查询词典 differential geometry

For the application of Mathematica in the differential geometry,this paper introduces how to processe the curve curvature and the torsion questions,the graphic expression of the curvature and the torsions,and draw curves by the curvature and the torsions. Curvature ; torsion ; solution curve ; osculating plane ; natural parameter ; natural equation

利用Mathematica，只要输入有关系统命令就可以得到期望的结果。1曲率和挠率及其图形意义假设R3上的曲线一般参数表示为r=r它的曲率和挠率计算公式是：κ=‖r′×r"‖‖r′‖3τ=‖r′×r‖我们知道，空间曲线r=r在一点(s=s0)邻近的近似方程为ξ=sη=120κs2ζ=160κ0τs3通过近似方程可以确定曲线在其基本三棱形的三个平面(即密切平面，法平面，从切平面)上的投

Riemannian normal coordinates contain information about the direction and distance from a specific point on a manifold to other points nearby. It is worth to translate this technique from its original setting in differential geometry, to the task of manifold learning.

黎曼正则坐标包含了流形中指定点到邻近点的方向和距离信息，如何将这种源于微分几何的技术应用到流形学习中也是值得研究的课题之一。

In 1986, R.D.Cook proposed differential geometry to assess local influence of minor perturbations of linear statistical models. Poon and Poon(1999) constructed a conformably invariant curvature , the conformal normal curvature, for the same purpose.

Cook(1986)用微分几何的方法评估了线性统计模型微小扰动的局部影响，Poon and Poon(1999)改进了Cook提出的统计曲率概念，定义了保形法曲率。

The interpolate algorithms of three-order NURBS curve and double three-orders NURBS surface are presented. The expressions of partial derivative and normal curvature of NURBS surface are derived by the theory of differential geometry. The geometric characteristics of different curvature area of the free-form surfaces are analyzed in detail. All these work lays a theoretical foundation for constructing the cutter location calculating model of free-form surfaces NC machining. 2 On the basis of analyzing the methods of cutter path generation, the standard of evaluating the various methods of cutter path generation is presented. The method of generating cutter path with constant scallop height is presented for the first time.

本文以提高复杂曲面多坐标数控加工精度和加工效率为目的，在对国内外研究现状进行深入分析的基础上，对数控编程中各环节的关键技术问题进行了深入研究，主要内容包括以下几方面： 1 分析了复杂曲面各种造型方法的优缺点，给出了根据各种边界条件所确定自由曲面的NURBS表示方法以及三次NURBS曲线曲面反算算法；用微分几何理论推导了NURBS曲面的偏导矢及法曲率计算表达式；对曲面不同曲率特性区域的几何特征进行了深入分析，为建立复杂曲面的数控加工刀位计算模型奠定了理论基础。

With differential geometry knowledge, the local characters of the blade surface are analyzed. Based on researching the cylindrical cutters osculating location, the methods to calculate the osculating location of the conic cutter and the torus cutter are discussed. A method of tool path planning based on the second order osculating method is preferred.

利用微分几何学知识，分析了螺旋桨桨叶曲面的局部特征，在研究圆柱刀二阶密切法规划刀位的基础上，探讨了圆锥刀和圆环刀的二阶密切刀位计算方法，采用二阶密切法规划刀位可以显著地提高加工精度。

The implicit or parametric surface has been defined very well in differential geometry.

在传统微分几何中，隐式曲面或参数曲面有完备的定义和计算公式。

The basic idea is as follows: with the help of the related results of differential geometry, the problem of interpolating curve on a parametric surface is converted to a similar one on its parametric plane.

基本思想是借助于微分几何的有关结论，曲面上曲线的插值问题被转化为其参数平面上类似的曲线插值问题。

By using the Li e group theory of differential geometry and Pontryagin's maximum principle, it is pointed out that the mobile CRS robot on surface is controllable, and the nec essary conditions and the structure equations of extremal trajectories are propo sed.

为了解决曲面上移动CRS机器人的路径规划问题，在曲面上建立了机器人的动态模型，利用微分几何的李群理论和庞特里亚金最大值原理，证明了曲面上CRS机器人是可控的，并给出了机器人的最小时间控制的必要条件和结构方程。

Thus, to study tooth surface curvature is significant. However, from the published information, the curvature of face gear drives hasn′t been well studied until now. Based on the knowledge of differential geometry, a method for calculating principal curvature and principal directions for face gears is established, and thus the principal v...

文中利用微分几何原理推导了面齿轮传动的齿面主曲率与主方向，由此得出面齿轮传动中诱导法曲率的两个主值；开发了相应的程序；进行了实例计算；分析了传动中的主要参数对曲率的影响，所获得的结论对面齿轮传动的强度计算与分析具有参考价值

In accordance with the characteristics,the maximum and minimum principal curvatures of surface were calculated,and then,automatic threshold was used to segment curvature images.

标 签 人耳识别特征提取边缘检测微分几何主曲率 ear recognition feature extraction edge detection differential geometry principal curvatures

Do you know, i need you to come back

你知道吗，我需要你回来

Yang yinshu、Wang xiangsheng、Li decang,The first discovery of haemaphysalis conicinna.

1〕 杨银书，王祥生，李德昌。安徽省首次发现嗜群血蜱。