An approach to automated decomposition of volumetric mesh

Mesh decomposition is critical for analyzing, understanding, editing and reusing of mesh models. Although there are many methods for mesh decomposition, most utilize only triangular meshes. In this paper, we present an automated method for decomposing a volumetric mesh into semantic components. Our method consists of three parts. First, the outer surface mesh of the volumetric mesh is decomposed into semantic features by applying existing surface mesh segmentation and feature recognition techniques. Then, for each recognized feature, its outer boundary lines are identified, and the corresponding splitter element groups are setup accordingly. The inner volumetric elements of the feature are then obtained based on the established splitter element groups. Finally, each splitter element group is decomposed into two parts using the graph cut algorithm; each group completely belongs to one feature adjacent to the splitter element group. In our graph cut algorithm, the weights of the edges in the dual graph are calculated based on the electric field, which is generated using the vertices of the boundary lines of the features. Experiments on both tetrahedral and hexahedral meshes demonstrate the effectiveness of our method.     

Layered tetrahedral meshing of thin-walled solids for plastic injection molding FEM

This paper describes a method for creating a well-shaped, layered tetrahedral mesh of a thin-walled solid by adapting the surface triangle sizes to the estimated wall thickness. The primary target application of the method is the finite element analysis of plastic injection molding, in which a layered mesh improves the accuracy of the solution. The edge lengths of the surface triangles must be proportional to the thickness of the domain to create well-shaped tetrahedrons; when the edge lengths are too short or too long, the shape of the tetrahedron tends to become thin or flat. The proposed method creates such a layered tetrahedral mesh in three steps: (1) create a preliminary tetrahedral mesh of the target geometric domain and estimate thickness distribution over the domain; (2) create a non-uniform surface triangular mesh with edge length adapted to the estimated thickness, then create a single-layer tetrahedral mesh using the surface triangular mesh; and (3) subdivide tetrahedrons of the single-layer mesh into multiple layers by applying a subdivision template. The effectiveness of the layered tetrahedral mesh is verified by running some experimental finite element analyses of plastic injection molding.     

Using sequential NETGEN as a component for a parallel mesh generator

A parallel tetrahedral mesh generator is developed using the existing sequential NETGEN mesh generator. Mesh generation algorithms developed decompose the geometry into multiple sub-geometries sequentially on a master node and then mesh each sub-geometry in parallel on multiple processors. Two methods are implemented. The first decomposes the geometry and produces conforming surface sub-meshes from which volume meshes can be generated in parallel. A second refinement based method also makes use of the CAD geometry information. A scalable mesh migration algorithm that utilizes “owner updates” rule is implemented. Results show that using the refinement based method, a mesh with a billion elements can be generated in about a minute.     

Quality encoding for tetrahedral mesh optimization

We define quality differential coordinates (QDC) for per-vertex encoding of the quality of a tetrahedral mesh. QDC measures the deviation of a mesh vertex from a position which maximizes the combined quality of the set of tetrahedra incident at that vertex. Our formulation allows the incorporation of different choices of element quality metrics into QDC construction to penalize badly shaped and inverted tetrahedra. We develop an algorithm for tetrahedral mesh optimization through energy minimization driven by QDC. The variational problem is solved efficiently and robustly using gradient flow based on a stable semi-implicit integration scheme. To ensure quality boundary of the resulting tetrahedral mesh, we propose a harmonic-guided optimization scheme which leads to consistent handling of both the interior and boundary tetrahedra.     

A modified advancing layers mesh generation for thin three-dimensional objects with variable thickness

A method of generating modified advancing layers mesh is proposed. In this paper the mesh generation process of semi-unstructured prismatic/tetrahedral mesh is presented for relatively thin three-dimensional geometries with variable thickness, as in the case of injection molding analysis. Prismatic meshes are generated by offsetting initial surface triangular meshes. During the mesh generation process, mesh quality is efficiently improved with the use of a new node relocation method. Finally, tetrahedral meshes are automatically generated in the rest of the domain. The mesh generating capability of the proposed algorithm is demonstrated with the several practical test cases.     

基于快速建立四面体网格的有限元心脏建模

针对目前通过医学成像技术获得心脏序列图像来提取相关心脏结构参数,判断心脏的功能的三维心脏建模技术的热点问题.提出了一种基于快速建立四面体网格的有限元心脏建模的方法,结合心脏这种形变模型的各种约束条件,模拟心脏的动态形变,利用有限元与生物力学原理构建心脏表面重建的有限元方程,由心脏表面三角网格数据点快速构建一系列不相重叠的四面体网格单元,以满足单元的应力矢量及单元节点位移矢量计算的需要,为模拟重建心脏运动奠定基础.实验结果表明了有效性和可行性.     

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。     

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.     

基于LEPP递变的四面体网格自适应剖分算法

为了更合理地进行四面体网格剖分,提出了一种根据待剖分对象形态不同进行网格密度自适应调整的四面体网格剖分方法。该方法首先采用BCC(body-centered cubic)网格初始化网格空间,并根据表面曲率的大小以及距离物体表面的远近,采用LEPP(longest edge propagation path)算法由外至内对初始化后的网格空间进行不同尺度的细分;然后对横跨表面的网格进行调整,以形成对象的表面形态;最后采用以质量函数引导的拉普拉斯平滑与棱边收缩(edge collapse)的方法对网格的质量进行优化来最终得到待剖分对象的四面体网格。结果表明,该方法所生成的网格不仅具有自适应的网格密度,而且网格质量比常用的Advancing Front算法也有所提高。对于基于3维断层图像或表面模型进行有限元建模,该方法不失为一种行之有效的好方法。     

保持特征的三角网格曲面去噪技术综述与展望

三角网格曲面去噪是计算机图形学领域一个经典问题,近年来不断涌现出各种新的去噪方法.该文主要关注保持特征的三角网格曲面去噪技术,总结了三角网格的几何表示以及一系列特征结构,依据算法类型将现有去噪技术分为优化法、滤波法、数据驱动法3类.针对不同的去噪模型和所利用的网格属性,对各分类下的去噪方法进行分析、讨论;简述了4类常用评估准则,从尖锐特征保持能力、体积保持、异常值去除能力、有无顶点漂移现象、有无面片翻转现象5个方面展示不同算法的优缺点;并根据这些算法存在的共性问题提出三角网格曲面去噪技术发展方向.     

有限元网格生成方法研究的新进展

总结了近10年来有限元网格生成方法的研究进展。首先，概述了目前研究与应用仍然较为活跃的通用网格生成方法，如映射法、基于栅格法、Delaunay三角化法和推进波前法的最新研究进展。其次，对当前的主要研究热点，如曲面网格生成、全六面体网格生成和并行网格生成等进行了阐述；最后，简要地探讨了该领域的发展趋势。     

弹性网格变形方法及其应用

1.引言 网格生成是数值计算中的基础问题.在微分方程数值方法的实现过程中,一个合适的计算网格可以提高计算精度,大大降低计算复杂性.近年来,人们所关注的数值求解微分方程自适应方法也包含了网格自动生成的研究.目前,国内外在这方面的研究工作很多.以网格类型而言,有结     

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．     

Spherical volume-preserving Demons registration

In order to analyze the brain shift situation accurately, we need to register the medical image and analyze its deformation. In this paper, we introduce a framework with volume-preserving registration for brain shift analysis. First, a volume-preserving mapping is introduced for general manifolds supported by a rigorous continuous theory. The registration is then performed on the spherical tetrahedron mesh with MRI gray values. The registration can retain the equality of local volume elements while registering the manifold to a template at the same time. We use simulated brain shift data to test our method. The results show that our method can efficiently register the brain while preserving the volume of each vertex.     

基于Hermite插值的网格拼接和融合-CIDE2013

网格模型的拼接和融合是3维形状编辑和造型中的一个重要方面。基于Hermite插值技术,提出了一种适用于具有一般边界点空间分布的三角网格模型之间无缝光滑拼接和融合方法。首先查找网格模型待拼接区域的边缘点集,并利用二次B样条曲线插值边缘点集分别得到边缘曲线;然后对边缘曲线进行Hermite插值得到拼接区域连续曲面;最后对拼接曲面分别进行三角网格化和Laplacian光顺平滑处理以实现网格模型的光滑拼接和融合。由于利用B样条曲线插值待拼接模型边界,本文方法适用于具有各种不同边界情形的网格模型拼接和融合,它不仅仅可以处理平面边界曲线情形也可以处理空间边界曲线情形。结合Hermite曲面插值拼接过渡区域,使得产生的拼接网格能光滑地衔接待拼接模型。实验结果表明,本文方法能够有效地实现三角网格模型的光滑拼接、模型修复和模型融合。     

基于Hermite插值的网格拼接和融合

网格模型的拼接和融合是3维形状编辑和造型中的一个重要方面。基于Hermite插值技术,提出一种适用于具有一般边界点空间分布的三角网格模型之间无缝光滑拼接和融合方法。首先查找网格模型待拼接区域的边缘点集,并利用二次B样条曲线插值边缘点集分别得到边缘曲线;然后对边缘曲线进行Hermite插值得到拼接区域连续曲面;最后对拼接曲面分别进行三角网格化和Laplacian光顺平滑处理以实现网格模型的光滑拼接和融合。由于利用B样条曲线插值待拼接模型边界,本文方法适用于具有各种不同边界情形的网格模型拼接和融合,它不仅仅可以处理平面边界曲线情形也可以处理空间边界曲线情形。结合Hermite曲面插值拼接过渡区域,使得产生的拼接网格能光滑地衔接待拼接模型。实验结果表明,本文方法能够有效地实现三角网格模型的光滑拼接、模型修复和模型融合。     

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。     

On control of adaptation in parallel mesh generation

A black-box methodology of a parallel generation of adaptive anisotropic meshes is described. A control of mesh adaptation, important for robustness and flexibility, may effect parallel properties of the methodology. This is demonstrated with a 3D example.     

复杂曲面混合网格的生成算法

有限元网格质量的好坏对金属成形模拟的精度和效率有很大影响。提出了一种复杂曲面混合网格自动生成算法，该算法根据所要划分的网格密度形成初始化边界节点，逐步向内铺砌混合网格，直至布满整个区域。应用实践表明．该算法具有稳定、准确和速度快的特点，生成的网格在相邻曲面边界处不会产生裂缝与覆盖，很好地满足了金属成形模拟分析软件对网格划分的要求。     

网格图形编辑的样条方法

提出基于样条的网格图形编辑方法,首先在网格表面附近构建近似的样条曲面,同时预计算网格顶点在样条上的对应点处局部标架下的坐标表示,并作为不变量在变形中进行保持;然后编辑样条的位置和形状,利用局部标架和细节坐标重建变形后的网格,同时进行网格光滑和网格细分,改善变形效果,以实现复杂模型简单快捷的编辑/变形.方法在保细节的同时允许对网格在多个尺度下编辑.实验结果表明,融合了样条的三角网格方法较传统的样条编辑方法可避免产生过多的控制点,大大地简化了操作.