体参数化模型具有诸多优良特性和广泛的应用前景,如何生成有效的体参数化模型是迫切需要解决的问题.方法 首先定义了样条体参数化模型表达式,提出控制点设定是体参数化的核心问题.给定6个表面样条曲面的控制点,从计算域到参数域的调和映射方程的差分形式出发,给出了生成体参数化模型控制点的方法.提出雅克比矩阵和等参网两种方法用以检测体参数化模型的网格质量.结果 基于点云模型,构建了体参数化模型,且将该方法与离散孔斯插值法、凸组合插值法两种方法生成的体参数化模型网格质量进行了对比.结果表明,离散调和函数法生成的体参数化模型相对更为稳定与优化.结论 离散调和映射能初步生成体参数化模型,但需要进一步优化并提供了良好初始化条件.     

Isometric Texture Mapping for Free-form Surfaces

Texture mapping is a frequently exploited technique in computer graphics aimed at the emulation of high-resolution details in surfaces. In this paper we present a distance-ratios preservation method for bivariate raster texture mapping to free-form surfaces in an arbitrarily precise manner. The proposed method reduces the original general problem of computing the inverse of a three-dimensional parametric surface mapping into a problem of two-dimensional image warping. Several examples that demonstrate the proposed approach are also provided.     

On-the-fly texture computation for real-time surface shading

Standard texture mapping hardware enables rapid rendering of color mapped surfaces with interpolated surface shading. New algorithms extend this to bump mapping, Phong shading, and reflection mapping. We first introduce the bidirectional reflectance function we wish to optimize, split into diffuse, specular and environment terms. Casting the diffuse term as a table lookup, we introduce lighting tables and efficient ways to compute them for distant lights. We also revisit the geometry of bump mapping, extending Blinn's (1978) results. We consider caching intermediate results for rendering animated rigid bodies, generalizing this to animated surfaces using a technique called parametric rasterization. Finally, we describe efficient reflection mapping and discuss implications for bump-mapped surfaces. We present a fast method for rendering Phong highlights and discuss a special case of a planar surface with simulated water ripples