共点直线

On depending on author's perception of teaching 《analytical geometry》,raising a warning about the phenomenon of student's neglect of the use of vector in exercise,this essay elucidate the preponderance of vector in solving problems about space.

在中学，解析几何课程主要研究平面上一些点、线的几何位置和几何性质，所涉及的点、直线、曲线均共面，它们都落在坐标系所在的平面内。

Traditional photogrammetry was based on forward intersection and resection using survey point, so collinear equation （object point, image point and center of projection lie in a line） was the kernel of the whole photogrammetry, and relative orientation and absolute orientation were based on ideology of coplanar corresponding image point.

传统摄影测量是基于测点的前方交会和后方交会，所以共线方程（即物点、像点与摄影中心位于一条直线上）是整个摄影测量的核心。

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.

摘要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。

The vanishing points of all lines in the same plane are colinear at the vanishing line of the plane.

同一平面上的所有直线对应的消失点共线于该平面的消失直线。

Recently, a linear algorithm of projective reconstruction based on the homography induced by the infinite plane was given by Hartley and Rother et al., but they needed 4 points on a reference plane be visible in all views.

因为空间中不在同一直线上的3个点恰好确定一个平面，所以它避免了Hartley和Rother等方法中需要确定空间4个点是否共面这一比较棘手的问题。

Construct an animation displaying a nephroid sliding along three fixed concurrent lines meeting at 120 degrees.

建构一动态绘图。展示肾脏线的滚动，沿著共点及间隔120度的三条直线。

A plane figure consisting of four points, no three of which are collinear, connected by straight lines.

四边形，四角形由四个角组成的平面图形，没有任何三个点共线，通过直线相连接

Mathematics A plane figure consisting of four points, no three of which are collinear, connected by straight lines.

四边形，四角形：由四个角组成的平面图形，没有任何三个点共线，通过直线相连接

Years ago, the great mathematician Archimedes trisection of an arbitrary angle with compass, ruler, and mark points on the feet, so that mark point to the foot end of the length of the radius is equal to angle; to straightedge movement, so that mark-point arc always on the move, adjust, and when the foot end of the marking points on the feet, and other requirements that have a total of three points simultaneously in ruler now has been online; a total of nine actions to complete.

2400年前，大数学家阿基米德作任意角三等分，用圆规，直尺，且在尺上做记号点，使记号点至尺端的长度等于角圆弧半径；将直尺移动，使记号点始终在圆弧上移动、调整，当尺端、尺上记号点、和其它有要求的一点，共三点同时在直尺的一直线上；共九个动作完成。

The special geometric restrictions like parallelism andperpendicularity implicated in vanishing elements are deeply studied. In single-view case,the theory is presented to interpret relationship between two planar lines by applying 3Dinvariants of vanishing points. In two-view case, the method on extraction vanishing pointof an arbitrary spatial line is described, and moreover, the theory is presented to interpretrelationship between two elements in 3D space, such as two lines, two planes, line andplane, and so on.

4详细论述了消失元素(消失点、消失直线、消失平面等)所体现的垂直、平行等特殊几何约束关系；对单视图，提出了一种利用消失点列的3D不变量解释平面直线关系的方法；对双视图，提出了利用自共轭三角形和对极几何约束，提取任意直线的消失点的算法，并在此基础了提出了一种利用消失元素的3D不变量解释直线间、直线与平面间、平面间等多种空间几何关系的方法。

Cynanchum Lingtai apricot production in the average weight 65 grams, the brightly-colored fruit, juicy rich, sweet-sour taste, sweet from the nucleolus, when the late Qing Dynasty famous Shaanxi, Gansu provinces, the Qing imperial court Tongzhi tribute for years.

灵台生产的牛心杏平均单果重65克，果实色泽鲜艳，汁多味浓，甜酸适口，离核仁甜，清末时就驰名陕、甘两省，清同治年间曾为朝廷贡品。

Chenopodium album,Solanum nigrum, and Amaranthus retroflexus were very susceptible to the herbicides. Polygonum persicaria and Abutilon theophrasti were relatively less susceptible to the herbicides, and Lycopersicon esculentum was not susceptible to it. The relationship between reduction rates of weed biomass and PPM values of weed leaves 2,4, and 6 days after treatment was established.

供试的6种杂草对该混剂的敏感性存在显著差异：红心藜Chenopodium album、龙葵Solanum nigrum和反枝苋Amaranthus retroflexus对该混剂最敏感，ED90值分别为47.65、71.67和29.17g/hm2；春蓼Polygonum persicaria和苘麻Abutilon theophrasti敏感，ED90值分别为96.91、114.20g/hm2；而番茄不敏感。