Differential geometry properties of lines of curvature of parametric surfaces and their visualization

We present algorithms for computing the differential geometry properties of lines of curvature of parametric surfaces. We derive a unit tangent vector, curvature vector, binormal vector, torsion, and algorithms to evaluate their higher-order derivatives of lines of curvature of parametric surfaces. Among these quantities, it is shown that the curvature and its first derivative of the lines of curvature lend a hand for the formation of curved plates in shipbuilding. We also visualize the twist of lines of curvature, which enables us to observe how much the osculating plane of the line of curvature turns about the tangent vector.     

Application of structural curvature of coalbed floor on CBM development in the Zaoyuan block of the southern Qinshui Basin

Based on controls of structural style and the position in coalbed methane(CBM)development,we used a method of curvatures to study its relations with CBM development parameters.We calculated structural curvatures of contours of the No.3coal seam floor of the Shanxi Formation in the Zaoyuan block of the Qinshui Basin and analyzed its relations with development parameters of coalbed methane wells.The results show that structural curvature is negatively related to coal reservoir pressure,while positively related to permeability.With an increase in structural curvature,the average production of coalbed methane wells increases at first and then decreases,reaching the highest production at 0.02 m-1 of structural curvature.Therefore,structural curvature can be an important index for potential evaluation of coalbed methane development and provide a basis for siting coalbed methane wells.     

一种带曲率补偿的高精度带隙电压基准源

本文提出了一种带运放失调电压补偿结构和分压式二阶曲率补偿结构的低温度系数带隙基准电路。设计目标为对便携设备提供0.8V的电压。基于华虹CZ6H工艺在CADENCE软件TT模型下仿真,仿真结果表明,带隙基准电压源在-40℃-120℃温度范围内温度系数仅为1.77×10-6/℃,电源抑制比(PRSS)在低频下为86.9dB。在3V-6V的电源电压工作范围内,输出电压摆幅为0.171mV。     

非轴对称光腔的矩阵光学分析

用矩阵光学理论对一般非轴对称光学谐振腔进行了研究,得出基模本征解。讨论了约束稳定、非约束稳定及准约束稳定的条件。指出这种腔在一般情况下存在双解。所得结果适用于多元件非轴对称光腔,具有普遍性。     

基于面图标的三维对称张量场可视化研究

现有的三维对称张量场可视化的面图标方法,仅表现了张量场的某一特征向量场在面图标上的方向信息,而没有表现出特征向量场的大小,基于此,提出了在面图标上通过绘制三维等值线及利用颜色属性来表现特征向量场的大小信息,这样,面图标就将特征向量场的方向和大小信息同时表现出来,从而进一步完善了三维对称张量场的面图标方法,更全面地揭示了张量场位于空间曲面上的信息。     

一类张角问题的研究

将工程设计计算中常遇到的要在一定范围内求对一物体有最大张角的点的位置问题，抽象为在平面曲线上确定对曲线外一线段有最大张角的点的位置，应用微分几何中关于曲线密切圆与曲率半径的有关理论推证，寻找到视角与曲线密切圆半径的关系，得到了可用简单的几何作图或解析计算求已知线角点，张角值区间，最大或最小张角点等问题的一般结论和方法。     

假捻器轴承优化设计分析

为了进一步提高HT825型假捻器轴承的综合机械性能,对其轴承的沟曲率半径、外圈沟心距、圆度、钢球等级、径向游隙参数进行优化设计,并从球轴承沟曲率半径系数、轴承游隙、接触角、原始偏转角、实际接触长度、径向基本额定动载荷、径向额定静载荷、当量动载荷和寿命等方面对HT825型轴承的设计参数进行计算,并对计算结果参照常用参数值进行分析验证。结果表明,优化后的假捻器轴承对提高转速有利,可提高轴承支承轴刚性,满足寿命及使用要求。     

青年男性肩点横截面曲线及其体型细分

为建立基于横截面曲线形态指标细分青年男性肩部体型的方法,选取了年龄在18~26周岁的213名在校青年男性,用三维人体扫描仪测量获得其肩部数据,借助IMAGEWARE 12.0与Mat Lab R2012b软件,利用冒泡排序算法实现了肩点的自动准确提取,且肩高相对误差控制在(0,0.011)之间;通过分析肩点横截面形态特征,提取了曲线曲率半径及矢额径比作为分类指标,对比曲率半径均值,确定了5个特征点角度为-50°、-35°、0°、50°与90°;应用K-Means聚类方法及方差分析,将肩部体型划分为4类,建立了依据特征点曲率半径与矢额径比细分肩部体型的方法,通过对比肩点截面曲线形态,进一步定性描述了4类肩部截面的曲线变化特征。     

Stereology of tubular structures

The morphology of a tubular structure can be characterized, in at least some of its important respects, through stereological methods. We study the geometric meaning of standard stereological quantities when applied to tubular structures, with particular regard to their curvature or tortuosity. Measures defined specifically in relation to tubular structures are also introduced for practical use. The ideal smooth bent cylinder, used here, is not realistic but provides general principles from which a more specialized investigation should be developed. The emphasis is placed on simple counting methods of measurement, specifically the tangent counts introduced by DeHoff, and counts of section profiles exhibiting a particular character (such as ‘figure-eights’). These measures convey information about the tortuosity of tubular structures, whereas the standard indices V_v, S_v, M_v give no information about tortuosity. Some data from human testicular tubules are discussed.