测地线

For the elliptic cylindrical surface which is the trunk of the blade,the geodesic and non- geodesic differential equations are deduced.

并针对叶片主干部分的椭圆柱面，分别推导其测地线和非测地线的微分方程式。

Based on the study on generation methods of cutting patterns, new methods for generating Geodesic Line, called Updated Geometrical Method, and for generating cutting pattern, called Secondary Geodesic Line Method, were put forward.

之后，在对各种裁剪分析方法比较和研究的基础上，提出了生成测地线的修正几何法和裁剪条元展开的二次测地线法，并编制了相应的计算程序。

A generalized Gaussian Laplacian eigenmap algorithm based on geodesic distance is proposed,which incorporates geodesic distance and generalized Gaussian function into the original Laplacian eigenmap algorithm.GGLE algorithm can adjust the similarities between nodes of neighborhood graph,and can preserve the different degrees of local properties by using super-Gaussian function,Gaussian function or sub-Gaussian function.Moreover,GGLE can avoid the deficiency of Euclidean distance by using geodesic distance when neighborhoods of data points are enlarged for preserving more neighborhood relations.Experimental results show that the global low-dimensional coordinates obtained by GGLE have different clustering properties and different degrees of preserving local neighborhood structures when different generalized Gaussian functions are used to measuring the similarities between high-dimensional data points.(3) An ensemble-based discriminant algorithm based on GGLE is proposed.

该算法将测地线距离和广义高斯函数融合到传统的拉普拉斯特征映射算法中，可以调整近邻图结点间的相似度，通过选择超高斯、高斯或者次高斯函数来实现不同程度的近邻局部特性的保持；而且当需要保持更多的近邻关系使得数据点邻域增大时，采用测地线距离可以避免欧氏距离度量不合理的缺陷；实验结果表明在用不同的广义高斯函数度量高维数据点间的相似度时，局部近邻结构保持的程度是不同的，GGLE获得的全局低维坐标也呈现出不同的聚类特性。

On the basis of the Updated Geometrical Method and Secondary Geodesic Line Method, the technique to find Geodesic Line between any two points in the curved surface is suggested.

在修正几何法和二次测地线法的基础上，解决了空间有限曲面上两点间无法做出测地线的问题。

In the field, the popular methods include: using Kalman filter or Particle filter to estimate motion, estimate the optical flow, utilizing the active contour model, the active shape model and the deformable template to tracking the objects, and using the Geodesic active contour model or Geodesic active region model which based the partial difference equation method and level set frame.

在该领域常用的方法有利用Kalman滤波及粒子滤波进行运动预测，通过计算光流评价目标运动，利用活动轮廓模型，活动形状模型，可变形模板等主动形状模型方法以及测地线活动轮廓模型，测地线活动区域模型等基于偏微分方程的方法来跟踪目标运动。

By the definition of Darboux type vector and rectifying Darboux type vector ,we constructed the rectifying type developable surfaces and Darboux type developable surfaces and tangential Darboux type developable surfaces ,and study these three developable surfaces relationship with Minkowski slant helices and Minkowski conical geodesic curves. Bying applying the singularity theoerical knowledge, We give a classification of special developable surfaces under the condition of the existence of such a special curve as geodesic.

通过定义三维Minkowski空间中的达布型向量以及修正达布型向量，构造出三维Minkowski空间中的三类可展曲面，即修正型可展曲面、达布型可展曲面和切达布型可展曲面，研究Minkowski斜螺线和Minkowski锥面测地线这两种特殊曲线和这些曲面的关系，并研究Minkowski斜螺线和Minkowski锥面测地线作为这些曲面的测地线的条件下，运用奇点理论的知识，对这三种可展曲面进行奇点分类。

For any two vertices u and v of a graph G, a u-v geodesic is the shortest path between u and v. The set I consists of all vertices lying on a u-v geodesic. For SV, I is the union of all sets I for vertices u, v∈S. The geodetic number g is the minimum cardinality among the subsets S of V with I=V.

对于图G内的任意两点u和v，u-v测地线是指在u和v之间的最短路。I表示位于一条u-v测地线上所有点的集合，对于SV，I表示所有I的并，这里u，v∈S，G的测地数g是使I=V的最小点集S的基数。

Additionally, the approximate flattening of surface strip using lines linking midpoints on perpendicular lines between geodesic curves and the unconditional extreme value method are discussed.

提出了用测地线方程、曲面上两点间短程线来计算膜结构曲面测地线的方法，同时，采用测地线间垂线的中点连线和用无约束极值法进行空间条状曲面近似展开的分析。

However,there have been no papers which have investigated Minkowski and Minkowski slant helices and Minkowski conical geodesic curves so far as.In this paper,our major study is to give the definition of Minkowski general helix and Minkowski slant helices and Minkowski conical geodesic curves in indicators 1 in pseudo-Euclidean three-space (that is, three-dimensional Minkowski space), and study the definition of equivalence Minkowski general helix, By considering geometric invariants of these space curves, we can estimate the order of contact with those special curves for general space curves.

本篇文章主要研究在指标数为1的3维伪欧氏空间(即三维Minkowski空间)中，我们给出Minkowski一般螺线、Minkowski斜螺线和Minkowski锥面测地线的定义，研究Minkowski一般螺线的等价定义，给出Minkowski斜螺线和Minkowski锥面测地线作为三维Minkowski空间中的特殊曲线所特有的性质，并通过考虑三维Minkowski空间曲线的几何不变量，估计Minkowski斜螺线和Minkowski锥面测地线这两种特殊曲线和一般Minkowski空间曲线切触的阶数。

The stable winding equations of the elbow torus and cylinder are established according to different geometry, and the winding pattern of the geodesics of torus and semi-geodesics of cylinder are also achieved.

根据微分几何建立弯管的圆环面及圆柱面稳定缠绕方程，给出了圆环面的测地线缠绕解及圆柱面的半测地线缠绕解，并提出了用OpenGL及VC++对所设计的线型进行仿真的具体实现办法。

In the negative and interrogative forms, of course, this is identical to the non-emphatic forms.

。但是，在否定句或疑问句里，这种带有"do"的方法表达的效果却没有什么强调的意思。

Go down on one's knees;kneel down

屈膝跪下。。。下跪祈祷