测地线

Furthermore, under the assumption that the covariant derivative of the sectionssatisfies the Lipschitz condition with L-average along the geodesic, the estimates of the radiiof convergence balls of Newton\'s method and uniqueness balls of singular points around thesingular points of sections on Riemannian manifolds are given.

当截面的协变导数满足沿着测地线的关于取正值非减可积函数L-平均的Lipschitz条件条件时，本文给出关于截面的Newton法的收敛球半径的估计，及在奇异点附近的关于截面的奇异点的唯一性球的半径的估计。

Under the assumptionthat the covariant derivative of the sections satisfies the Lipschitz condition with L-averagealong the piecewise geodesic, a unified convergence criterion for Newton\'s method and theradii of the uniqueness balls of singular points around the initial points of sections are es-tablished.

本章的主要内容包括以下两个方面：当截面的协变导数满足沿着分段测地线的关于取正值非减可积函数L-平均的Lipschitz条件条件时，本文给出了关于截面的Newton法收敛的统一判据，同时给出了在初始点附近的关于截面的奇异点的唯一性球的半径的估计。

It is based on the discrete model of finite analysis to get curvature ,normal vector, direction and geodesic curve,then to analyze and design the structure.

基于有限元分析的离散模型，将离散微分几何领域的最新成果运用于膜结构设计，求解曲面曲率，法向量，主方向及测地线，进行结构分析设计。

It is impossible to logically infer the classically expressed geodesic differential equation from the ontology differential geometry. Besides, the initial proposition how to construct a functional extreme value problem for the shortest curve on a surface, which was supposed first by Gauss, would be an improper formal expression with a wrong premise.

不仅仅无法由"实体论"微分几何逻辑地推导出经典的测地线方程，而且Gauss曾经为"曲面上最短线"问题所构造的泛函极值命题，实质上属于一个"前提认定"完全错误的不当表述。

Curvature of Surfaces, Gaussian Curvature and the Gauss map, Geodesics, Minimal

行移动和测地线，最小曲面，高斯朋涅定理等。

Then 3D surface can be flattened to 2D plane from the center line by geodesic curvature method, and an accurate 2D pattern can be created through carrying out the numerical simulation.

然后以仿测地线曲率法，从摊平基准线将3D 曲面摊平展开至2D 平面上。并进一步透过数值迭代运算得到精确的2D 裁片外形。

We use multi-source points, compute the initial section with geodesic distance and determine the key point while the section moves front.

本文提出一种从散乱点集上自动抽取骨架的算法，它使用多个起始点，根据测地线距离计算初始截面，此后在截面推进过程中自动判别关节点。

The main advantages of EGGLE include:the fixed neighborhood parameter k,only one time for constructing neighborhood graph and geodesic distance matrix,only needing to choose generalized Gaussian functions many times for constructing many Laplacian matrixes,obtaining multiple independent low-dimensional coordinate sets, independently training multiple classifiers,and combining classification results of these component classifiers to produce the final identification.

3提出了一种基于GGLE的集成判别算法，该算法的主要优点是：近邻参数k固定，邻接矩阵和测地线距离矩阵都只构造一次，只需要多次选择广义高斯型函数构造多个拉普拉斯矩阵，获取多个独立的低维空间坐标集合，独立学习分类器，集成分类识别。

In the fifth chapter, some usual cutting pattern methods such as Least Square method, Dynamic Programming method, Geodesic Line method are introduced.

本文第五章总结了一些膜结构的裁剪分析方法如最小二乘法，动态规划法，测地线法等。

Based on form-finding of the force density method,load analysis of the nonlinear finite element method and geodesic line cutting method,this paper summarizes some outlines in the design and construction of membrane structures.

以小商品城入口膜结构工程为例，结合力密度法找形、非线性有限元荷载分析、测地线裁切等基本理论，给出大型张力膜结构的设计与施工方法，总结了膜结构设计、施工的一些要点和经验，能给同类工程提供有益的参考。

I bought a nice wrist watch as a surprise for my wife's birthday.

我买了一个漂亮的手表想要给我妻子的生日一个惊喜。

We don t expect students to be sponges. You can t expect to absorb everything and not have any questions to ask.

我们并不期待我们的学生是一块海绵，你没可能接收所有的东西而不提出任何问题。