基于二维轮廓序列的膝关节三维重建

提出了一个基于二维轮廓序列的四面体网格生成方法,用于医学图像三维几何模型重构.该方法首先对各选定的断层图像提取目标轮廓并做分支匹配等处理,然后生成各轮廓内部平面域的三角网格,最后在相邻断层之间根据三角网格连接四面体单元.该方法被应用于人体膝关节虚拟手术系统的三维几何建模,得到的膝部股骨模型包含494个节点和2 046个四面体单元,膝部脂肪模型包含2 854个节点和14011个四面体单元,这些模型被成功地应用于膝关节手术仿真,从而证明了该三维模型重建方法的可行性和有效性.     

支持裂纹扩展的三维有限元网格生成算法

描述了任意形状三维区域的非结构四面体网格生成算法,该算法对不含裂纹的区域、含单裂纹或多裂纹的区域都适用。算法首先使用八叉树来确定网格单元大小,然后采用前沿推进技术来生成网格。在前沿推进过程中,采用基于几何形状和基于拓扑结构的两个步骤来保证前沿向前移动过程中发生问题时仍能进行正确执行,并且使用了一种局部网格优化方法来提高网格划分的质量。最后,将算法运用到带有裂纹的复杂实体模型,实验结果表明该算法具有较强的适用性和较高的性能。     

一个高效可靠的三维AFT四面体网格生成算法

针对三维推进波前算法(AFT-Advancing Front Technique)存在的效率与收敛性问题,文中提出了一整套改进方案,给出了基于拓扑连接的网格数据结构和基于Hash表的网格元素的插入、查找、删除算法,提高了整个算法的效率.通过在网格生成过程中动态维护前沿的尺寸信息,提高四面体单元的整体质量.在内核回退求解时通过引入前沿优先因子,改变前沿推进的路径,大大增加了回退求解的成功概率;对于极少数不能回退求解的内核采用基于线性规划的插点方法加以解决,这样就基本保证了整个算法的收敛.在网格生成以后,通过删除不必要的内部节点、合并相关四面体单元以及对所有内部节点进行基于角度的优化,从而进一步有效提高了网格质量.数值算例表明,文中提出的改进算法具有接近线性的时间复杂度,生成网格质量好.该算法已经得到工程应用.     

三维实体仿真建模的网格自动生成方法

有限元网格模型的生成与几何拓扑特征和力学特性有直接关系。建立网格模型时，为了更真实地反映原几何形体的特征，在小特征尺寸或曲率较大等局部区域网格应加密剖分；为提高有限元分析精度和效率，在待分析的开口、裂纹、几何突变、外载、约束等具有应力集中力学特性的局部区域，网格应加密剖分。为此，该文提出了基于几何特征和物理特性相结合的网格自动生成方法。该方法既能有效地描述几何形体，又能实现应力集中区域的网格局部加密及粗细网格的均匀过渡。实例表明本方法实用性强、效果良好。     

Tetrahedral finite element mesh generation from NURBS solid models

In this paper, the development and the implementation of a tetrahedral meshing algorithm for generation of finite element meshes from NURBS solid models is presented. The meshing algorithm is based on a Delaunay technique, and makes use of some spatial data structures. The algorithm is capable of generating both uniform and varying size four-node and ten-node tetrahedral meshes. The algorithm has been implemented in a building block approach as part of a software library. It has been used as a practical tool in engineering design processes. Several representative test cases illustrate the effectiveness of the automatic solid mesh generator.     

Feature-preserving adaptive mesh generation for molecular shape modeling and simulation

We describe a chain of algorithms for molecular surface and volumetric mesh generation. We take as inputs the centers and radii of all atoms of a molecule and the toolchain outputs both triangular and tetrahedral meshes that can be used for molecular shape modeling and simulation. Experiments on a number of molecules are demonstrated, showing that our methods possess several desirable properties: feature-preservation, local adaptivity, high quality, and smoothness (for surface meshes). We also demonstrate an example of molecular simulation using the finite element method and the meshes generated by our method. The approaches presented and their implementations are also applicable to other types of inputs such as 3D scalar volumes and triangular surface meshes with low quality, and hence can be used for generation/improvement of meshes in a broad range of applications.     

Template-based finite-element mesh generation from medical images

The finite-element (FE) method is commonly used in biomedical engineering to simulate the behaviour of biological structures because of its ability to model complex shapes in a subject-specific manner. However, generating FE meshes from medical images remains a bottleneck. We present a template-based technique for semi-automatically generating FE meshes which is applicable to prospective studies of individual patients in which FE meshes must be generated from scans of the same structure taken at different points in time to study the effects of disease progression/regression. In this "template-based" meshing approach, the baseline FE (tetrahedral) volume mesh is first manually aligned with the follow-up images. The triangulated surface of the mesh is then automatically deformed to fit the imaged organ boundary. The deformed surface nodes are then smoothed using a Laplacian smoothing algorithm to correct triangle (surface nodes) distortion and thus preserve triangle quality. Finally, the internal mesh nodes are smoothed to correct distorted tetrahedral elements and thus preserve tetrahedral element quality. This template-based approach is shown to be as accurate and precise as the previous technique used by our group, while preserving element quality and volume.     

Fun sheet matching: towards automatic block decomposition for hexahedral meshes

Depending upon the numerical approximation method that may be implemented, hexahedral meshes are frequently preferred to tetrahedral meshes. Because of the layered structure of hexahedral meshes, the automatic generation of hexahedral meshes for arbitrary geometries is still an open problem. This layered structure usually requires topological modifications to propagate globally, thus preventing the general development of meshing algorithms such as Delaunay??s algorithm for tetrahedral meshes or the advancing-front algorithm based on local decisions. To automatically produce an acceptable hexahedral mesh, we claim that both global geometric and global topological information must be taken into account in the mesh generation process. In this work, we propose a theoretical classification of the layers or sheets participating in the geometry capture procedure. These sheets are called fundamental, or fun-sheets for short, and make the connection between the global layered structure of hexahedral meshes and the geometric surfaces that are captured during the meshing process. Moreover, we propose a first generation algorithm based on fun-sheets to deal with 3D geometries having 3- and 4-valent vertices.     

改进的三维ODT四面体网格质量优化算法

针对密度非均匀四面体网格,提出一种改进的三维ODT(optimal Delaunay triangulation)网格光顺算法,提高了ODT的适应性.在四面体网格中,以每一内部节点为核心节点,创建由与该节点相连接的四面体单元构成的星形结构;根据网格尺寸场把其星形结构转换到以核心点为中心的归一化空间内,然后在归一化空间内应用经典ODT光顺算法对核心点位置进行优化;通过中值重心坐标将核心点转换回物理空间;这样,通过逐一优化内部节点的空间位置达到优化四面体网格整体质量的目的.算例表明,该算法有效、健壮;对于密度非均匀的四面体网格,其光顺效果比经典的ODT算法更好.     

Adaptive Skin Meshes Coarsening for Biomolecular Simulation

In this paper, we present efficient algorithms for generating hierarchical molecular skin meshes with decreasing size and guaranteed quality. Our algorithms generate a sequence of coarse meshes for both the surfaces and the bounded volumes. Each coarser surface mesh is adaptive to the surface curvature and maintains the topology of the skin surface with guaranteed mesh quality. The corresponding tetrahedral mesh is conforming to the interface surface mesh and contains high quality tetrahedra that decompose both the interior of the molecule and the surrounding region (enclosed in a sphere). Our hierarchical tetrahedral meshes have a number of advantages that will facilitate fast and accurate multigrid PDE solvers. Firstly, the quality of both the surface triangulations and tetrahedral meshes is guaranteed. Secondly, the interface in the tetrahedral mesh is an accurate approximation of the molecular boundary. In particular, all the boundary points lie on the skin surface. Thirdly, our meshes are Delaunay meshes. Finally, the meshes are adaptive to the geometry.     

A CPU–GPU framework for optimizing the quality of large meshes

The automatic generation of 3D finite element meshes (FEM) is still a bottleneck for the simulation of large fluid dynamic problems. Although today there are several algorithms that can generate good meshes without user intervention, in cases where the geometry changes during the calculation and thousands of meshes must be constructed, the computational cost of this process can exceed the cost of the FEM. There has been a lot of work in FEM parallelization and the algorithms work well in different parallel architectures, but at present there has not been much success in the parallelization of mesh generation methods. This paper will present a massive parallelization scheme for re-meshing with tetrahedral elements using the local modification algorithm. This method is frequently used to improve the quality of elements once the mesh has been generated, but we will show it can also be applied as a regeneration process, starting with the distorted and invalid mesh of the previous step. The parallelization is carried out using OpenCL and OpenMP in order to test the method in a multiple CPU architecture and also in Graphics Processing Units (GPUs). Finally we present the speedup and quality results obtained in meshes with hundreds of thousands of elements and different parallel APIs.     

Implementation and evaluation of automated tetrahedral–prismatic mesh generation software

An open-source implementation of an efficient mesh generation procedure for hybrid prismatic–tetrahedral meshes intended for use in Reynolds-averaged Navier–Stokes solutions is presented. The method employed combines the established, and very fast, Delaunay-based tetrahedral mesh generator TetGen with a novel technique for the creation of a prismatic layer, where constrained global optimization of the envelope is employed. Once a well-shaped envelope is thus obtained, a semi-structured layer of pentahedral elements is extruded between wall and envelope surface. Satisfactory mesh quality is demonstrated by comparing solutions obtained using the new meshes with reference data computed on high-quality advancing-front grids. Mesh generation time is shown to be substantially smaller than with many other methods. Overall, the presented implementation is deemed a valuable tool for cases where many meshes need to be generated for routine analyses and turnaround time is critical.This is an extended version of the paper presented at the 23rd International Meshing Roundtable in London, October 2014.     

一种基于逻辑栅格的网格自动生成算法

针对基于栅格法对表面变动较大的模型进行网格划分适应性差的问题,提出一种基于逻辑栅格的六面体网格自动生成算法。该算法对基于栅格法的思想进行改进,避开一次生成模型初始栅格,将模型离散为一系列截面,对相邻截面采用矢量求交方法形成一对截面的初始栅格,修正初始栅格形成两截面之间的一层网格,形成整体模型。采用改进的栅格法进行复杂地形拱坝坝肩块体网格自动生成,取得较好的效果,结果证明改进的栅格法对复杂地形适应性强,模型表面变动较大时能自动进行网格退化。     

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.     

网格融合技术在列车过隧道运动网格数值模拟中的应用

在高速列车过隧道问题的数值模拟中,为提高模拟准确性而考虑转向架、受电弓导流罩、车厢连接处等细部结构后,几何模型变得复杂。为了得到质量高、适用性强的计算网格,在列车附近生成非结构化四面体网格,运动网格及计算区域其余部分划分块结构化六面体网格。在融合面上,利用网格融合技术处理四面体网格的三角形面网格和六面体网格的四边形面网格的联结问题,通过控制节点位置的变化满足拓扑一致,实现无缝连接。通过三维数值模拟计算结果与一维实验结果的对比发现,在同等精度要求下,采用网格融合技术及分区思想生成的网格整体上数量更少,生成速率更高,该方法可推广应用于更复杂几何模型的网格划分中。     

从表面重构的体数据实现三维网格剖分

针对有限元分析中网格最优化问题,本文提出一种改进的生成四面体网格的自组织算法。该算法首先应用几何方法将三角形表面模型重新构造成规定大小的分类体数据,同时由该表面模型建立平衡八叉树,计算用以控制网格尺寸的三维数组;然后将体数据转换成邻域内不同等值面的形态一致的边界指示数组;结合改进的自组织算法和相关三维数据的插值函数,达到生成四面体网格的目的。实验对比表明,该方法能够生成更高比例的优质四面体,同时很好地保证了边界的一致。在对封闭的三维表面网格进行有限元建模时,本文算法为其提供了一种有效、可靠的途径。     

Efficient tetrahedral mesh generation based on sampling optimization

We present a heuristic approach to tetrahedral mesh generation for implicit closed surfaces. It consists of a surface sampling step and a volume sampling step that both work in a unified optimization framework. First, high‐quality isotropic samplings as well as a triangular mesh on the surface are generated. Then uniform volume samplings are determined by optimizing the point distribution inside the closed surface domain. Finally, the tetrahedral mesh is easily obtained by constrained Delaunay triangulation. Experimental results show that the new method can generate ideal tetrahedral meshes for closed implicit surfaces efficiently that are Delaunay based. Our method has the advantage of high efficiency and nice performance at surface boundaries. Copyright © 2015 John Wiley & Sons, Ltd.     

Variational tetrahedral mesh generation from discrete volume data

In this paper, we propose a novel tetrahedral mesh generation algorithm, which takes volumic data (voxels) as an input. Our algorithm performs a clustering of the original voxels within a variational framework. A vertex replaces each cluster and the set of created vertices is triangulated in order to obtain a tetrahedral mesh, taking into account both the accuracy of the representation and the elements quality. The resulting meshes exhibit good elements quality with respect to minimal dihedral angle and tetrahedra form factor. Experimental results show that the generated meshes are well suited for Finite Element Simulations.     

多边形单元网格自动生成技术

近年来兴起的多边形有限元方法,在有限元计算中采用多边形单元划分网格,不仅可以更好地适应求解区域的几何形状,而且增加了网格划分的灵活性。为了更方便有效地生成多边形单元网格,在Delaunay三角形的基础上,通过将共圆Delaunay三角形合并为一个圆内接多边形,首先提出了Delaunay多边形的概念,进而提出了一种多边形网格自动生成的Delaunay多边形化算法。利用该Delaunay多边形化技术,对工程中常见的几何形状进行网格划分的具体算例表明,Delaunay多边形化方法可以生成性质优良的多边形单元网格。     

TUM.GeoFrame: automated high-order hexahedral mesh generation for shell-like structures

This paper presents a fully automated high-order hexahedral mesh generation algorithm for shell-like structures based on enhanced sweeping methods. Traditional sweeping techniques create all-hexahedral element meshes for solid structures by projecting an initial single surface mesh along a specified trajectory to a specified target surface. The work reported here enhances the traditional method for thin solids by creating conforming high-order all-hexahedral finite element meshes on an enhanced surface model with surfaces intersecting in parallel, perpendicular and skew-angled directions. The new algorithm is based on cheap projection rules separating the original surface model into a set of disjoint single surfaces and a so-called interface skeleton. The core of this process is reshaping the boundary representations of the initial surfaces, generating new sweeping templates along the intersection curves and joining the single swept hex meshes in an independently generated interface mesh.