On sorting triangles in a delaunay tessellation

In a two-dimensional Delaunay-triangulated domain, there exists a partial ordering of the triangles (with respect to a vertex) that is consistent with the two-dimensional visibility of the triangles from that vertex. An equivalent statement is that a polygon that is star-shaped with respect to a given vertex can be extended, one triangle at a time, until it includes the entire domain. Arbitrary planar triangulations do not possess this useful property which allows incremental processing of the triangles.This work was partially supported by the National Science Foundation's US-Italy Collaborative Research Program under Grant INT-8714578 and Information, Robotics, and Intelligent Research Grant IRI-8704781.     

Applications of the discrete element method in mechanical engineering

Compared to other fields of engineering, in mechanical engineering, the Discrete Element Method (DEM) is not yet a well known method. Nevertheless, there is a variety of simulation problems where the method has obvious advantages due to its meshless nature. For problems where several free bodies can collide and break after having been largely deformed, the DEM is the method of choice. Neighborhood search and collision detection between bodies as well as the separation of large solids into smaller particles are naturally incorporated in the method. The main DEM algorithm consists of a relatively simple loop that basically contains the three substeps contact detection, force computation and integration. However, there exists a large variety of different algorithms to choose the substeps to compose the optimal method for a given problem. In this contribution, we describe the dynamics of particle systems together with appropriate numerical integration schemes and give an overview over different types of particle interactions that can be composed to adapt the method to fit to a given simulation problem. Surface triangulations are used to model complicated, non-convex bodies in contact with particle systems. The capabilities of the method are finally demonstrated by means of application examples. Commemorative Contribution.     

Mesh data structure selection for mesh generation and FEA applications

The data structure representing a mesh and the operators to create and query such a database play a crucial role in the performance of mesh generation and FE analysis applications. The design of such a database must balance the conflicting requirements of compactness and computational efficiency. In this article, 10 different mesh representations are reviewed for linear tetrahedral and hexahedral meshes. A methodology for calculating the storage and computational costs of mesh representations is presented and the 10 data structures are analysed. Also, a system for ranking different data structures based on their computational and storage costs is devised and the various mesh representations are ranked according to this measure. Copyright © 2002 John Wiley & Sons, Ltd.     

《周培德三角剖分不是最小权三角剖分》一文商榷——反例不成立

周培协三角剖分是否能得到最小权三角剖分，周培德在《周培德三角部分不是最小权三角剖分》一文撰写之前已有新的结论，本文还指出《周培德三角剖分不是最小权三角剖分》一文所举反例不成立。     

Projection center calibration by motion

Camera calibration is the first step of three-dimensional machine vision. A fundamental parameter to be calibrated is the position of the camera projection center with respect to the image plane. This paper presents a method for the computation of the projection center position using images of a translating rigid object, taken by the camera itself.

Many works have been proposed in literature to solve the calibration problem, but this method has several desirable features. The projection center position is computed directly, independently of all other camera parameters. The dimensions and position of the object used for calibration can be completely unknown.

This method is based on a geometric relation between the projection center and the focus of expansion. The use of this property enables the problem to be split into two parts. First a suitable number of focuses of expansion are computed from the images of the translating object. Then the focuses of expansion are taken as landmarks to build a spatial back triangulation problem, the solution of which gives the projection center position.     

A faster divide-and-conquer algorithm for constructing delaunay triangulations

An easily implemented modification to the divide-and-conquer algorithm for computing the Delaunay triangulation ofn sites in the plane is presented. The change reduces its (n logn) expected running time toO(n log logn) for a large class of distributions that includes the uniform distribution in the unit square. Experimental evidence presented demonstrates that the modified algorithm performs very well forn2¹⁶, the range of the experiments. It is conjectured that the average number of edges it creates—a good measure of its efficiency—is no more than twice optimal forn less than seven trillion. The improvement is shown to extend to the computation of the Delaunay triangulation in theL _p metric for 1<p.This research was supported by National Science Foundation Grants DCR-8352081 and DCR-8416190.     

逆向工程中带孔洞的曲面对象三角剖分法研究

在分析现有的一些三角剖分方法的基础上，提出一种新的基于边界扩展的3D三角剖分方法，该方法首先采用一种空间栅格装点法来进行初始点云数据精简；再构造种子三角形，通过连接已剖分网格区域的边界边与最优扩展点来形成三角形网格从而向外扩展。该法可以对带有内孔等其他非凸壳的复杂曲面对象点云直接进行三角剖分，无需人工分区。实际应用表明采用该法可以快速、有效地从三维数据点集建立几何模型。     

基于块段模型的三维GIS混合数据结构模型研究*

为了有效地表示三维GIS空间实体,在地质块段模型的基础上,提出了基于八叉树和四面体格网的混合数据结构模型(block octree tetrahedron,BOT模型).采用BOT模型生成算法对块段模型进行重新分割,八叉树作整体描述,四面体格网作局部精确描述,并以不同的灰度值表示不同的单元块属性.同时,为节省存储空间,提出了线性BOT编码技术.实验结果表明,BOT模型充分发挥了八叉树和四面体格网的优点,可以在不增加存储空间的前提下实现对三维目标更高效、更精确的表达.     

二维有限元自适应网格规划生成

在设计基准点、沿指定曲线等网格加密生成方式的基础上，根据二维区域几何特征和分析对象物理特性估计，通过选择合适的网格加密生成方式，作用于分析对象上，规划构造有限元自适应网格单元尺寸信息场，进而提出基于Delaunay部分的动态节点一单元一体化算法，实现几何特征和物理特性整体自适应的有限元网格自动生成。算例表明此方法可生成高质量、符合分析要求的有限元自适应网格。     

基于GP2Y0A02距离测量的仿真与辅助设计

为了实现非接触距离测量,利用多个仿真与设计软件设计了采用GP2Y0A02模块的距离光学测试系统。在PROTEUS中测量GP2Y0A02电压值,并在Matlab中采用多元线性回归建立GP2Y0A02电压与距离的拟合曲线,最后在开发的测量程序中利用拟合曲线求解得到距离量。测试结果表明,对于非线性位置测量采用适当数据处理方法能得到满意的测量精度。