二维域的有限三角剖分

本文提出了一种适用于多连通的多边形区域的三角剖分和非爱的受限数据的三角剖分算法。该算法简单、直观，采用翼边型数据结构，用Ｄｅｌａｕｎａｙ剖分方法实现。     

二维域的有限三角剖分

本文提出了一种适用于多连通的多边形区域的三角剖分和非连通的受限数据的三角剖分算法。该算法简洁、直观，采用翼边型数据结构，用Ｄｅｌａｕｎａｙ剖分方法实现。     

三维德洛内三角剖分算法探析

三维德洛内三角剖分算法是一种新颖的适用于实时有限元分析的四面体网格生成算法,该算法在并行插入与删除网格节点的前提下,能够最大限度的保证网格生成的质量和保真度。     

两种不同剖分方式的声线束追踪法声衰减计算

提出一种基于空间剖分的声线束追踪算法,对两种不同剖分方式算法进行比较。算法采用三棱柱和四面体两种空间剖分方式对声源点、障碍物所在空间结构进行剖分;利用得到的剖分结构快速追踪声线束并生成树形结构体;反向追踪声线束生成路径并结合声音排放传播模型得到三维空间声场;对两种剖分方式在计算精度、效率上进行比较,并对其误差和局限性进行讨论。完成该算法模型建立和比较,并通过实验对其进行检验。实验数据显示算法有较高的运算速度和精确度,两种剖分方式各有优势。     

基因遗传算法在三维数据场造型中的应用

将基因遗传算法应用于三维数据场的造型研究之中,提出了遗传三角剖分算法。针对三维三角剖分的特殊性,提出了虚拟交叉算子和三角变异算子,能够确保在遗传进化过程中,解群中的每一个串始终代表一个合法的三角剖分。     

一种裁剪曲面自适应三角剖分算法

本文介绍了一种裁剪曲面按精度三角剖分算法。三角剖分过程在参数域和曲面空间同时进行，参数域上控制三角片的拓扑关系，曲面空间进行精度检测。算法的核心思想是将裁剪曲面三角剖分视为约束剖分问题，从而使得三角形的细分操作拓展为有效域内插入散乱节点的三角剖分问题。算法简便、实用，三角化结果品质良好，已成功地应用于数控加工刀具轨迹干涉处理等具有精度要求的应用领域。     

飞行器RCS计算中曲面剖分技术研究与实现

飞行器RCS预估计算是隐身技术研究中的重要研究内容。论述了利用飞行器外形的特点,在满足飞行器设计误差的前提下使用平面和柱面对飞行器的整机作NURBS曲面逼近,然后用柱面和平面剖分代替曲面的剖分。实现了飞行器整机模型的指定边长的三角剖分。这种方法不同于有限元计算的网格剖分,具有网格单元与曲面曲率无关和剖分速度快等特点。     

虚拟手术中实时碰撞检测技术研究

碰撞检测是虚拟手术的关键技术,为提高检测速度,满足系统实时性的要求,提出空间剖分和层次包围盒相结合的方法。使用八叉树表示法对虚拟场景进行空间剖分,在叶节点构建层次包围盒。进行碰撞检测时属于不同八叉树节点的几何元素不会相交,否则使用层次包围盒算法继续进行检测,对于有可能相交的几何元素再进行精确相交检测。     

散乱数据点三角剖分方法综述

构造散乱数据插值曲面首先必须对散乱数据点实行三角剖分。本文简要阐述三角剖分的基本概念。并按优化准则将现有的各种三角剖分方法进行分类比较,为建立更好的凸域三角剖分算法提供依据,并为解决复杂多边形区域散乱数据点三角剖分奠定基础。     

使用多重网格算法的一种途径

采用坐标变换方法，将物理平面中任意几何区域上的非均匀网格剖分映射到计算平面中规则区域上的均匀网格剖分，这种处理使得对某些问题的多重网格算法成为方便可行，文后给出了两个算例。     

Inserting a surface into an existing unstructured mesh

In this work, a new method for inserting a surface as an internal boundary into an existing unstructured tetrahedral mesh is developed. The surface is discretized by initially placing vertices on its bounding curves, defining a length scale at every location on each boundary curve based on the local underlying mesh, and equidistributing length scale along these curves between vertices. The surface is then sampled based on this boundary discretization, resulting in a surface mesh spaced in a way that is consistent with the initial mesh. The new points are then inserted into the mesh, and local refinement is performed, resulting in a final mesh containing a representation of the surface while preserving mesh quality. The advantage of this algorithm over generating a new mesh from scratch is in allowing for the majority of existing simulation data to be preserved and not have to be interpolated onto the new mesh. This algorithm is demonstrated in two and three dimensions on problems with and without intersections with existing internal boundaries. Copyright © 2015 John Wiley & Sons, Ltd.     

Automatic merging of tetrahedral meshes

A generic algorithm is proposed to merge arbitrary solid tetrahedral meshes automatically into one single valid finite element mesh. The intersection segments in the form of distinct nonoverlapping loops between the boundary surfaces of the given solid objects are determined by the robust neighbor tracing technique. Each intersected triangle on the boundary surface will be triangulated to incorporate the intersection segments onto the boundary surface of the objects. The tetrahedra on the boundary surface associated with the intersected triangular facets are each divided into as many tetrahedra as the number of subtriangles on the triangulated facet. There is a natural partition of the boundary surfaces of the solid objects by the intersection loops into a number of zones. Volumes of intersection can now be identified by collected bounding surfaces from the surface patches of the partition. Whereas mesh compatibility has already been established on the boundary of the solid objects, mesh compatibility has yet to be restored on the bounding surfaces of the regions of intersection. Tetrahedra intersected by the cut surfaces are removed, and new tetrahedra can be generated to fill the volumes bounded by the cut surfaces and the portion of cavity boundary connected to the cut surfaces to restore mesh compatibility at the cut surfaces. Upon restoring compatibility on the bounding surfaces of the regions of intersection, the objects are ready to be merged together as all regions of intersection can be detached freely from the objects. All operations, besides the determination of intersections structurally in the form of loops, are virtually topological, and no parameter and tolerance is needed in the entire merging process. Examples are presented to show the steps and the details of the mesh merging procedure. Copyright © 2012 John Wiley & Sons, Ltd.     

Interface handling for three‐dimensional higher‐order XFEM‐computations in fluid–structure interaction

Three‐dimensional higher‐order eXtended finite element method (XFEM)‐computations still pose challenging computational geometry problems especially for moving interfaces. This paper provides a method for the localization of a higher‐order interface finite element (FE) mesh in an underlying three‐dimensional higher‐order FE mesh. Additionally, it demonstrates, how a subtetrahedralization of an intersected element can be obtained, which preserves the possibly curved interface and allows therefore exact numerical integration. The proposed interface algorithm collects initially a set of possibly intersecting elements by comparing their ‘eXtended axis‐aligned bounding boxes’. The intersection method is applied to a highly reduced number of intersection candidates. The resulting linearized interface is used as input for an elementwise constrained Delaunay tetrahedralization, which computes an appropriate subdivision for each intersected element. The curved interface is recovered from the linearized interface in the last step. The output comprises triangular integration cells representing the interface and tetrahedral integration cells for each intersected element. Application of the interface algorithm currently concentrates on fluid–structure interaction problems on low‐order and higher‐order FE meshes, which may be composed of any arbitrary element types such as hexahedra, tetrahedra, wedges, etc. Nevertheless, other XFEM‐problems with explicitly given interfaces or discontinuities may be tackled in addition. Multiple structures and interfaces per intersected element can be handled without any additional difficulties. Several parallelization strategies exist depending on the desired domain decomposition approach. Numerical test cases including various geometrical exceptions demonstrate the accuracy, robustness and efficiency of the interface handling. Copyright © 2009 John Wiley & Sons, Ltd.     

An L∞–Lp mesh‐adaptive method for computing unsteady bi‐fluid flows

This paper discusses the contribution of mesh adaptation to high‐order convergence of unsteady multi‐fluid flow simulations on complex geometries. The mesh adaptation relies on a metric‐based method controlling the L ^p‐norm of the interpolation error and on a mesh generation algorithm based on an anisotropic Delaunay kernel. The mesh‐adaptive time advancing is achieved, thanks to a transient fixed‐point algorithm to predict the solution evolution coupled with a metric intersection in the time procedure. In the time direction, we enforce the equidistribution of the error, i.e. the error minimization in L ^∞ norm. This adaptive approach is applied to an incompressible Navier–Stokes model combined with a level set formulation discretized on triangular and tetrahedral meshes. Applications to interface flows under gravity are performed to evaluate the performance of this method for this class of discontinuous flows. Copyright © 2010 John Wiley & Sons, Ltd.     

An imprint and merge algorithm incorporating geometric tolerances for conformal meshing of misaligned assemblies

A size tolerant algorithm for imprinting and merging adjacent part geometries is presented in this paper. This approach cleans up misaligned and dirty assembly geometry that is intended for conformal mesh generation. The algorithm first discretizes the boundary edges of adjacent faces into linear segments. The segments are then intersected and a partial intersection graph is calculated from the intersection results. The intersections are calculated by accounting for size tolerances to minimize the effect of misaligned parts on the meshing process. The partial intersection graph is next used to imprint the adjacent faces as appropriate. The imprints are generated using virtual geometry so that the tolerant topology created therein can be employed. Several examples are given to demonstrate the resulting improvement in the mesh quality of conformal meshes. The approach is shown to work robustly with misaligned and poorly defined parts. Copyright © 2004 John Wiley & Sons, Ltd.     

参数曲面与平面求交的一种新方法

本文提出了一种新的参数曲面与平面求交算法，基于平面的半空间性质，通过参数域平面的二向线性插值，将求交问题转化为一系列简单的离散、判断、比较、排序等运算，能较好的解决曲面片内的交线不连续和交线丢失问题，算法简便，可靠性好，计算精度高，在ＮＣ自动编程中具有广泛的应用场合。     

Plane intersections of a three-dimensional mesh

In order to detect geometric anomalies in 3D boundary element mesh or to obtain the contour plotting of stresses on a plane intersecting the 3D mesh, a computer program PP3D-COUPE has been developed to generate the contours on the intersection plane. The automatic mesh M2D is used to discretize the surfaces bounded by the contours for further computations.     

Automatic metric 3D surface mesh generation using subdivision surface geometrical model. Part 2: Mesh generation algorithm and examples

In this paper, a new metric advancing front surface mesh generation scheme is suggested. This new surface mesh generator is based on a new geometrical model employing the interpolating subdivision surface concept. The target surfaces to be meshed are represented implicitly by interpolating subdivision surfaces which allow the presence of various sharp and discontinuous features in the underlying geometrical model. While the main generation steps of the new generator are based on a robust metric surface triangulation kernel developed previously, a number of specially designed algorithms are developed in order to combine the existing metric advancing front algorithm with the new geometrical model. As a result, the application areas of the new mesh generator are largely extended and can be used to handle problems involving extensive changes in domain geometry. Numerical experience indicates that, by using the proposed mesh generation scheme, high quality surface meshes with rapid varying element size and anisotropic characteristics can be generated in a short time by using a low‐end PC. Finally, by using the pseudo‐curvature element‐size controlling metric to impose the curvature element‐size requirement in an implicit manner, the new mesh generation procedure can also generate finite element meshes with high fidelity to approximate the target surfaces accurately. Copyright © 2003 John Wiley & Sons, Ltd.     

Aspects of three-dimensional constrained Delaunay meshing

Presented in this paper are the theoretical aspects of node addition to a non-convex, multiboundary mesh of tetrahedral elements as used in finite element modelling. The method used is derived from Watson¹ and Shenton and Cendes² and is extended to deal with node addition on inter-material boundaries. Several situations are identified that result in an illegal insertion polyhedron (IP), these could be caused by the ‘constrained’ nature of the mesh, adjacent objects with different material properties, or degenerate node configurations. A new Delaunay algorithm is described that checks for illegal cases of the IP and then corrects them, this checking relies on the consistent ordering of the element nodes. It is shown that a particular type of illegal IP can easily be identified and corrected using this technique. The Delaunay algorithm is then applied to automatic mesh generation, and modification to the basic Delaunay algorithm is described so that previously meshed edges and faces of the current object being meshed are not deleted during the addition of subsequent nodes. This ‘protection’ method only becomes viable by recognizing the node ordering sense of the IP faces.