Automatic Delaunay mesh generation method and physically-based mesh optimization method on two-dimensional regions

Delaunay mesh generation method is a common method for unstructured mesh (or unstructured grid) generation. Delaunay mesh generation method can conveniently add new points to the existing mesh without remeshing the whole domain. However, the quality of the generated mesh is not high enough if compared with some mesh generation methods. To obtain high-quality mesh, this paper developed an automatic Delaunay mesh generation method and a physically-based mesh optimization method on two-dimensional regions. For the Delaunay mesh generation method, boundary-conforming problem was ensured by create nodes at centroid of mesh elements. The definition of node bubbles and element bubbles was provided to control local mesh coarseness and fineness automatically. For the physically-based mesh optimization method, the positions of boundary node bubbles are predefined, the positions of interior node bubbles are adjusted according to interbubble forces. Size of interior node bubbles is further adjusted according to the size of adjacent node bubbles. Several examples show that high-quality meshes are obtained after mesh optimization.

     

墙式网孔

提出了一种新的网孔－墙式网孔．墙式网孔是一种三度网孔,它通过从普通四度网孔的每个节点删去一度而获得,其节点度节省了２５％,但其直径同普通四度网孔几乎一样．它在计算能力上同普通四度网孔是等价的,因为四度网孔可以有效地嵌入到墙式网孔中,其伸张度为３,拥塞度为４．于是所有现存的基于四度网孔的并行算法都可以毫不费力地移植到三度网孔中且只有常数的减速比．墙式网孔可以通过边界节点回卷相连而产生墙式环托,它是点     

基于四边形网格均值坐标的K-2环网格曲面构造

为在曲面造型中避免产生扭曲、褶皱等现象,将四边形网格中内点的 K-2 环网格作为控制网格, 提出一种简单、灵活的曲面构造方法。给定一个 K-2 环控制网格,构造一个与其具有同样拓扑结构的平面网格。 再将平面网格拓展成空间四边形网格,同时在平面网格内进行采样。然后计算采样点关于空间四边形网格顶点 的四边形网格均值坐标,最后利用四边形网格均值坐标生成曲面,保证曲面上的每一点都满足 C∞ 。在这个过 程中设置了一个全局形状因子 h,用于控制曲面与初始控制网格的逼近程度,通过实例证明,h 越小,曲面越 逼近初始控制网格。     

Adaptive modification of time evolving meshes

The accuracy of a finite element computation depends on the mesh size and the distribution of mesh points. Adapting the mesh to capture the salient features in the finite element computation can provide a much more accurate solution without imposing an excessive increase in mesh size and computational cost. When the shape of the meshed domain is evolving in time mesh adaptation is essential in order to maintain conformity of the mesh with the domain boundaries. Mesh adaptation for time evolving domains can be accomplished through a combination of mesh movement with mesh modification by selective coarsening and enrichment of various regions in the mesh. Large deformations of the computational domain and boundary can be accommodated if overall mesh quality is maintained after each adaptation cycle.     

面向法向域网格建模的非线性引导滤波

网格建模是数字几何处理领域的基础性研究问题.为了提高网格建模的简便性和鲁棒性,首先提出了一种非线性的引导滤波算法.滤波过程在法向域进行,滤波后的法向是引导网格法向的局部二次变换;然后,应用上述算法研究了建模方面的2个重要问题:网格去噪和网格平滑,其中的难点在于如何构造合适的引导网格.针对去噪问题,每次迭代时利用双边法向滤波得到引导网格;针对平滑问题,引导网格以高斯滤波结果作为初始值,进而结合原始网格不断进行更新;最后,在形状复杂或特征丰富的网格模型上进行了去噪、平滑等实验,结果表明,该算法简单实用、鲁棒,去噪时能够有效地去除强噪声,保持模型的几何特征;平滑时能够提取出中小尺度的特征,保留大尺度的特征.     

骨骼蒙皮动画中网格优化的研究与实现

在骨骼蒙皮动画中需要处理大量的网格三角形，而在很多骨骼蒙皮动画的应用中都需要很高的动画实时性，为了提高骨骼蒙皮动画的实时性，对网格的优化是其中一项重要的工作。该文提出了一种优化网格的方法，并予以实现。     

Quasi-angle-preserving mesh deformation using the least-squares approach

We propose an angle-based mesh representation, which is invariant under translation, rotation, and uniform scaling, to encode the geometric details of a triangular mesh. Angle-based mesh representation consists of angle quantities defined on the mesh, from which the mesh can be reconstructed uniquely up to translation, rotation, and uniform scaling. The reconstruction process requires solving three sparse linear systems： the first system encodes the length of edges between vertices on the mesh, the second system encodes the relationship of local frames between two adjacent vertices on the mesh, and the third system defines the position of the vertices via the edge length and the local frames. From this angle-based mesh representation, we propose a quasi-angle-preserving mesh deformation system with the least-squares approach via detail-preserving mesh editing examples are presented to handle translation, rotation, and uniform scaling. Several demonstrate the effectiveness of the proposed method.     

A strategy of automatic hexahedral mesh generation by using an improved whisker-weaving method with a surface mesh modification procedure

One of the demands for three dimensional (3D) finite element analyses is the development of an automatic hexahedral mesh generator. For this problem, several methods have been proposed by many researchers. However, reliable automatic hexahedral mesh generation has not been developed at present. In this paper, a new strategy of fully automatic hexahedral mesh generation is proposed. In this strategy, the prerequisite for generating a hexahedral mesh is a quadrilateral surface mesh. From the given surface mesh, combinatorial dual cycles (sheet loops for the whisker-weaving algorithm) are generated to produce a hexahedral mesh. Since generating a good quality hexahedral mesh does not depend only on the quality of quadrilaterals of the surface mesh but also on the quality of the sheet loops generated from it, a surface mesh modification method to remove self-intersections from sheet loops is developed. Next, an automatic hexahedral mesh generator by the improved whisker-weaving algorithm is developed in this paper. By creating elements and nodes on 3D real space during the weaving process, it becomes possible to generate a hexahedral mesh with fewer bad-quality elements. Several examples will be presented to show the validity of the proposed mesh generation strategy.     

骨骼蒙皮动画中网格优化的研究与实现

在骨骼蒙皮动画中需要处理大量的网格三角形,而在很多骨骼蒙皮动画的应用中都需要很高的动画实时性,为了提高骨骼蒙皮动画的实时性,对网格的优化是其中一项重要的工作.本文提出了一种优化网格的方法,并予以实现.     

网格模型的局部编辑算法

提出一种新的网格模型局部编辑算法，该算法可以精确地控制变形区域的大小、边界和变形点的位移，克服了FFD及其改进算法的缺点．首先交互地定义一个附着在模型表面的控制网格；然后建立模型变形区域与控制网格间点的映射，再依据变形要求来编辑控制网格；最后根据映射关系反算出模型变形区域点的新位置．控制网格可以是参数曲面的控制网格，也可采用一般三角网格或预先定义的网格模板．为达到精确变形的目的，对模型与控制网格重叠的区域进行自适应细分．该算法计算简便、易于实现，并能达到很好的效果．     

四边形网格生成中的前沿边生长改进算法

为提高B样条曲面重构中点云四边形网格的生成效率和质量,对现有的四边形网格Q-Morph前沿边生长算法进行改进,提出面向四边形网格生成的三角网格拓扑优化方法,通过设定生长限制条件和调整网格顶点度,保证全局四边形网格质量,实现适合复杂曲面重构的规则四边形网格获取。实例结果表明,该算法效率高、适应性好,生成的四边形网格具有分布均匀、不规则网格数量少的优点。     

一种基于特征线的曲面网格分割方法

各类网格分割法将曲面网格进行分割后,各子网格区域之间的交界线便可以作为曲面网格的封闭特征线。相反,如果根据网格模型的几何、拓扑特征,确定了网格模型的封闭特征线后,网格曲面便被这些特征线分割开来。为此,从曲面网格封闭特征线的角度出发,提出一种基于特征线的曲面网格分割方法。实验验证了该方法的可行性和有效性。     

隐式曲面重新多边形化

首先用Bloomenthal的多边形化算法生成一个粗糙的初始网格;然后在初始网格上分布若干个新顶点,新顶点可以均匀分布,也可以按曲率分布;再把初始网格上的老顶点和新顶点连接起来,生成一个中间网格,从中间网格上删除初始网格上的老顶点,得到重新多边形化的网格;最后细分这个网格．实验结果表明：该算法可以生成近似等边的、大小由曲率指导的三角网格．     

A parallel log-barrier method for mesh quality improvement and untangling

The development of parallel algorithms for mesh generation, untangling, and quality improvement is of high importance due to the need for large meshes with millions to billions of elements and the availability of supercomputers with hundreds to thousands of cores. There have been prior efforts in the development of parallel algorithms for mesh generation and local mesh quality improvement in which only one vertex is moved at a time. But for global mesh untangling and for global mesh quality improvement, where all vertices are simultaneously moved, parallel algorithms have not yet been developed. In our earlier work, we developed a serial global mesh optimization algorithm and used it to perform mesh untangling and mesh quality improvement. Our algorithm moved the vertices simultaneously to optimize a log-barrier objective function that was designed to untangle meshes as well as to improve the quality of the worst quality mesh elements. In this paper, we extend our work and develop a parallel log-barrier mesh untangling and mesh quality improvement algorithm for distributed-memory machines. We have used the algorithm with an edge coloring-based algorithm for synchronizing unstructured communication among the processes executing the log-barrier mesh optimization algorithm. The main contribution of this paper is a generic scheme for global mesh optimization, whereby the gradient of the objective function with respect to the position of some of the vertices is communicated among all processes in every iteration. The algorithm was implemented using the OpenMPI 2.0 parallel programming constructs and shows greater strong scaling efficiency compared to an existing parallel mesh quality improvement technique.     

限制失真的网格参数化方法

针对当前网格参数化效率较低、映射失真较严重的问题，提出一种限制失真的网格参数化方法。首先，预处理原始网格模型。输入原3D网格模型，采用Half-Edge数据结构来重新组织网格并切割网格模型产生相应的切缝；构建Tutte映射把3D网格映射到一个2D凸多边形域，即构建2D网格模型。然后，进行限制失真的网格参数化计算。将Tutte映射后的2D网格模型作为限制失真计算的初始数据，建立相对于原3D模型网格的失真度量函数；求得该度量函数的最小值点，即为映射后的网格坐标集合；将映射后的网格作为限制失真映射的输入网格，设定迭代终止条件，循环迭代直至迭代结束，得到收敛的最优网格坐标；在计算映射失真度时，针对等距映射失真采用Dirichlet能量函数度量，针对共形映射失真采用尽可能等距（MIPS）能量函数度量；在求解映射失真度量函数的最小值点时采用代理函数法结合组合牛顿法的最优解方法。最终，实现了该方法并开发了一个原型系统。在原型系统中，分别设计了限制等距失真和限制共形失真的网格参数化实验，对程序执行时间和失真能量下降情况进行了统计和对比，提供了相应的纹理映射效果展示。实验数据表明，所提出的方法执行效率高、映射失真能量下降快，最优值收敛质量稳定；纹理映射时纹理着色均匀、布局紧致、线条均匀，符合实际应用的标准。     

基于曲面拟合的三角形网格简化

针对有限元网格简化问题,将边折叠和三角形折叠算法相结合,提出一种基于曲面拟合的网格简化方法。根据节点离散度识别网格特征,对具有不同特征的部位采用不同的简化策略从而实现自适应变密度网格简化。按长高比最优原则对合并后的节点进行预测,运用曲面拟合技术最终确定合并后的节点,达到优化网格和保持网格特征的目的。实验结果证明,该方法能在保证网格质量的前提下有效简化网格模型,提高CAE分析速度,最多可缩短75%的计算时间。     

CAD mesh model segmentation by clustering

CAD mesh models have been widely employed in current CAD/CAM systems, where it is quite useful to recognize the features of the CAD mesh models. The first step of feature recognition is to segment the CAD mesh model into meaningful parts. Although there are lots of mesh segmentation methods in literature, the majority of them are not suitable to CAD mesh models. In this paper, we design a mesh segmentation method based on clustering, dedicated to the CAD mesh model. Specifically, by the agglomerative clustering method, the given CAD mesh model is first clustered into the sparse and dense triangle regions. Furthermore, the sparse triangle region is separated into planar regions, cylindrical regions, and conical regions by the Gauss map of the triangular faces and Hough transformation; the dense triangle region is also segmented by the mean shift operation performed on the mean curvature field defined on the mesh faces. Lots of empirical results demonstrate the effectiveness and efficiency of the CAD mesh segmentation method in this paper.     

基于商空间粒度理论的三维网格分割方法

通过研究已有的网格分割和模型简化方法 ,分析三维模型的网格分割中的商空间粒度思想 ,并将商空间粒度计算引入到网格分割中 ,对网格分割过程进行描述 ,提出了基于粒度分层合成技术的网格分割方法。该算法通过分别提取模型中各三角形网格区域的几何特征构成不同的粒度区域 ,再根据粒度合成理论。将这些所形成的粒度组织起来 ,从而实现对三维网格的最终分割 ,为三角网格模型的简化提供了快速有效的方法。实验表明了该算法对于网格分割的有效性和正确性。     

Matrix-based pairwise key establishment for wireless mesh networks

Wireless communication in wireless mesh networks (WMNs), like other types of wireless networks, is vulnerable to many malicious activities such as eavesdropping. As one of the fundamental security technologies, pairwise key establishment has been widely studied to secure wireless communication. In this paper, we propose a new matrix-based pairwise key establishment scheme for mesh clients in WMNs. A fact in WMNs is that mesh routers are more powerful than mesh clients, in both communication and storage. Motivated by this fact, expensive operations can be delegated to mesh routers to alleviate the overhead of mesh clients when establishing pairwise keys between them. Compared with other matrix-based schemes, our scheme has significant advantages: any two mesh clients can directly establish pairwise keys while communication and storage costs of mesh clients are significantly reduced.     

Surface mesh enhancement with geometric singularities identification

A method for generating geometric surface meshes from a discrete surface, called a reference mesh, is presented. First, the geometrical singularities are extracted from the reference mesh. Then, an almost smooth surface interpolating the reference mesh vertices is associated to the reference mesh. Finally, the reference mesh is adaptively refined via the smooth geometry in order to obtain an adequate approximation of the underlying geometry. Some numerical examples are given to show the efficiency of our approach. The method can transform a mesh composed of linear elements to a mesh constituted by quadratic elements.