四面体胞的尽可能刚性网格变形算法

提出一种基于四面体胞的尽可能刚性三角形网格变形算法。用户通过操作网格上的若干顶点以得到所需的模型变形结果。首先,算法对网格模型内部进行稀疏四面体化,以产生一个贴合模型表面的四面体胞集。在模型变形过程中,算法通过最小化相应的变形能量函数,以保持网格模型表面局部区域的刚性以及每个四面体胞的刚性,从而有效避免模型表面及其内部的扭曲。同时,针对大尺度编辑可能造成的模型局部塌陷,提出一种简单的四面体胞自适应剖分方法,根据模型局部体积的剧烈变化,自动剖分对应的四面体胞以增加模型内部的局部变形自由度,进而消除不正确的变形效果。此外,自适应的四面体胞剖分允许算法在初始时只需对网格模型进行稀疏的四面体化,而在变形过程中根据需要进一步提高四面体胞的局部稠密度,因而保证了算法的鲁棒性及其效率。实验结果表明,该变形算法可以有效保持模型的表面细节以及模型的内部体积,并能够有效避免模型形状在大尺度变形时的局部退化。     

基于投影法的四面体网格切割算法

四面体网格切割算法是有限元仿真中的重要组成部分，切割的结果决定了刚度矩阵的更新速度和精度。本文在研究Cotin算法和Bielser算法的基础上，采用了预投影的方法，将部分顶点投影到切割平面上，使原先的四面体分割转化为相邻四面体分离，以达到简化分割的目的。与Cotin算法和Bielser算法相比，由该算法得到的网格切割边界更加合理，剖分比更低，提高了刚度矩阵更新的速度和精度。     

高性能非结构化四面体网格解耦并行生成算法

针对大规模科学计算领域非结构化网格生成问题,提出一种基于AFT-Delaunay方法的三维复杂域解耦并行四面体网格生成算法.该算法以待剖分三维域的闭合的表面三角形网格为输入,采用边界一致约束Delaunay剖分方法串行地生成较小规模的初始四面体网格;采用界面优先策略扩展三维AFT-Delaunay方法,以几何分界面为参考指引前沿推进方向,在分界面处生成一层由四面体单元构成的有厚度的"墙",递归、并行地将初始四面体网格分割成完全解耦的子区域;此时,各子区域均为不含内部节点的四面体网格,继续利用AFT-Delaunay方法解耦并行地生成各子区域内部四面体网格.算例结果表明,文中算法很好地解决了分界面处网格质量差的难题以及收敛性问题,具有较好的并行效率及几何适应性,可在PC平台全自动地完成108量级的非结构四面体网格生成.     

三维实体有限元自适应网格规划生成

为实现三维实体有限元网格自适应生成,设计了中心点、沿指定曲线和基于实体表面等网格加密生成方式;并根据分析对象几何特征和物理特性经验估计,以规划的方式构造自适应网格单元尺寸信息场．在此基础上,提出基于Delaunay剖分的动态节点单元一体化算法,生成几何特征和物理特性整体自适应的有限元网格．     

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.     

基于四面体剖分的并行地质块体建模方法

针对传统三维地质建模面临的内存消耗大,运行效率低的问题,提出了一种基于非结构四面体网格的并行地质块体建模方法。该方法采用“分治合并”的思想。首先将地质层位散点融合分割成若干个独立封闭块体;然后对每个块体进行表面三角形网格剖分,限定四面体剖分等步骤,形成块体的四面体网格剖分;最后将所有块体网格合并成最终地质模型。该方法中的块体剖分步骤应用多进程并行进行,提高了方法效率,并分摊计算机内存压力,可满足大尺度地质构造块体建模需求。该方法可为基于非结构网格的数值方法（如有限体积法、有限元方法等）的地震正演、偏移等算法提供合适的模型数据。     

基于STL文件的非均匀网格剖分技术研究

有限差分法广泛用于铸造过程中流场和温度场等的模拟,而对复杂模拟对象进行三维网格自动划分是十分重要的。在传统的网格剖分算法基础上,研究了非均匀剖分的步长自动确定算法,并开发了网格剖分前处理软件。对实际模型的应用研究表明,本算法可以根据铸件的壁厚、拐角等特征自动确定网格空间步长,节省网格剖分所需时间,减少人工参与网格划分的工作量,从而提高了网格剖分效率,为快速求解温度场等物理量奠定了基础。     

基于STL文件的非均匀网格剖分算法

铸件及铸型实体的三维网格自动剖分是金属凝固模拟按实际形状顺利进行的前提条件.文章在传统的均匀剖分算法基础上,提出了基于STL文件三角形面片法向矢量的自适应分层算法.该算法根据给定的加工精度,求出相应的符合精度要求的分层厚度,从而得出剖分该模型的所有平行且间距不等的剖切面,然后根据有限差分均匀网格剖分的算法来实现非均匀网格的剖分.最后用VC++编程通过实例验证,其结果是正确的.     

织物模拟中的自适应网格剖分研究

本文提出一种在织物模拟中的动态网格剖分方法，针对传统模拟算法中因网格剖分固定和曲面整体网格均匀剖分造成模拟误差与计算耗费，分别从织物物理和几何角度出发，提出在动态模拟过程中的自适应的网格剖分方法。利用模拟过程中曲面片局部形变信息，对网格进行动态剖分与合并，有效提高了模拟效率。经实际应用表明：该算法具有模拟效率高、易于计算机实现等优点，特别在对非均匀形变物体模拟中，该算法从模拟效率和精度均得到满意结果。     

全规整重网格化三维模型的压缩

通过保形自适应重采样,可将三维网格模型转化为规则排列的二维几何图像,从而可借鉴成熟的图像压缩技术对其进行压缩.提出了保形自适应采样算法,根据网格模型表面的有效顶点分布密度自适应地调整采样网格,并可最大限度地通过原始网格顶点进行采样.在不增加采样率的前提下,该压缩方法所得解压模型具有更小的失真度.通过大量实例对文中方法进行了验证,并与同类方法进行对比.实验结果表明该方法是切实可行的,且具有更好的压缩效果.     

A sharpness-dependent filter for recovering sharp features in repaired 3D mesh models

This paper presents a sharpness-based method for hole-filling that can repair a 3D model such that its shape conforms to that of the original model. The method involves two processes: interpolation-based hole-filling, which produces an initial repaired model; and post-processing, which adjusts the shape of the initial repaired model to conform to that of the original model. In the interpolation-based hole-filling process, a surface interpolation algorithm based on the radial basis function creates a smooth implicit surface that fills the hole. Then, a regularized marching tetrahedral algorithm is used to triangulate the implicit surface. Finally a stitching and regulating strategy is applied to the surface patch and its neighboring boundary polygon meshes to produce an initial repaired mesh model, which is a regular mesh model suitable for post-processing. During post-processing, a sharpness dependent filtering algorithm is applied to the initial repaired model. This is an iterative procedure whereby each iteration step adjusts the face normal associated with each meshed polygon to recover the sharp features hidden in the repaired model. The experiment results demonstrate that the method is effective in repairing incomplete 3D mesh models.     

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。     

Adaptive physics based tetrahedral mesh generation using level sets

We present a tetrahedral mesh generation algorithm designed for the Lagrangian simulation of deformable bodies. The algorithm’s input is a level set (i.e., a signed distance function on a Cartesian grid or octree). First a bounding box of the object is covered with a uniform lattice of subdivision-invariant tetrahedra. The level set is then used to guide a red green adaptive subdivision procedure that is based on both the local curvature and the proximity to the object boundary. The final topology is carefully chosen so that the connectivity is suitable for large deformation and the mesh approximates the desired shape. Finally, this candidate mesh is compressed to match the object boundary. To maintain element quality during this compression phase we relax the positions of the nodes using finite elements, masses and springs, or an optimization procedure. The resulting mesh is well suited for simulation since it is highly structured, has topology chosen specifically for large deformations, and is readily refined if required during subsequent simulation. We then use this algorithm to generate meshes for the simulation of skeletal muscle from level set representations of the anatomy. The geometric complexity of biological materials makes it very difficult to generate these models procedurally and as a result we obtain most if not all data from an actual human subject. Our current method involves using voxelized data from the Visible Male [1] to create level set representations of muscle and bone geometries. Given this representation, we use simple level set operations to rebuild and repair errors in the segmented data as well as to smooth aliasing inherent in the voxelized data.     

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.     

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．     

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.     

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.     

Facial hexahedral mesh transferring by volumetric mapping based on harmonic fields

Hexahedral mesh has obvious mechanical advantages over tetrahedral mesh, but it is no trivial task to generate hexahedral mesh for complex object shapes such as individual faces. This paper presents a novel method to generate patient-specific hexahedral meshes of facial soft tissue models, based on a volumetric cross-parameterization mapping from a standard hexahedral mesh to the individual model. The volumetric parameterization is constructed based on triple of the volumetric harmonic fields, which are adapted to be as close to mutually orthogonal as possible, to achieve some quasi-conformal effect. In addition, some piecewise constraints on the harmonic fields are added to ensure anatomical feature correspondence. Experimental results show that our approach works efficiently for facial soft tissue modeling, avoids element flipping and preserves mesh element angles to a significant extent.     

An Efficient Optimization Procedure for Tetrahedral Meshes by Chaos Search Algorithm

A simple and efficient local optimization-based procedure for node reposition-ing/smoothing of three-dimensional tetrahedral meshes is presented.The initial tetrahedral mesh is optimized with respect to a specified element shape measure by chaos search algorithm,which is very effective for the optimization problems with only a few design variables.Examples show that the presented smoothing procedure can provide favorable conditions for local transformation approach and the quality of mesh can be significantly improved by the combination of these two procedures with respect to a specified element shape measure.Meanwhile,several commonly used shape measures for tetrahedral element,which are considered to be equivalent in some weak sense over a long period of time,are briefly re-examined in this paper.Preliminary study indicates that using different measures to evaluate the change of element shape will probably lead to inconsistent result for both well shaped and poorly shaped elements.The proposed smoothing approach can be utilized as an appropriate and effective tool for evaluating element shape measures and their influence on mesh optimization process and optimal solution.     

基于SC/Tetra重叠网格法的交叉旋转模型分析

为解决流体力学计算中部分区域作复杂相对运动以及固体空间接触等问题,介绍重叠网格法的计算原理,基于SC/Tetra软件,利用八叉树方法对含有2块各自绕轴旋转的板的交叉旋转模型进行网格划分,计算得到其流场的矢量流速分布,结果表明由于网格过渡得很好,旋转区域的形状对计算结果影响很小,旋转区域与周围区域的变量能得到很好的过渡.SC/Tetra软件具有完善的重叠网格计算功能,能有效解决相对运动问题,且操作简单、计算结果准确.