On transformations of special spines and special polyhedra

Special spines of 3-manifolds and special polyhedra are examined. Special transformations of spines and polyhedra are considered. Two triangulations of the same 3-manifold are known to have a common stellar subdivision, and two Heegaard splittings of the same 3-manifold are stably equivalent. We prove similar assertions for spines and polyhedra. Spines with the structure of a branched surface are studied. Translated fromMatematicheskie Zametki, Vol. 65, No. 3, pp. 354–361, March, 1999.     

关于非均匀剖分下多元样条空间S_2~1(△_(mn)~(2))的拟插值算子

１引言随着计算机科学技术的发展,多元样条在力学和计算机辅助几何设计（ＣＡＧＤ）中的应用越来越引起人们极大兴趣．然而,由于一般剖分下样条空间的研究有相当的难度,迄今为止只对于一些特殊剖分的样条空间取得了一定的进展,如：矩形剖分,均匀的１－型,２－型三角剖分等．王仁宏和崔锦泰讨论了均匀２－型三角剖下的拟插值算子以及其逼近性质,鉴于在工程和实际应用中均匀剖分具有一定局限性,作者在文献（［１］,［３］）的基础上,对于非均匀２－型三角剖分,给出了一类拟插值算子,并研究了它的逼近性质．同时,利用其构造了一类…     

Counting 5‐connected planar triangulations

Let t_n be the number of rooted 5‐connected planar triangulations with 2n faces. We find t_n exactly for small n, as well as an asymptotic formula for n → ∞. Our results are found by compositions of lower connectivity maps whose faces are triangles or quadrangles. We also find the asymptotic number of cyclically 5‐edge connected cubic planar graphs. © 2001 John Wiley & Sons, Inc. J Graph Theory 38: 18–35, 2001     

Adaptive delaunay triangulation with multidimensional dissipation scheme for high-speed compressible flow analysis

IntroductionHigh-speed compressible flows normally involve many complex flow phenomena,suchas shock waves,flow expansions,and shock-shock interactions[1].Effects of thesephenomena are critical in the design of high-speed structures.These flows are charact…     

高精度激光三角位移传感器的技术现状

三角测量法是一种传统的位移测量方法.随着激光器、光电探测器和计算机的发展,三角测量法有了很多新的进展和应用.对激光三角位移测量系统进行概述和讨论.根据光线的不同入射方式激光三角位移传感器主要分为两种:直入射式和斜入射式.分别介绍了这两种方法的测量原理,并对它们各自的特点进行了比较.最后阐述了高精度激光三角位移传感器的应用方向及发展趋势.     

网格单元形状对数值计算的影响

实现了二维非结构化网格上的N-S方程的离散,编制了非结构化同位网格上的SIMPLE程序,针对CFD/NHT 中几个有基准解的问题进行了试算考核。结果表明,在步长基本相同的情况下,四边形网格的收敛速度和解的精度都优于 三角形网格,尤其是收敛速度更明显;使用考虑边界贴体特性的边界层网格,解的精度优于均匀网格。     

提高CCD在激光三角测距中分辨率的方法

激光三角测距系统的精度主要取决于光斑象在探测器上的定位，用ＣＣＤ摄象机作为探测器时，光斑象的定位精度又取决于ＣＣＤ摄象机的分辨率。通常用光斑的采样灰度质心作为象点的准确位置可将ＣＣＤ的分辨率提高到亚象元级，但这种方法存在其固的的局限，边缘灰度跳变与高频干扰噪音影响。     

平面上两个点集间距离的O(nlogn)算法

定理“平面上两个点集的距离所在边是Voronoi图的Delaunay三角剖分中一条边”是本文的核心。在该定理基础上，本文提出如何用Voronoi图的Delaunay三角剖分算法求平面上两个点集的距离．并分析其复杂性．     

A Monte Carlo study of size and angular properties of a three-dimensional Poisson-Delaunay cell

On the basis of simulation of 1.2×10⁶ three-dimensional Poisson-Delaunay cells, the statistical properties of their size and angular parameters have been studied. The moments of the volume, face area, and edge length distributions are found to be equal to those obtained from the exact expressions of Miles and of Moller. The volume, surface area, and face area distributions can be described by the two-parameter gamma distribution. The normal distribution can be used to describe the distributions of the total edge length of a cell and the perimeter of a face. The edge length distribution has also been studied. The distribution of the angle in a face is found to be in accordance with its theoretical distribution.