面向四面体网格生成的曲面Delaunay三角化算法

提出了一种曲面域Delaunay三角网格的直接构造算法。该算法在曲面网格剖分的边界递归算法和限定Delaunay四面体化算法的基础上,利用曲面采样点集的空间Delaunay四面体网格来辅助曲面三角网格的生成,曲面上的三角网格根据最小空球最小准则由辅助四面体网格中选取,每个三角形都满足三维Delaunay空球准则,网格质量有保证,并且极大的方便了进一步的曲面边界限定下的Delaunay四面体化的进行。     

曲面品质分析的可视化后置处理技术

曲面品质分析结果的可视化显示是实现对自由曲面设计质量进行评估的关键。目前,国内还无文章系统地阐述这种技术。笔者提出了一套较完整的自由曲面品质分析的后置处理方法,实现了下列曲面品质分析曲面曲率图,等反射线,高亮线,等照度线。该方法的主要特点是用统一的方式处理边界、非边界等值点,闭合、开等值线,同一场量值对应的多条等值线,单、多个曲面的等值线生成,算法简单实用;对前置处理产生的曲面一次离散三角片中有等值线通过的,依据等值线段对该三角片进行二次离散处理,能较好地消减曲面一次离散三角片链显示颜色云图中的颜色过渡处的走样,锯齿,具有较好的效率和效果。     

一种非均匀插值移位分形曲面生成方法

提出了一种非均匀插值移位生成分形曲面的方法，在递归线性插值生成控制点的过程中，控制线性插值比系数的取值方式、对各插值方向选取不均等的插值比数值，使有序的插值离散点进行插值移位变成无序的插值离散点，由此，生成确定性的或随机性的分形曲面，算法中形成的插值移位量和控制点相关，使分形曲面的精细结构随控制点位置的改变而作相应地调整，增强了精细结构的可控性，给出的实例说明方法简明，易于实现。     

基于广义等值面提取的多视场深度像融合

建立等值面方程是隐式曲面造型问题的一个重要方面。一旦等值面方程被建立起来，可以设计相应的算法从深度数据中提取等值面，从而实现多视场深度像的融合。笔者提出一种广义的等值面方程，其理论依据是“空间点对应的向量图解”和“最小二乘逼近的法则”。在广义的等值面方程中注入了采样点的方向信息，提供了一个清晰的物理和几何含义的描述，由此可以解释设置“权函数”的标准以及隐式曲面造型中其他的一些几何关系。它为设计等值面提取算法提供了一个新的方法。     

多变量问题等值线形成的数学方法及物理意义

本文应用广义逆解法,将多变量散乱数据曲面(超曲面)拟合,把拟合后的曲面(超曲面)作为多变量问题等值线形成的数学模型,从而把超曲面、等值面、等值线这些几何概念,与等值线形成的物理意义结合起来,使人们能够从离散数据中揭示出所蕴含的物理规律。     

基于MKSA算法的曲面自适应采样

针对在机测量传统采样方法存在的采样点过于集中和采样区域遗漏影响曲面轮廓度的问题,将MacQueen K-means(MK)算法与模拟退火(SA)算法相结合,提出基于MKSA的复杂曲面在机测量自适应采样方法。利用MK算法生成二维质心Voronoi结构(CVT结构),将复杂曲面离散点云数据的高斯曲率绝对值作为生成CVT结构的密度函数,以方差函数为收敛准则,通过全局算法SA的退火准则设置降温系数,提高MK算法的全局寻优能力,生成全局最优的二维CVT结构;将质心点映射回原曲面,获得质心位置对应的曲面采样点,从而实现复杂曲面的自适应采样。仿真及实验结果表明:MKSA算法使曲面测量采样点分布更合理,拟合曲面与CAD模型的最大偏差及平均偏差均小于传统方法,更逼近CAD模型的理论曲面。     

三维图像中连续隐边界曲面的逼近计算

三维图像中感兴趣目标的边界曲面的检测与重构是三维图像分析中的一个重要问题.本文提出了从三维图像中计算连续隐边界曲面离散采样点的新方法.基于这些计算得到的离散采样点及其灰度值,可以推导出更合适的等值面或者自适应曲面去近似表示三维图像中的连续隐边界曲面.     

定义在三维曲面域上的四维曲面插值

本文对定义在三维曲面域上的四维曲面的构造进行了系统的分析。提出了对三维曲面域上的离散点集进行三角剖分的算法,基于Shepard思想构造了定义在三维曲面域上的四维曲面的插值方案,对四维曲面的图形表示进行了分析,建立了曲面上等值线三角形追踪算法,并进行了填充处理。最后,列举了一些实例,展示了该成果的应用前景。文中所有算法均在IBM PC机上实现,算法简单,而且具有通用性,易于在工程中得到应用。     

基于散乱点网格化的可控地形图技术

针对真实感地形的计算机模拟,文中以实现分形布朗运动fbm的随机中点位移法为基础,提出了一种基于散乱数据点网格化方法的可控地形图的生成算法,通过网格化算法,利用已有的离散高程采样数据计算每个网格节点的高程值。在地形建模时,将传统的随机中点位移(MPD)法和散乱数据点网格化的算法结合起来控制地形的起伏。通过离散化所给出的散乱点,可以快速且方便地调节生成地形的起伏。     

Nurbs曲面的自适应离散

本文针对ＣＡＤ／ＣＡＭ中ｎｕｒｂｓ曲面的离散问题，提出了一种自适应二叉树分割方法。与传统的四叉树方法相比，能以较小的代价、较高的精度逼近同样的曲面。对二叉树分割方法，本文提出了一种相邻子片的快速查找算法。     

A new automatic adaptive 3D solid mesh generation scheme for thin‐walled structures

A new algorithm to generate three‐dimensional (3D) mesh for thin‐walled structures is proposed. In the proposed algorithm, the mesh generation procedure is divided into two distinct phases. In the first phase, a surface mesh generator is employed to generate a surface mesh for the mid‐surface of the thin‐walled structure. The surface mesh generator used will control the element size properties of the final mesh along the surface direction. In the second phase, specially designed algorithms are used to convert the surface mesh to a 3D solid mesh by extrusion in the surface normal direction of the surface. The extrusion procedure will control the refinement levels of the final mesh along the surface normal direction. If the input surface mesh is a pure quadrilateral mesh and refinement level in the surface normal direction is uniform along the whole surface, all hex‐meshes will be produced. Otherwise, the final 3D meshes generated will eventually consist of four types of solid elements, namely, tetrahedron, prism, pyramid and hexahedron. The presented algorithm is highly flexible in the sense that, in the first phase, any existing surface mesh generator can be employed while in the second phase, the extrusion procedure can accept either a triangular or a quadrilateral or even a mixed mesh as input and there is virtually no constraint on the grading of the input mesh. In addition, the extrusion procedure development is able to handle structural joints formed by the intersections of different surfaces. Numerical experiments indicate that the present algorithm is applicable to most practical situations and well‐shaped elements are generated. Copyright © 2004 John Wiley & Sons, Ltd.     

Generation and optimization of tetrahedral meshes by advancing front technique

An algorithm for tetrahedron mesh generation and optimization with respect to a shape and a size criterion is presented. A well distributed set of nodes is first generated by an octree method, and the set is then triangulated. The advancing front technique is used to mesh the whole volume. Emphasis has been placed on management of the front. The method involves priority construction of enhanced quality tetrahedra. Each face is assigned to a front corresponding to the quality of the best tetrahedron which can be constructed. Elements are destroyed in the case of non-convergence. Optimization procedures make local use of the algorithm used to mesh the complete model. Industrial examples of relatively complex volumes are given, demonstrating that a high quality and optimized mesh can be obtained by the proposed method. © 1998 John Wiley & Sons, Ltd.     

Simultaneous surface and tetrahedron mesh adaptation using mesh‐free techniques

We present a method to adapt a tetrahedron mesh together with a surface mesh with respect to a size criterion. The originality of our work lies in the fact that both surface and tetrahedron mesh adaptation are carried out simultaneously and that no CAD is required to adapt the surface mesh. The adaptation procedure consists of splitting or removing interior and surface edges which violate a given size criterion. The enrichment process is based on a bisection technique. In order to guarantee mesh conformity during the refinement process, all possible remeshing configurations of tetrahedra have been examined. Once the tetrahedron mesh has been adapted, surface nodes are projected on a geometrical model. The building of a surface model from discrete data has already been presented in this journal. The method is based on a mesh‐free technique called Hermite Diffuse Interpolation. Surface and volume mesh optimization procedures are carried out during the adaptation and at the end of the process to enhance the mesh. Copyright © 2003 John Wiley & Sons, Ltd.     

KK节点中表面裂纹应力强度因子的数值分析

海洋平台中的管节点在出现疲劳裂纹后,其残余寿命的估算依赖于对焊缝处表面裂纹应力强度因子的精确计算。首先介绍了包含表面裂纹的KK节点的有限元网格产生方法。采用了五种不同类型的单元,即六面体单元、四分之一结点的裂纹单元、棱柱单元、棱锥单元以及四面体单元来形成KK节点焊缝处表面裂纹的网格。然后通过交互J积分法计算出了KK节点表面裂纹的应力强度因子分布情况。     

复合材料细观结构三维有限元网格模型的建立

提出了针对颗粒夹杂为椭球形状并呈随机分布的多相复合材料的三维有限元网格的建立方法,为复合材料细观结构研究提供了一种全自动的建模工具。引入了以体积为标度的任意两椭球骨料侵入的判别准则,实现了一种三维随机骨料的投放算法;在基于映射法的颗粒表面有限元网格生成算法中通过扫描线布点和局部连接技术较好地解决了网格极化现象;采用改进的三维AFT方法生成基体的四面体网格,并利用AFT特性一次生成所有颗粒夹杂的四面体网格;为进一步的复合材料细观结构与宏观力学性能的多尺度计算打下了基础。最后用几个算例验证了算法的有效性。     

Recovery of an arbitrary edge on an existing surface mesh using local mesh modifications

This study describes an algorithm for recovering an edge which is arbitrarily inserted onto a pre‐triangulated surface mesh. The recovery process does not rely on the parametric space of the surface mesh provided by the geometric modeller. The topological and geometrical validity of the surface mesh is preserved through the entire recovery process. The ability of inserting and recovering an arbitrary edge onto a surface mesh can be an invaluable tool for a number of meshing applications such as boundary layer mesh generation, solution adaptation, preserving the surface conformity, and possibly as a primary tool for mesh generation. The edge recovery algorithm utilizes local surface mesh modification operations of edge swapping, collapsing and splitting. The mesh modification operations are decided by the results of pure geometrical checks such as point and line projections onto faces and face‐line intersections. The accuracy of these checks on the recovery process are investigated and the substantiated precautions are devised and discussed in this study. Copyright © 2001 John Wiley & Sons, Ltd.     

三维Delaunay剖分的断层直接插入算法

研究了在三维空间中进行的Delaunay四面体剖分。在讨论了四面体网格与插入的受限平面数据的各种相交构形的基础上,提出了一种断层直接插入的算法。该算法可以应用于三维数据点集的受限四面体剖分,也可以应用于不同的数据场网格之间的相交运算等问题。     

Automatic sizing functions for unstructured surface mesh generation

Accurate sizing functions are crucial for efficient generation of high‐quality meshes, but to define the sizing function is often the bottleneck in complicated mesh generation tasks because of the tedious user interaction involved. We present a novel algorithm to automatically create high‐quality sizing functions for surface mesh generation. First, the tessellation of a Computer Aided Design (CAD) model is taken as the background mesh, in which an initial sizing function is defined by considering geometrical factors and user‐specified parameters. Then, a convex nonlinear programming problem is formulated and solved efficiently to obtain a smoothed sizing function that corresponds to a mesh satisfying necessary gradient constraint conditions and containing a significantly reduced element number. Finally, this sizing function is applied in an advancing front mesher. With the aid of a walk‐through algorithm, an efficient sizing‐value query scheme is developed. Meshing experiments of some very complicated geometry models are presented to demonstrate that the proposed sizing‐function approach enables accurate and fully automatic surface mesh generation. Copyright © 2016 John Wiley & Sons, Ltd.     

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.