网格曲面中孔洞的光滑填充算法研究

三角网格模型是几何描述的一种重要形式，有着广泛的应用。但三角网络模型常常会存在孔洞缺陷。这些孔洞的存在一方面影响视觉效果，另一方面会影响许多后续的操作，如快速原型制造、有限元分析等，因此有必要对这些孔洞进行修补。目前绝大多数孔洞填充算法是将网格模型中的孔洞提取成空间多边形，并对孔洞多边形进行三角化。这种处理方法的主要缺陷是没有考虑网格曲面在孔洞附近的几何形态，因而填充部分不能与整个曲面光滑地融为一体。笔者提出了一种三角网格曲面中孔洞的光滑填充算法。该算法根据孔洞周围网格曲面的几何信息来增加孔洞内部的采样点，然后再对增加的采样点进行三角化，较好地解决了填充部分与整体曲面光滑连接的问题。     

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。     

任意多边形边界内散乱点的三角划分

本文提出了一种简洁通用、用于处理平面上任意多边形内不规则分布点的三角划分算法，并给出了该算法在离散数据参数Ｂｅｚｉｅｒ三角曲面造型中的应用。     

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。     

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。     

基于回溯双向波前法虚拟修补点云孔洞

针对虚拟修补边界点凹凸不平且分布不均的点云孔洞效果欠佳的问题,提出了回溯双向波前法虚拟修补包含复杂边界的孔洞.以具有复杂边界孔洞的青铜器模型为例:首先,三角网格化青铜器点云数据并依据网格化结果提取出孔洞边界,通过比较边界点集的曲率波动幅度以去除伪孔洞边界;其次,以孔洞边界点集的回溯结果为初始点集,并结合向量叉积对初始点集进行凹凸性分类,再对凹、凸点分别采用正、反向波前法逐圈新增点集直至补全;最后,利用最小二乘法拟合曲面平滑新增点集,获得最终修补结果.实验结果表明该方法与划分子洞波前法、曲线流收缩法相比,结构相似性的平均值分别提高了81.14%和93.8%,且曲率差异性更低,修补网格的顶点密度与原始网格更相近且过渡自然,能有效修补复杂边界孔洞.     

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。     

复连通多边形的三角剖分

文章简要回顾了多边形的三角剖分 ;基于将复连通多边形假定看作简单多边形的思想 ,着重讨论了复连通多边形的三角剖分 ;通过对具体实例的分析 ,将判断多边形顶点的凹凸性与判断某点在三角形的外部或内部的问题合二为一 ,简化算法函数     

列车车轮三维结构光检测中的点云处理研究

列车轮对作为转向架的关键零部件,其检测手段仍以人工检测为主,现有的自动检测方案,大多针对车轮某一断面的参数尺寸进行测量,难以真实反映车轮轮缘踏面的损伤情况。为此,该文提出一种列车车轮三维结构光检测中的点云处理方案。首先,利用三维结构光测量仪器采集列车车轮的三维点云数据;其次,根据列车车轮三维点云的特点,确定包括离群点去除、点云配准、点云平滑处理以及孔洞修补在内的点云处理方案,并对各处理步骤的最优参数进行分析;最后,利用贪婪投影三角化算法,进行列车车轮三维点云数据的曲面重建,使用拉普拉斯平滑算法对重建后的曲面进行平滑处理。结果表明,该文所提出的列车车轮点云处理方案能够实现对三维点云数据的处理,最终得到的列车车轮的三维曲面模型与基准模型的标准偏差为1.768 mm,实现对于列车车轮的三维检测。     

斜坡面上孔底设计高程计算方法

在爆破平场的炮孔测量实践中,探索出了一种斜坡面孔底设计高程的计算方法。在已知设计地面四个角点坐标和高程的情况下,不但可以计算四点共面的矩形内钻孔孔深,还可以将矩形划分为两个直角三角形计算四点异面的钻孔孔深。原理简单,既适用于少量炮孔的手工计算,也适用于通过计算机编程来计算大批量炮孔孔深。     

斜坡面上孔底设计高程计算方法

在爆破平场的炮孔测量实践中,探索出了一种斜坡面孔底设计高程的计算方法。在已知设计地面四个角点坐标和高程的情况下,不但可以计算四点共面的矩形内钻孔孔深,还可以将矩形划分为两个直角三角形计算四点异面的钻孔孔深。原理简单,既适用于少量炮孔的手工计算,也适用于通过计算机编程来计算大批量炮孔孔深。     

PERIODICITY AND FINE STRUCTURE IN TWO-DIMENSIONAL GRAVITATIONAL RANDOM PACKING

ABSTRACT

Gravitational random packing of equal disks can be viewed as the evolution of a Markov chain in which a state is the shape of the front line formed by joining the centers of touching disks at the upper boundary. The placement of a new disk adds two straight-line segments and deletes one or more old ones. The replaced segments plus the two new ones form a polygon. Triangles, rhombi, and pentagons are most common, but hexagons and heptagons have been observed. The latter appear only in the early stages of packing while the numbers of triangles and pentagons in horizontal strips decay exponentially with height. Thus, the packing evolves to a purely rhombic structure.

The appearance of triangles, pentagons, or higher polygons indicates a choice between mutually exclusive sites. These branch points, which disrupt the rhombic structure, will occur whenever certain constraints are not satisfied. If the rhombic structure persists long enough, a diamond-shaped repeating unit is formed. The limiting packing density is simply the density of this repeating unit. Since units may differ greatly in their density, estimates should be based on the repeating units from many different runs.     

PERIODICITY AND FINE STRUCTURE IN TWO-DIMENSIONAL GRAVITATIONAL RANDOM PACKING

Gravitational random packing of equal disks can be viewed as the evolution of a Markov chain in which a state is the shape of the front line formed by joining the centers of touching disks at the upper boundary. The placement of a new disk adds two straight-line segments and deletes one or more old ones. The replaced segments plus the two new ones form a polygon. Triangles, rhombi, and pentagons are most common, but hexagons and heptagons have been observed. The latter appear only in the early stages of packing while the numbers of triangles and pentagons in horizontal strips decay exponentially with height. Thus, the packing evolves to a purely rhombic structure.

The appearance of triangles, pentagons, or higher polygons indicates a choice between mutually exclusive sites. These branch points, which disrupt the rhombic structure, will occur whenever certain constraints are not satisfied. If the rhombic structure persists long enough, a diamond-shaped repeating unit is formed. The limiting packing density is simply the density of this repeating unit. Since units may differ greatly in their density, estimates should be based on the repeating units from many different runs.     

Universal meshes: A method for triangulating planar curved domains immersed in nonconforming meshes

We introduce a new method to triangulate planar, curved domains that transforms a specific collection of triangles in a background mesh to conform to the boundary. In the process, no new vertices are introduced, and connectivities of triangles are left unaltered. The method relies on a novel way of parameterizing an immersed boundary over a collection of nearby edges with its closest point projection. To guarantee its robustness, we require that the domain be C²‐regular, the background mesh be sufficiently refined near the boundary, and that specific angles in triangles near the boundary be strictly acute. The method can render both straight‐edged and curvilinear triangulations for the immersed domain. The latter includes curved triangles that conform exactly to the immersed boundary, and ones constructed with isoparametric mappings to interpolate the boundary at select points. High‐order finite elements constructed over these curved triangles achieve optimal accuracy, which has customarily proven difficult in numerical schemes that adopt nonconforming meshes. Aside from serving as a quick and simple tool for meshing planar curved domains with complex shapes, the method provides significant advantages for simulating problems with moving boundaries and in numerical schemes that require iterating over the geometry of domains. With no conformity requirements, the same background mesh can be adopted to triangulate a large family of domains immersed in it, including ones realized over several updates during the coarse of simulating problems with moving boundaries. We term such a background mesh as a universal mesh for the family of domains it can be used to triangulate. Universal meshes hence facilitate a framework for finite element calculations over evolving domains while using only fixed background meshes. Furthermore, because the evolving geometry can be approximated with any desired order, numerical solutions can be computed with high‐order accuracy. We present demonstrative examples using universal meshes to simulate the interaction of rigid bodies with Stokesian fluids. Copyright © 2014 John Wiley & Sons, Ltd.     

A new algorithm for contact detection between spherical particle and triangulated mesh boundary in discrete element method simulations

In discrete element method (DEM) simulations of real scale, the spherical particles are commonly employed for increasing the computation speed, and the complex boundary models are represented by triangle meshes with controllable accuracy. A new contact detection algorithm has been developed to resolve the contacts between the spheres and the triangle mesh boundaries. The application of the barycentric coordinates makes this algorithm more efficient to identify contacts in the intersection test. As a particle probably collides with several triangles at the same time, the multiple contacts would be reported as face contacts, edge contacts, or vertex contacts. Moreover, the particle embedding in a triangle can be also contact with the edges or vertices of the next triangles. These contacts should be considered as invalid for updating contact forces in the DEM. To exclude invalid records from the multiple contacts, the algorithm gives attention to the mesh structure nearby contacts and analyzes all possible collision situations. Numerical experiments have been conducted to verify this algorithm by using the algorithm in the DEM simulation framework. The numerical results suggest that the algorithm can resolve all contacts precisely and stably when the spherical particles collide on the complex boundary circumstances. Copyright © 2013 John Wiley & Sons, Ltd.     

一种基于单调多边形的三角剖分算法

提出了一种基于单调多边形三角化算法,被三角化的多边形可以含有任意个内孔。先根据边界y（x）方向的局部极值顶点作水平（垂直）分割线,将多边形划分成单连通y（x）单调多边形,然后再将各单调多边形三角化。算法考虑了各种几何奇异情况,因此比较稳定。