基于背景网格变形的动态网格移动方法

基于Delaunay背景网格插值技术的动态网格生成方法无需迭代计算,效率较高。但对复杂构形大幅运动的动边界问题,尤其当边界大幅转动时,背景网格极易交叉重叠。重新生成背景网格和重新定位网格节点信息不仅费时而且会导致网格质量的严重下降。本文提出改进的基于背景网格的动态网格变形方法,通过在初始Delaunay背景网格中添加辅助点,生成一层新的背景网格和新的映射关系;采用ball-vertex弹簧法驱动新背景网格的变形,进而牵动目标网格的变形。算例表明,本文提出的动态网格变形方法对所关心区域的网格具有良好保形性,边界可转动更大角度而不会出现网格交叉重叠问题,总体上提高了动态网格更新的效率和质量。     

高质量点集的快速局部网格生成算法

高效及高质量的局部网格生成算法是基于节点有限元并行方法设计的关键。泡泡布点算法能够在复杂区域上不经过人工干预生成高质量的节点集,本文提出了基于该方法所生成的节点集的快速局部网格生成算法。该算法充分利用泡泡布点方法提供的节点集及节点邻接链表信息,避免了桶数据结构的建立以及节点的局部搜索过程,只需应用Delaunay三角剖分的外接圆准则从中心节点的邻接链表中去除极少数的非卫星点,可快速地生成局部网格,比现有的局部网格生成算法更为快捷。算例结果表明,该算法高效可靠,生成网格与Delaunay三角剖分网格一致。     

Beta‐decomposition for the volume and area of the union of three‐dimensional balls and their offsets

Given a set of spherical balls, called atoms, in three‐dimensional space, its mass properties such as the volume and the boundary area of the union of the atoms are important for many disciplines, particularly for computational chemistry/biology and structural molecular biology. Despite many previous studies, this seemingly easy problem of computing mass properties has not been well‐solved. If the mass properties of the union of the offset of the atoms are to be computed as well, the problem gets even harder. In this article, we propose algorithms that compute the mass properties of both the union of atoms and their offsets both correctly and efficiently. The proposed algorithms employ an approach, called the Beta‐decomposition, based on the recent theory of the beta‐complex. Given the beta‐complex of an atom set, these algorithms decompose the target mass property into a set of primitives using the simplexes of the beta‐complex. Then, the molecular mass property is computed by appropriately summing up the mass property corresponding to each simplex. The time complexity of the proposed algorithm is O(m) in the worst case where m is the number of simplexes in the beta‐complex that can be efficiently computed from the Voronoi diagram of the atoms. It is known in ?³ that m = O(n) on average for biomolecules and m = O(n²) in the worst case for general spheres where n is the number of atoms. The theory is first introduced in ?² and extended to ?³. The proposed algorithms were implemented into the software BetaMass and thoroughly tested using molecular structures available in the Protein Data Bank. BetaMass is freely available at the Voronoi Diagram Research Center web site. © 2012 Wiley Periodicals, Inc.     

用激光三角法重构混凝土断裂面三维轮廓与断裂能分析

采用基于激光三角法的测试方法对混凝土断面表面轮廓进行了三维重构,初步的断面分析结果表明,相对于传统断面分析方法,本试验方法实现了断面的无损、快速和准确的测量分析,在测量到的断面基础上,给出了本试验所得到的混凝土材料断裂能与分维的关系。     

任意平面区域三角形网格的全自动生成算法

本文基于波前法提出了一种对任意平面区域生成三角形网格自动生成算法。算法具有区域适应性强,边界网格质量高,自动化程度高的优点。算法还包括了网格的拓扑优化,光滑及加密处理。此外,初边值条件的自动给定大大减少了数值计算中数据输入和避免了边界搜索计算。大量算例显示了算法的可靠性和适用性。     

一类三角剖分下样条空间S_3~1(Δ)维数

首次提出了一种判别样条空间S13(Δ)维数不依赖剖分几何性质的协调条件·　依此 ,在一类较一般的三角剖分下 ,获得了S13(Δ)的维数·     

环面上近三角剖分地图的计数

本文提供了环面上带边数和根面次这两个参数的有根近三角剖分的函数方程及其参数表达式，并给出了根面次为1以边数为参数的有根近三角剖分地图的精确解．     

Light power density distribution of image spot of laser triangulation measuring

HaiMing Wang [Wang HaiMing, Long range optical triangulation utilising collimated probe beam. Optics and Lasers in Engineering, 23(11), 1995, 41–52] studied the influences of the size of the object spot on the image spot in laser triangulation measuring. This paper points out that the study method of HaiMing Wang is inappropriate from two points of view. The size and relative power density distribution of the image spot can be calculated either when assuming the object spot is an ideal point, which emits a uniform spherical wave over the object, or when assuming that the object surface is a light scattering surface. Both the conditions show that the size of the image spot is much bigger than that of HaiMing Wang’s.     

r-regular shape reconstruction from unorganized points

In this paper, the problem of reconstructing a surface, given a set of scattered data points is addressed. First, a precise formulation of the reconstruction problem is proposed. The solution is mathematically defined as a particular mesh of the surface called the normalized mesh. This solution has the property to be included inside the Delaunay graph. A criterion to detect faces of the normalized mesh inside the Delaunay graph is proposed. This criterion is proved to provide the exact solution in 2D for points sampling a r-regular shapes with a sampling path < sin(π/8)r. In 3D, this result cannot be extended and the criterion cannot retrieve every face. A heuristic is proposed in order to complete the surface.     

一种标定三角测量法激光位移计的方法

三角测量的原理公式中因变量、自变量及系统结构参数之间具有非线性关系，并且这些系统结构参数在工程上难以精确测量，因此激光位移计的标定变得很困难。本文通过设置辅助变量及组合参数，使变量之间关系线性化，然后采用最小二乘法拟合出组合参数的准确值，实现激光位移计的准确标定。在此过程中对自变量的测量值做适量修正，可部分消除光学系统畸变对组合参数拟合结果的影响，减小拟合残差。本文给出了用该方法标定激光位移计的实验结果