裁剪曲面的三角化及图形显示

结合自主版权的超人ＣＡＤ／ＣＡＭ系统的开发，本文提出了一种适合于裁剪曲面图形显示的曲面三角化算法，该算法将曲面的三角化转化为曲面参数域的三角化，并将二维图形的集合运算与Ｄｅｌａｕｎａｙ三角剖分应有和于曲面参数域边界的处理，从而使裁剪曲面在边界上的三角形分布均匀。     

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。     

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。     

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。     

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。     

一种trimmedNURBS曲面的裁剪方法

所研究trimmed NURBS曲面的裁剪方法分三步完成裁剪算法。其主要特点是将所有trimmed NURBS曲面与裁剪轮廓面的交线都转为封闭环,从而可以统一的方式处理各类裁剪问题。实验结果表明,该算法可方便地解决目前一些曲面造型系统对已裁剪的内部和外部边界无法再裁剪等问题,亦可应用于一般形式的trimmed参数曲面的裁剪操作。     

一种曲面裁剪的快速新算法

曲面裁剪算法是曲面造型的关键算法之一。传统的裁剪算法是通过对重点和重边进行较复杂的特殊处理并基于环的两两并、交、差来实现的。本文首先提出并严格的定义了入点、出点等概念,在此基础上,提出了一种 对被裁剪曲面参数域进行快速组环的分裂、组环方法,从而实现了对曲面的快速裁剪,该算法已实现并用在ＳｕｐｅｒｍａｎＣＡＤ／ＣＡＭ曲面造型系统。     

多裁剪曲面的三角划分算法

提出一种新的多裁剪曲面三角划分的方法。把裁剪曲面展开,得到曲面的平面展开图。在平面展开图内进行三角划分,把三角形上点的拓扑关系映射到裁剪曲面,生成三角网格。由于平面展开图上两点的欧氏距离接近这两点在裁剪曲面上的测地距离,所以生成的三角网格保持了平面展开图中三角形的形态,解决了在参数域内进行三角划分所产生的狭长三角形的问题。此外,还提出了一种对带孔的平面散乱点进行三角划分的办法,有效的防止了划分网格出现裂缝和覆盖等现象。     

光线跟踪技术显示NURBS裁剪曲面

本文针对曲面造型系统中ＮＵＲＢＳ裁剪曲面的真实感显示需求，提出使用四叉树的数据结构和参数和空间映射的新技术，实现了光线跟踪技术的快速计算和图形的反走样处理，同时，参数域上的扫描线判断法能快速正确地识别曲面上的裁剪区域。     

三维点集Delaunay三角部分的自动生成与修改算法

本文在已有算法的基础上，提出了一个三维点集Ｄｅｌａｕｎａｙ三角剖分的自动生成及其修改算法。自动生成算法对点在空间的位置没有任何限制，修改算法充分利用已完成的计算量，当动态增加或减少一点时，仅在局部进行适当的调整即可保证整体三角剖分符合Ｄｅｌａｕｎａｙ性质。文中给出了算法正确性的证明。     

裁剪面的一类参数变换

给出了一类可以保持几何与拓扑信息一致性的裁剪面的参数变换定理及其算法。首先,确定了参数变换对裁剪面表示信息的影响。然后,根据参数变换后几何与拓扑信息的一致性要求,给出了对裁剪面表示信息进行调整的方法。最后,通过建立参数变换的关系,以裁剪球面为例阐述了这类参数变换的具体实现方法。     

Stress analysis of solids with open-ended tubular holes by BFM

Two kinds of special surface elements, curvilinear tube element and triangular element with negative parts, are proposed for modeling solids containing many slender open-ended tubular shaped holes in the framework of boundary face method. The surfaces of each tubular hole in the solid are modeled by the tube elements, and the outer surfaces that intersected and trimmed by the holes are modeled by triangular elements with negative parts. Substantial savings in both modeling effort and computational cost have been achieved. In addition, all the special surface elements are defined in the parametric space of the surface, and the exact geometry data are obtained directly from a CAD model of the solid. Therefore, automatic analysis is possible. Several numerical examples are presented to demonstrate the efficiency and accuracy of the proposed method.     

Graded tetrahedral finite element meshes

Vertices in the body centred cubic (bcc) lattice are used to create a tetrahedral spatial decomposition. With this spatial decomposition an octree approach is combined with Delaunay triangulations to decompose solids into tetrahedral finite element meshes. Solids must have their surfaces triangulated and the vertices in the triangulation are finite element nodes. Local densities of interior tetrahedra are controlled by the densities of surface triangles. Accuracy of the decomposition into finite elements depends on the accuracy of the surface triangulation which can be constructed with state of the art computer aided design systems.     

基于Voronoi最小邻近点集的Delaunay三角化方法

针对局部条件下网格生成的需求,提出一种基于节点的Delaunay三角化生成算法,该算法以Delaunay三角形及其对偶Voronoi图的局部性特征为基础,通过在局部搜索最小Voronoi邻近点集,来生成约束点附近的局部网格,通过建立背景索引网格,来提高算法效率。给出算法的原理证明、程序实现、效率分析和测试结果,并给出了算法的应用领域。     

Efficient three-dimensional Delaunay triangulation with automatic point creation and imposed boundary constraints

A method is described which constructs three-dimensional unstructured tetrahedral meshes using the Delaunay triangulation criterion. Several automatic point creation techniques will be highlighted and an algorithm will be presented which can ensure that, given an initial surface triangulation which bounds a domain, a valid boundary conforming assembly of tetrahedra will be produced. Statistics of measures of grid quality are presented for several grids. The efficiency of the proposed procedure reduces the computer time for the generation of realistic unstructured tetrahedral grids to the order of minutes on workstations of modest computational capabilities.     

Automatic generation of anisotropic quadrilateral meshes on three‐dimensional surfaces using metric specifications

A new algorithm for constructing full quadrilateral anisotropic meshes on 3D surfaces is proposed in this paper. The proposed method is based on the advancing front and the systemic merging techniques. Full quadrilateral meshes are constructed by systemically converting triangular elements in the background meshes into quadrilateral elements.By using the metric specifications to describe the element characteristics, the proposed algorithm is applicable to convert both isotropic and anisotropic triangular meshes into full quadrilateral meshes. Special techniques for generating anisotropic quadrilaterals such as new selection criteria of base segment for merging, new approaches for the modifications of the background mesh and construction of quadrilateral elements, are investigated and proposed in this study. Since the final quadrilateral mesh is constructed from a background triangular mesh and the merging procedure is carried out in the parametric space, the mesh generator is robust and no expensive geometrical computation that is commonly associated with direct quadrilateral mesh generation schemes is needed. Copyright © 2002 John Wiley & Sons, Ltd.     

GradH‐Correction: guaranteed sizing gradation in multi‐patch parametric surface meshing

In this paper a new method, called GradH‐Correction, for the generation of multi‐patch parametric surface meshes with controlled sizing gradation is presented. Such gradation is obtained performing a correction on the size values located on the vertices of the background mesh used to define the control space that governs the meshing process. In the presence of a multi‐patch surface, like shells of BREP solids, the proposed algorithm manages the whole composite surface simultaneously and as a unique entity. Sizing information can spread from a patch to its adjacent ones and the resulting size gradation is independent from the surface partitioning. Theoretical considerations lead to the assertion that, given a parameter λ, after performing a GradH‐Correction of level λ over the control space, the unit mesh constructed using the corrected control space is a mesh of gradation λ in the real space (target space). This means that the length ratio of any two adjacent edges of the mesh is bounded between 1/λ and λ. Numerical results show that meshes generated from corrected control spaces are of high quality and good gradation also when the background mesh has poor quality. However, due to mesh generator imprecision and theoretical limitations, guaranteed gradation is achieved only for the sizing specifications and not for the generated mesh. Copyright © 2004 John Wiley & Sons, Ltd.