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.     

Chromatic sums of biloopless nonseparable near-triangulations on the projective plane

In this paper, the chromatic sum functions of rooted biloopless nonseparable near-triangulations on the sphere and the projective plane are studied. The chromatic sum function equations of such maps are obtained. From the chromatic sum equations of such maps, the enumerating function equations of such maps are derived. An asymptotic evaluation and some explicit expression of enumerating functions are also derived.     

三维精确局部加密网格划分在行波管模拟软件中的应用

通过半径与最小边之比控制网格质量,用三维分段线性结构（3D-PLC）作为网格初始数据进行自适应,用PLC进行局部加密形成Delaunay自适应网格划分方法,最后以螺旋线和电子枪为实例证明该方法的可行性。     

Perturbations for Delaunay and weighted Delaunay 3D triangulations

The Delaunay triangulation and the weighted Delaunay triangulation are not uniquely defined when the input set is degenerate. We present a new symbolic perturbation that allows to always define these triangulations in a unique way, as soon as the points are not all coplanar. No flat tetrahedron exists in the defined triangulation. The perturbation scheme is easy to code. It is implemented in cgal, and guarantees that both vertex insertion and vertex removal are fully robust.     

基于片光的货车侧面防护栏安装尺寸测量

提出了一种基于片光的货车侧面防护装置安装尺寸的测量方法。将线激光光源和摄像机固定在线性传动机构上,通过装置的线性移动,使激光光束在货车侧表面上产生移动,并用相机采集运动过程中的图像,利用激光三角法原理,对采集到的时序图像进行处理,实现对货车侧表面轮廓的三维重建,从而实现对货车侧面防护装置安装尺寸的测量。该方法避免了在普通视觉二维测量过程中,由于防护栏与前后轮胎不共面而造成的测量误差。通过对搭建的实验平台进行的研究表明,测量误差小于1mm,远小于原二维测量方案测量精度10mm,完全满足系统设计的要求。     

A MAP estimator based on geometric Brownian motion for sample distances of laser triangulation data

The proposed algorithm is designed to enhance the line-detection stability in laser-stripe sensors. Despite their many features and capabilities, these sensors become unstable when measuring in dark or strongly-reflective environments. Ambiguous points within a camera image can appear on dark surfaces and be confused with noise when the laser-reflection intensity approaches noise level. Similar problems arise when strong reflections within the sensor image have intensities comparable to that of the laser. In these circumstances, it is difficult to determine the most probable point for the laser line. Hence, the proposed algorithm introduces a maximum a posteriori estimator, based on geometric Brownian motion, to provide a range estimate for the expected location of the reflected laser line.     

Planar Triangulations with Real Chromatic Roots Arbitrarily Close to 4

We exhibit infinite families of planar triangulations with real chromatic roots arbitrarily close to 4, thus resolving a long-standing conjecture in the affirmative. Received November 12, 2005