The Number of Normal Components of Essentially Disconnected Coronoid Systems

An essentially disconnected coronoid system is defined as a coronoid system with some Kekulé structures and fixed bonds. The number of Kekulé structures (or perfect matchings) of a coronoid system G is the product of the number of perfect matchings of each normal component in G. In this article, it is proved that the boundary polygon of a normal component without any vertex lying on the boundary of an essentially disconnected coronoid system is a hexagon. Consequently, a lower bound on the number of normal components of an essentially disconnected coronoid system is obtained.     

与给定多边形相切的C1连续广义Ball闭曲线

讨论了与给定多边形相切的分段三次广义Ball闭曲线,所构造的曲线是C1连续,且对给定的多边形是保形的.曲线上的所有广义Ball曲线段的控制点由给定的多边形的顶点直接产生.最后给出了一个算例.     

凹多边形裁剪

多边形裁剪是计算机图形处理及辅助设计的典型课题之一。所谓凹边形裁剪是指凹多边形被矩形窗口裁去位于窗口范围以外的部分。凹多边形经裁剪后的输出应仍然是多边形。但这种多边形应消除退化边界,并且是成(?)的、封闭的、一个或多个多边形。这就是凹多边形裁剪的主要困难。国外已发表了多种凹多边形裁算法。 本文提出一种多边形裁剪的新概念,即不仅凹多边形被矩形窗口裁剪,而且矩形窗口要被凹多边形反裁剪。这是一种相互裁剪算法。 该算法的特点是计算速度快,功能强,程序简单,占用内存少,并能极简便地解决多边形裁剪中最为困难的问题——退化边界问题及多边形的成块输出问题。 该算法用FORTRAN77编程,在微机IBM—PC上运引,取得了良好效果,并已装入机械CAD软件包中。     

基于MATLAB的多边形电解槽静电场分析

推导出不等距边界网格条件下二维Laplace方程的有限差分公式,用MAT-LAB语言编写程序,实例分析并绘制了等腰梯形、钻形电解槽的等位线和电场强度分布图。实例计算结果表明：MATLAB在解决实际的工程和数学问题中,具有使用更为简便、语句功能更强的特点,能直观地演示多边形电解槽的空间电势分布和场强分布。     

计算复杂多边形面积的组合三角形法

具有全凸直线边界的多边形,可以离散成由三角形组成的几何体系,全凸直边界多边形的面积和各个组合三角形面积的总和,只要通过秦九韶公式得到三角形的面积后,就能够得以全凸直边界多边形的面积。通过一定的算法,在对任意凹曲多边形边界的凹凸属性进行判断后,可以把任意凹曲平面图形修补剪裁成全凸直线边界多边形,所以,任意凹曲复杂平面图形的面积等于修剪凸多边形的面积与被修剪部分面积的代数和,这种方法称为组合三角形算法,文中给出的算法表明,该方法得到的多边形面积避免了传统积分算法的近似性特征,具有解析解特点。     

On a convex hull algorithm for polygons and its application to triangulation problems

A frequently used algorithm for finding the convex hull of a simple polygon in linear running time has been recently shown to fail in some cases. Due to its simplicity the algorithm is, nevertheless, attractive. In this paper it is shown that the algorithm does in fact work for a family of simple polygons known as weakly externally visible polygons. Some application areas where such polygons occur are briefly discussed. In addition, it is shown that with a trivial modification the algorithm can be used to internally and externally triangulate certain classes of polygons in 0(n) time.     

一种改进的多边形数据内点自动生成算法

基于最小外切矩形(MBR)的多边形内点生成算法在奇异情况下容易失效。针对该问题,引入矢量数据的不确定性区间,提出一种改进的多边形数据内点自动生成算法。采用不确定性区间和相交区间的处理方法对奇异情况进行统一修正,避免MBR算法对于切割线与节点相交情况的过多异常处理和分支结构。通过对比实验验证了该算法的健壮性和高效性。     

A new linear algorithm for triangulating monotone polygons

Let P = (p₁, p₂,…,p_n) be a monotone polygon whose vertices are specified in terms of cartesian coordinates in order. A new simple two-step procedure is presented for triangulating P, without the addition of new vertices, in O(n) time. Unlike the previous algorithm no specialized code is needed since the new approach uses well-known existing algorithms for first decomposing P into edge-visible polygons and subsequently triangulating these.     

四杆机构从动件在两端极限位置的冲击效应研究

先讨论了冲击载荷对构件寿命的影响,然后从四杆机构的二阶传动函数的分析中,得出了从动件在两极限位置时,加速度为零的一类传动机构的设计原理。依此原理提出了从动件在两极限位置时,加速度为零的一种由曲柄滑块机构和移动凸轮机构组成的平面五杆机构。给出了已知从动件位移的该类传动机构的设计方法。     

A method of dealing polygon’s self-intersection contour in SLA

In the Stereolithography (SLA) Rapid Prototypingsystem, the part is saved with STL format. After sli-cing, the contour of each slice is a polygon, which arecomposed of a great deal of small lines. The structureof the part manufactured by SLA system is usu…