一种新的基于弧段提取的椭圆检测方法

为了克服椭圆检测过程中对椭圆完整性和边缘梯度信息依赖性较强的缺点,实现椭圆目标的快速有效检测,提出了一种新的基于弧段提取的椭圆拟合方法。首先将梯度方向符号相同的相邻边缘点连接成弧段,然后根据弧段的凸性和象限分类组成包含三段弧的弧组,定义了新的弧选择策略,利用位置约束和弧对的椭圆中心估计提取候选椭圆,最后采用改进的拟合算法拟合椭圆。实验结果表明,基于弧段提取的椭圆拟合方法相对于LMEDS算法和RHT3具有更好的准确性、鲁棒性和稳定性,实时性也有一定的提高。     

Relative mean curvature configurations for surfaces in ℝ<Superscript><Emphasis Type="Italic">n</Emphasis></Superscript>, <Emphasis Type="Italic">n</Emphasis> ≥ 5

We define the relative mean curvature directions on surfaces immersed in ℝⁿ, n ≥ 4, generalizing the concept of mean curvature directions for surfaces in 4-space studied by Mello. We obtain their differential equations and study their corresponding generic configurations. *Work partially supported by DGCYT grant no. MTM2004-03244 and Unimontes-BR. †Work partially supported by DGCYT grant no. MTM2004-03244. ‡Work partially supported by DGCYT grant no. BFM2003-0203.     

三角形的九点二次曲线

在任意三角形内,三边中点,三高的垂足,以及连接顶点与垂心的三线段的中点,都在同一圆上,此圆即为三角形九点圆.三角形的九点圆是欧氏几何中著名的优美定理,被称为欧拉圆和费尔巴哈圆.本文试图把垂心改换为平面内的任意点,相应地把三条高线改换为过每个顶点各一条的共点直线组时,则将把三角形的九点圆有趣地推广为三角形的九点二次曲线.并具体讨论在不同的区域内得到的九点二次曲线.     

Genuinely multidimensional characteristic‐based scheme for incompressible flows

This paper presents a novel multidimensional characteristic‐based (MCB) upwind method for the solution of incompressible Navier–Stokes equations. As opposed to the conventional characteristic‐based (CB) schemes, it is genuinely multidimensional in that the local characteristic paths, along which information is propagated, are used. For the first time, the multidimensional characteristic structure of incompressible flows modified by artificial compressibility is extracted and used to construct an inherent multidimensional upwind scheme. The new proposed MCB scheme in conjunction with the finite‐volume discretization is employed to model the convective fluxes. Using this formulation, the steady two‐dimensional incompressible flow in a lid‐driven cavity is solved for a wide range of Reynolds numbers. It was found that the new proposed scheme presents more accurate results than the conventional CB scheme in both their first‐ and second‐order counterparts in the case of cavity flow. Also, results obtained with second‐order MCB scheme in some cases are more accurate than the central scheme that in turn provides exact second‐order discretization in this grid. With this inherent upwinding technique for evaluating convective fluxes at cell interfaces, no artificial viscosity is required even at high Reynolds numbers. Another remarkable advantage of MCB scheme lies in its faster convergence rate with respect to the CB scheme that is found to exhibit substantial delays in convergence reported in the literature. The results obtained using new proposed scheme are in good agreement with the standard benchmark solutions in the literature. Copyright © 2007 John Wiley & Sons, Ltd.     

Classroom note: A Generalization of Leibniz rule for higher derivatives

This note provides a simple method to extend the usual Leibniz rule for higher derivatives of the product of two functions to several functions, which is within the reach of freshman calculus students.     

束流相空间与束流发射度椭圆的对应

研究了束流传输理论沿用的束流相空间与实测束流发射度椭圆之间的对应关系,推导了束流相空间参数与束流椭圆对应关系的表达式,为束流传输理论与束流测量实验之间的相互验证提供了直接依据。     

椭圆曲率中心轨迹——星形线的特性

采用微分几何方法分析了椭圆星形线的多项特性,指出了其中星形线划分平面的特性对于椭圆上的点离已知点距离极值存在性的决定性作用,同时指出了星形线划分平面的特性对于确定椭圆上距离任意已知点最远或最近的点的位置具有决定性意义,提出了确定最远点及最近点的几何方法,阐明了最远点及最近点在各极值点之间的替换过程,为工程中确定圆柱面绕任意轴回转所形成的包络面的特性提供了依据.     

Representation of a Monotone Curve by a Contour with Regular Change in Curvature

The problem of modelling a smooth contour with a regular change in curvature representing a monotone curve with specified accuracy is solved in this article. The contour was formed within the area of the possible location of a convex curve, which can interpolate a point series. The assumption that if a sequence of points can be interpolated by a monotone curve, then the reference curve on which these points have been assigned is monotone, provides the opportunity to implement the proposed approach to estimate the interpolation error of a point series of arbitrary configuration. The proposed methods for forming a convex regular contour by arcs of ellipses and B-spline ensure the interpolation of any point series in parts that can be interpolated by a monotone curve. At the same time, the deflection of the contour from the boundaries of the area of the possible location of the monotone curve can be controlled. The possibilities of the developed methods are tested while solving problems of the interpolation of a point series belonging to monotone curves. The problems are solved in the CAD system of SolidWorks with the use of software application created based on the methods developed in the research work.     

实现任意方向椭圆绘制的简便方法

在分析VC中椭圆绘制方法的基础上，描述了绘制任意方向椭圆的一种简便方法，从任意方向椭圆的绘制也可以引申到任意方向的双曲线和抛物线的绘制。     

一种基于长轴和对偶性的椭圆检测新算法

提出一种新的基于椭圆长轴信息的椭圆检测算法,利用椭圆长轴信息来确定椭圆的四个参数,并利用累积的方法得出短轴的值。在确定长轴时,利用椭圆的对偶性对长轴做出验证。实验表明,该算法比原长轴算法降低了运算时间。