参数曲率

The surface representation in discrete form and its differential computation are important issues in computer graphics and geometric design.

0引言一般来说，曲面的一阶微分量是指曲面的切平面方向和法向量，二阶微分量是指曲面的曲率等有关量·它们作为重要的曲面信息度量指标，在计算机图形学，机器人视觉和计算机辅助设计等领域发挥了重要的作用·传统的曲面是连续形式的参数曲面和隐式曲面，其微分量的计算已经有了较完备的方法·随着激光测距扫描等三维数据采样技术和硬件设备的长足进步，以及图形工业对任意拓扑结构光滑曲面造型的需求日益迫切，离散形式的曲面———细分曲面、网格曲面和点云曲面正在逐渐成为计算机图形学和几何设计领域的新宠·于是，对这种离散形式的曲面如何估

The abc are to get the generic "default parameters" for use in the comparison program CONTRAST which aligns protein sequenes based on their 3D-structure, to confirm the efficiency of the differential -geometric representation of protein backbone by comparing 3 different algorithms of the curvatures and tortions, and tO find apropriate gap penalty function.

中国科学院上海生物化学研究所，上海 200031摘要：继前面的工作把测试蛋白从三族扩大到十一族，寻求联配参数的普适"缺省值"；比较不同的主链曲率和挠率的计算方法，进一步确认主链的折线线分几何刻划方法的有效性；寻找有效的可变缺失突变惩罚函数的形式。

A family of straight lines of the indenter's curvature versus the external load under different contact zone is obtained.

由此可以得到以接触区尺寸为参数的接触压力与压头曲率的关系直线族。

Then the influence of the different Coanda surface shapes including the circle, elliptical and logarithmic spiral TE geometries on the performance of the circulation control airfoil were investigated.

在此基础上研究了具有圆、椭圆和对数螺线形式柯恩达表面的环量控制翼型性能的变化，初步探讨了射流层附壁与高曲率表面特征参数的关联。

In the last part of this dissertation, we discuss how to model an image is discussed and how to segment an image by EDEK.Zero-Cross principle is a classical concept in signal processing. We generalize the concept to be zero normal curvature after the geometry frame built. Furthermore, we present the explanation to choose the dual parameters in SPMVIF. And we research why the Laplacian gradient superior to edge gradient.

梯度方向二阶导数过零原理是信号处理中的经典结论，在运用微分几何的知识建立SPMVIF的几何框架的同时，将这个结论推广到零-法曲率的形式；另外我们对SPMVIF的双参数选取规则进行了讨论并给出它们的几何意义，并且对SPMVIF中法向矢量选取时拉普拉斯梯度优于边缘图像梯度的结论给予统计信息熵的解释。

The errors and area limits caused by the lunar curvature were avoided in this model established under the Selenocentric Orthogonal Coordinate System, the accidental errors of exterior line elements were reduced by orbit fitting and interpolation, the polynomial orders of systematic errors in satellite orbits were decreased with their expression in the flying coordinate system moving and rotating with satellites, and the reliability of exterior orientation solution was enhanced under the condition of sparse and low accuracy control points by appending constraint of orbit and attitude parameters.

该模型通过在月心直角坐标系进行影像空中三角测量来消除月球曲率引起的误差和测图范围限制，通过轨道形状的拟合与插值来减小摄影时刻轨道位置的偶然误差，在飞行坐标系中建立轨道修正模型来减少定向参数的数目，对轨道和姿态增加约束条件来提高月面控制点数目稀少及精度低条件下外方位解算的精度与可靠性。

M-φ hysteretic model is given on the basis of integral calculation and parameter analyze for CFST compression-bending member.

在有限元模拟和参数分析的基础上，提出了钢管混凝土压弯构件弯矩—曲率滞回模型。

Consider a plane curve with parametric equation.

设平面曲线的参数方程为，则曲率为

The quadratic patches is fixed,and its parametric representation method is gained.The cubic patches reduce to three local factors through reducing Bernstein coefficients to control shape of curve,two of them are used to join segments into G2- continuity approximating curves for given sequence data in space,and the other is used to adjust shape of segment.

先固定二次曲面片，并得到其参数形式，然后约简三次曲面片所对应的Bernstein系数，使之为带有三个形状调整的形状因子，其中两个分别代表曲线段端点处的曲率，另外一个作为形状的调整。

In addition to measure the refractive index profile of a GRIN lens, we also measure the refractive profile and radius curvature of a Plano-convex lens by means of this imaging ellipsometric technique.

本文将此简式影像式椭圆偏光术应用在非均匀平面材料光学参数之量测，及平凸透镜之量测；我们不但量出了渐变式光纤折射率的径向分布并证明其表面的平整度，另外也量出平凸透镜的曲率半径及折射率。此法可将椭圆偏光术延伸到曲面薄膜量测。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。