共线点

通过一题十种证法试图说明，共点线（共线点）问题的证明在高等几何中的重要作用。

This paper intends to illustrate the important role of the proof of concurent line or collinear point in higher geometry through ten solutions to one question .

共线点电荷系的电力线方程

The Power Line Equation for Collinear Point Charge

用共线点列标定摄像机镜头畸变

Camera lens distortion calibration with co-line points

非共线点的拼五小组

Pentad of noncollinear points

对射影几何中的共点线（共线点）定理之间的关系进行探讨，给出它们有关的对偶关系和等价关系。

This paper discusses the relations between concurrent lines theorem and collinear points theorem of the projection geometry , and obtains their duality relation and equivalence relation .

提出一种用共线点列标定摄像机镜头畸变参数的方法，先根据交叉比不变性确定畸变中心，再利用直线的中心投影仍为直线这一性质确定畸变系数。

A camera calibration method with co-line points is proposed , in which distortion center is located according to cross ratio invariability , and then distortion coefficients are calculated based on a line 's central projection is a line .

介绍了基于AutoCAD绘图平台用VISUALLISP语言编程计算任意不共线三点的圆心坐标；并介绍同时绘制图形以及生成部分加工程序的方法。

Introduces the method of calculating the centre of a circle coordinate of 3 unconditional and unco-linear points and drawing graphs and generating part of process procedures on AutoCAD using Visual LISP language .

地&月系共线平动点L2相对地球和月球不变的空间位置使得它在月球背面探测任务中起着十分重要的作用。

The collinear libration point L2 of the earth-moon system plays an important role in exploration of the back of the moon for its relatively fixed position with respect to the earth and the moon .

而某些探测任务，探测器定位在共线平动点附近的条件拟周期轨道（对应Lissajous轨道）上亦可以。

For some missions , requirements can be met to position an explorer in the conditional quasi-periodic orbits ( Lissajous Orbits ) around the collinear libration points .

深空探测器需要定位在日-地（月）系的共线平动点L1或L2附近执行探测任务，但由于共线平动点的不稳定性，必须在运行期间进行轨控。

Deep space explorers should be positioned around collinear libration points L_1 or L_2 of the Sun-Earth ( Moon ) system to carry out exploration missions . Due to instability of collinear libration points , station-keeping must be implemented during operation to achieve this .

圆型限制性三体问题（CRTBP）共线平动点附近存在着大量的周期轨道族。

There are plenty of families of periodic orbits surrounding the collinear libration points in Circular Restricted Three-body Problem ( CRTBP ) model .

进而，基于日地系共线拉格朗日点附近无控运动的周期性，设计了保持控制方案，对传统靶点法和基于周期轨道单值矩阵的Floquet法进行了仿真研究。

Then , after analyzing the periodic characters of the uncontrolled movements near the Sun-Earth collinear Lagrange points , the station keeping schemes are designed . The target-point method and Monodromy matrix based Floquet method are presented with simulations .

深空探测器定位在共线平动点附近的线性策略

Linear Strategy for Positioning of Spacecraft around the Collinear Libration Points

关于探测器定点在共线平动点附近的控制问题

On Orbit Control of Spacecraft around Collinear Libration Points

关于共线平动点的特征及其在深空探测中的应用

On Characteristics of Collinear Libration Points and Their Applications in Deep Space Exploration

最近分数，最近有理近似法共线平动点附近周期轨道的分析研究方法

Analyzing the periodic orbits around the collinear liberation points

基于共线特征点的摄像机镜头畸变校正

Correcting distortion of camera lens with collinear points

复共线影响点的主成分诊断

The Principal Component Diagnosis For the Multicollinearity-Influential Cases

在测量过程中只要能够保证公共区域中包含3个以上的非共线参考点，就能够实现点云数据的自动拼合，不需要人工干预。

Only three non-collinear points belongs to public area must be identified during measure process , the registration process is completed automatically after that .

用靶标上任意3个非共线特征点的三维坐标建立单位正交基，从而求得多视点云坐标系初始变换矩阵。

By establishing unit orthogonal basis using 3 arbitrary non-colinear points on the target , the original coordinate frame transformation matrix for multi-view point clouds was found .

这种类型的轨道可以离共线平动点较近，那么只需要在控制过程中考虑线性项即可，控制条件简单。

Orbits of this type can be positioned near collinear libration points , and for simplicity it is adequate to take linear terms into consideration in the control process .

不考虑机构末端动平台的自由度形式，空间刚体的位置和姿态可以由选定的与刚体固联的不共线三点决定。

Without taking the DOF types into consideration , the position and orientation of a rigid body can be determined by three non-collinear points attached to the rigid body .

提出一种基于未知世界坐标共线特征点的未标定摄像机畸变校正算法以及基于预计算模板的快速实现方法。

A method for distortion correction of un-calibrated lens with unknown collinear feature points is proposed and the improved fast distortion correction calculating method based on pre-computing template is implemented .

非线性系统最优控制辛算法的研究与应用。（1）针对共线平动点附近轨道上航天器编队重构中非线性轨迹优化需求，提出非线性系统最优控制的辛算法。

The research and application of the symplectic algorithm for nonlinear optimal control . ( 1 ) For the nonlinear trajectory optimization requirement of spacecrafts formation reconfiguration near the libration , the symplectic algorithms for nonlinear optimal control are proposed .

首先论证了奇异的运动学原理：物体上非共线三点的速度的三个法平面的交点，能落于该三点决定的平面上。

This paper firstly proves the kinematics principle of singularity , that the intersecting point of the three normal planes of the three velocities at the three non-collinear points in a rigid body lies in the plane determined by the three corresponding points .

本文讨论平面上无三点共线的有限点集。设P为一个无三点共线的有限平面点集。

In this paper we consider only finite planar point sets in which no three points are collinear .

该规约采用变长帧传输数据（最长可达255字节），提高了通信系统的速率，且适用于点对点、多点共线及一点对多点的通信方式。

Long variable frames ( as long as 255 bytes ) are adopted to improve the rate of communication .

提出了利用3个不共线的控制点对相机外参数近似值进行快速求解的一种方法。

The paper puts forward a method to calculate quickly synoptical elements of exterior orientation by three control points .

本文从仿射变换的角度出发，对于不共线三个点，构造出过面积最小的椭圆，并进行了证明。

We give the proof and construction of the minimum-area ellipse through three non-collinear points from the geometric point of view , and present a new method of determining knots .

该方法利用了透视投影中的交比不变性质，在畸变模型为一阶径向畸变的情况下，只需要空间共线的4个点的图像坐标和其交比，建立一元二次方程即可标定畸变参数。

It overcomes the disadvantages of existing distortion calibration approaches . Assumed only with one order radial distortion , image coordinates of only 4 special collinear points are needed as well as the cross ratio of them .