由区域生长算法实现四边形网格划分

针对当前各种三角形网格转化为四边形网格算法的缺陷，提出一种实现这种转化的算法——区域生长算法．该算法通过有选择地合并三角形来获得高质量的四边形网格，并且对两个三角形的合并增加约束条件以避免在生成四边形网格的过程中产生残余三角形；同时对生成的四边形网格进行一系列的质量改善操作。     

三角形网格转化为四边形网格

现有的全自动网格划分算法大部分生成三角形网格。生成四边形网格更困难。为了缓解这个问题，本文研究并实现了三角形网格转化为四边形网格的线性算法。该算法是对已有的Ｏ（Ｎ＾２）算法的改进。     

基于三角形连接的有限元网格划分

文中创新地提出了三角形连接的有限元网格划分的算法,但是三角形并不是有限元计算的基本单元,而是根据已经生成的三角形生成较为规整的四边形。在实际的项目过程中,创新地提出了三种有效的算法,并利用C＋＋面向对象的MFC程序设计和编写。本程序可以从模型文件读取边界以及点约束和线约束特征数据,程序自动计算出一个较为合理的边界间距值,并且根据需要人工或自动选择一种划分算法,从而自动完成高质量的四边形网格划分。三种算法皆可以处理大量数据点和线,并且划分速度较为高效。本程序模块成功应用于有限元计算软件中。     

四边形网格优化中的螺旋条带生成

已有的四边形网格的简化及优化方法大多数都是三角形网格简化在局部几何上的推广.四边形网格的结构受螺旋条带的影响,移除四边形网格中的螺旋条带则可以在拓扑结构上明显提高四边形网格的质量.文中具体讨论了四边形网格上螺旋条带与网格上奇异点的关系及其性质,并根据这个性质给出了四边形网格中螺旋条带的一般生成算法.实验结果表明,该算法可以有效地搜索四边形网格上的螺旋条带,进而通过删除螺旋条带优化四边形网格的拓扑结构.     

四边形网格间接生成方法

研究了基于背景三角网格的四边形网格间接生成算法,并针对三角形合并过程中容易残留三角形的缺陷提出了确定侧边的详细算法,该算法主要是依据背景三角网格中边的位置和前沿边的情形,通过背景三角网格中已存在的边、边交换或边分割确定侧边,以避免在三角形合并过程中残留三角形单元。最后给出实例验证了算法的有效性。     

曲面的有限元网格顶点法矢算法

分析计算有限元三角形网格顶点法矢的各种算法原理,比较各种算法的结果精度,指出Max方法考虑了三角形网格的形状,且本质上是一种通过对四面体进行外接球面拟合的计算方法,结果精度很高.在此基础上,针对曲面在有限元网格划分后可能同时存在三角形网格和四边形网格,提出适应于单独的三角形网格和四边形网格与两者并存的混合网格的顶点法矢求取算法,计算结果表明了算法的适应性和有效性.     

多边形网格的非流形封闭三角形网格正则化

为了提高基于网格模型的算法与应用的效率和稳定性,提出一种将任意多边形网格模型转化为正则三角网格模型的算法.首先对输入多边形网格模型中非三角形的面片进行三角剖分,然后查找并移除模型中的重合或重叠元素,再通过模型内部三角形求交对模型进行边和面的分割,从而修正模型的拓扑结构;在求交的过程中,根据边和三角形的位置关系对共面求交进行细致的分类处理,减少了求交次数,提高了算法的稳定性;最后循环搜索在网格模型中可以确定法向的种子三角形,通过拓扑结构调整与之相邻的三角形的法向,最终构成一个或多个法向确定的闭合曲面.实验结果表明,该算法能够将多边形网格转化为正则三角形网格模型.     

二维域多约束四边形有限元网格生成算法

以Q-Morph算法思想为基础,实现增加约束后自动生成二维域多约束四边形有限元网格．通过增加约束修补子算法,使原算法思想适用于附加的多约束;同时调整了原有算法中单元四边形顶边的生成子算法和四边形内多余三角形删除子算法的烦琐之处．实例测试结果表明,用文中算法生成的约束四边形网格具有网格分布较均匀、网格形状较规整等特点．     

前沿法生成四边形网格的改进方法

针对传统前沿法生成四边形网格时算法不稳定,有残余三角形等缺点,该文提出泛前沿的概念。泛前沿是对目前前沿概念的更高层次上的抽象,不但避免了前沿拆分和合并带来的不稳定,而且使得前沿操作起来更简单有效。然后文章通过消除坏四边形单元,消除残余三角形单元等操作,最终得到了质量较好的全四边形网格。最后,给出了用此法划分的例子。     

基于三角形折叠的网格简化算法

在计算机图形学中，物体常常用三角形网格模型来描述。本文提出了一种新的基于三角形折叠的网格简化算法。该网格简化算法不仅能减少模型中的三角形数目而且能保持模型拓扑结构。算法给出了一种基于点到平面距离的有效的误差控制方法，并能在用户指定的误差范围内通过使原始网格中的三角形折叠达到大量简化的目的。该算法实现简单并且速度快。另外为了有效地支持多分辨率模型的表示以及相邻层次模型间的连续过渡，本文还给出了一种基     

Automatic generation of finite element meshes

This paper describes a new algorithm for the automatic generation of finite element meshes of arbitrary multiply connected domains. The strategy is based upon the construction of a mapping from the generated mesh into a regular one. The scheme is designed for maximum flexibility and is able to generate meshes of triangular or quadrilateral curved elements. Several examples are presented to illustrate the applicability of the algorithm.     

Automatic construction of quadrilateral network of curves from triangular meshes

The aim of this study is to propose a method for building quadrilateral network of curves automatically from a huge number of triangular meshes. The curve net can be served as the framework of automatic surface reconstruction. The proposed method mainly includes three stages: mesh simplification, quadrangulation and curve net generation. Mesh simplification is employed to reduce the number of meshes in accordance with a quadratic error metric for each vertex. Additional post-processing criteria are also employed to improve the shape of the reduced meshes. For quadrangulation, a front composed of a sequence of edges is introduced. An algorithm is proposed to combine each pair of triangles along the front. A new front is then formed and quadrangulation is continued until all triangles are combined or converted. For curve net generation, each edge of quadrilateral meshes is projected onto the triangular meshes to acquire a set of slicing points first. A constrained curve fitting is then employed to convert all sets of slicing points into B-spline curves, with appropriate continuity conditions across adjacent curves. Several examples have been presented to demonstrate the feasibility of the proposed method and its application in automatic surface reconstruction.     

Motorcycle graph enumeration from quadrilateral meshes for reverse engineering

Recently proposed quad-meshing techniques allow the generation of high-quality semi-regular quadrilateral meshes. This paper outlines the generation of quadrilateral segments using such meshes. Quadrilateral segments are advantageous in reverse engineering because they do not require surface trimming or surface parameterization. The motorcycle graph algorithm of Eppstein et al. produces the motorcycle graph of a given quadrilateral mesh consisting of quadrilateral segments. These graphs are preferable to base complexes, because the mesh can be represented with a smaller number of segments, as T-joints (where the intersection of two neighboring segments does not involve the whole edge or the vertex) are allowed in quadrilateral segmentation.The proposed approach in this study enumerates all motorcycle graphs of a given quadrilateral mesh and optimum graph for reverse engineering is then selected. Due to the high computational cost of enumerating all these graphs, the mesh is cut into several sub-meshes whose motorcycle graphs are enumerated separately. The optimum graph is then selected based on a cost function that produces low values for graphs whose edges trace a large number of highly curved regions in the model. By applying several successive enumeration steps for each sub-mesh, a motorcycle graph for the given mesh is found. We also outline a method for the extraction of feature curves (sets of highly curved edges) and their integration into the proposed algorithm. Quadrilateral segments generated using the proposed techniques are validated by B-spline surfaces.     

Simultaneous untangling and smoothing of quadrilateral and hexahedral meshes using an object-oriented framework

In this work, we present a simultaneous untangling and smoothing technique for quadrilateral and hexahedral meshes. The algorithm iteratively improves a quadrilateral or hexahedral mesh by minimizing an objective function defined in terms of a regularized algebraic distortion measure of the elements. We propose several techniques to improve the robustness and the computational efficiency of the optimization algorithm. In addition, we have adopted an object-oriented paradigm to create a common framework to smooth meshes composed by any type of elements, and using different minimization techniques. Finally, we present several examples to show that the proposed technique obtains valid meshes composed by high-quality quadrilaterals and hexahedra, even when the initial meshes contain a large number of tangled elements.     

接触面的一致性三角形网格生成算法*

为了简化数值模拟中三角形网格模型之间的接触问题,设计了在接触面上生成一致性三角形网格的算法,基本步骤为构造网格拓扑关系、搜索重叠网格、完善重叠网格、拷贝网格、修补边界空隙。采用面向配对顶点的搜索方法、点投影的判定方法、基于边界环的孔洞搜索方法,准确地确定了接触区域,利用最短对角线的方法修补了边界空隙,较好地生成了一致性网格,并采用三轴分块排序表提高了效率。实验结果表明,该算法准确、高效地实现了接触面上网格的一致性。     

Approximate topological matching of quad meshes

In this paper, we study the problem of approximate topological matching for quadrilateral meshes, that is, the problem of finding as large a set as possible of matching portions of two quadrilateral meshes. This study is motivated by applications in graphics that involve the modeling of different shapes that have results needing to be merged in order to produce a final unified representation of an object. We show that the problem of producing a maximum approximate topological match of two quad meshes is NP-hard and that its decision version is NP-complete. Given these results, which make an exact solution extremely unlikely, we show that the natural greedy algorithm derived from polynomial-time graph isomorphism can produce poor results, even when it is possible to find matches with only a few nonmatching quads. Nevertheless, we provide a “lazy-greedy” algorithm that is guaranteed to find good matches when mismatching portions of mesh are localized. Finally, we provide empirical evidence that this approach produces good matches between similar quad meshes.

基于NURBS曲面拟合的三角网格曲率计算

针对三角网格提出了一种基于NURBS曲面拟合的计算Gauss曲率和平均曲率的算法。首先选取边界检测后的二阶邻点作为局部拟合数据,采用直接投影法实现参数化,由二次NURBS曲面进行最小平方拟合反算控制点矩阵,最后由拟合曲面计算曲率。并从三角网格分辨率和噪声两方面进行了比较,实验结果表明本文算法精度高、较其他算法稳定,因而更具通用性。     

Biorthogonal wavelet construction for hybrid quad/triangle meshes

Ever since its introduction by Stam and Loop, the quad/triangle subdivision scheme, which is a generalization of the well-known Catmull–Clark subdivision and Loop subdivision, has attracted a great deal of interest due to its flexibility of allowing both quads and triangles in the same model. In this paper, we present a novel biorthogonal wavelet—constructed through the lifting scheme—that accommodates the quad/triangle subdivision. The introduced wavelet smoothly unifies the Catmull–Clark subdivision wavelet (for quadrilateral meshes) and the Loop subdivision wavelet (for triangular meshes) in a single framework. It can be used to flexibly and efficiently process any complicated semi-regular hybrid meshes containing both quadrilateral and triangular regions. Because the analysis and synthesis algorithms of the wavelet are composed of only local lifting operations allowing fully in-place calculations, they can be performed in linear time. The experiments demonstrate sufficient stability and fine fitting quality of the presented wavelet, which are similar to those of the Catmull–Clark subdivision wavelet and the Loop subdivision wavelet. The wavelet analysis can be used in various applications, such as shape approximation, progressive transmission, data compression and multiresolution edit of complex models.

基于Delaunay三角剖分的图象变形技术研究

提出了一种新的图象变形方法 ,即基于 Delaunay三角剖分的图象变形方法 .与四边形网格方法相比 ,用三角形网格定义特征区域 ,特征点的选取更自由、数目更少 .针对变形过程中运算量最大的坐标变换 ,提出了一种基于 Bresenham算法的坐标变换算法 .该算法完全采用加减运算 ,避免了乘法及舍入取整运算 ,大大加快了图象变形的运算速度 .计算机仿真试验表明 ,在同等数目控制点的条件下 ,该算法变形效果及运算速度均优于四边形网格方法 .