共点面

In this paper, cross ratios of the four collinear points and five coplanar points were analyzed first, then some affecting factors were concluded, and some constraints were proposed on constructing model-based object recognition system.

首先对共线4点和共面5点构成的交比不变量的稳定性进行了分析，得出了影响稳定性的因素，然后提出在构造目标识别系统的模型时应注意的约束条件，实验表明：在这些条件下构造模型的抗噪声能力大大提高。

And an evaluating method for coplanarity is adopted,which is based on least condition principle.

提出一种基于激光跟踪原理对空间点的坐标进行测量，采用"最小条件"法为基础的共面性评价方法，实现了对由多个非连续铅垂面形成大平面的平面度的高精度测量，实际测得共面度为0。

With the constraints of these feature points, perspective projection, coplanarity and colinearity, the curved surfaces can be recovered by minimizing the linearly constrained quadric objective function.

把特征点的位置、共面、共线、透视投影等作为约束，通过最小化线性约束下的二次目标函数实现曲面重建。

In the roof reconstruction, a TIN-based region growing is applied to extract the roof planes. The coplanarity and adjacency between triangles are considered for TIN-based region growing. Then, a least squares regression is selected to determine the coplanarity function of planar segment.

在建物屋顶面重建中，使用建物轮廓线内部的光达点云进行屋顶面之共面分析，研究中使用三角网区域成长法侦测共平面之屋顶面，以相邻三角网法向量夹角做为共平面门槛，并以最小二乘法回归出屋顶面之平面，产生房屋模型。

We develop a control unit to accept and recognize the user inputs in forms of trajectories of the pointed point based on finite state machine and neural network.

在系统环境中，我们利用两重建平面与投影平面三面共点的特性，便可重建出指向点在真实世界中的位置。

Based on the theory of gearing and differential geometry, a series of geometric relationships between conjugate tooth surfaces are analyzed, basic relationships of normal curvature as well as geodesic torsion between conjugate tooth surfaces are derived mathematically for the most general form of gearing.

基于微分几何和齿轮啮合理论，分析了共轭啮合齿面间的一系列几何关系，从而揭示了两个作空间共轭啮合运动的齿面之间的法曲率、短程挠率的内在几何联系。作为上述理论的具体应用，研究了准双曲面齿轮传动两齿面之间在给定参考点处的法曲率、短程挠率的关系

Firstly, This paper processes geometry filtration based on character of orbit's apogee and perigee after orbit model is analyzed and based. Secondly Space Debris is separated into two kinds, coplanar and not coplanar according as location interrelation of target and debris. In Dynamic filtration's processing, considering prediction time limit and orbit perturbation, secular effects which have increaser effect is considered so that some need catching danger time point is appeased, some law about time when target and debris pass intersectant line each other is inferred, when debris and object are in different plane and some similar law also is inferred otherwise. The time list is arithmetical progression. These laws can improve calculation efficiency remarkably; Lastly orbit predict is a course approaching least distance. Danger time point in the last step become beginning time point from which debris and object's position and velocity are calculated by SXP4 Model which is an analytic model.By result, determine that relative movement trend is closer or apart, farther calculate the interval apart from time when predictive least relative distance occurs. Least relative distance and time when least distance occurs is calculated finally. It is a fast approach course adopting varied interval.

本文在分析、建立轨道摄动计算模型的基础上，首先采用基于轨道远、近地点特征对大量编目在册的空间碎片进行初步几何静态筛选，然后根据碎片与目标轨道面的相对位置特点把碎片分为异面与准共面两种情况以进行动态筛选，在筛选过程中考虑到预报时限长度和轨道摄动影响，引入了轨道摄动中具有积累效应的长期项以满足危险时间点的捕捉要求，利用了长期项摄动变化线性的特点导出了碎片与目标异面情况下各自过交线的时间序列成准等差数列的规律性和准共面情况下类似的规律性，从而显著地提高了前期轨道筛选的计算效率；最后对剩余危险碎片和目标飞行器利用SXP4轨道预报模型在前期轨道筛选的基础上以各个危险探测时间点为预报的时间起点，并根据预报计算结果，分析目标和碎片在该时间点的运动趋势是相互远离还是相互接近，推出预计最小相对距离发生时刻相对此刻的时间长度，得到其随时间变化的局部最小相对距离以及危险距离发生的时刻和相对速度，这是一个采用变时间步长、快速逼近最小相对距离的过程。

Simulation results of theimproved algorithm show that the proper rotation matrix is always obtained,which inturn improves the accuracy of the translation vector.

本文提出了增加旋转矩阵约束条件的改进方法，建立了共面特征点的共线性方程，得到了一种快速、准确且能全局收敛的位置、姿态测量算法。

We have researched a method of coordinate rotation of 3D converted wave data, binning and calculating 3D converted point, that is to make coordinate rotation for all seismic traces in each gather of converted wave common-shot point.

研究了三维转换波资料坐标旋转、面元划分及三维共转换点计算方法，即将每一个转换波共炮点道集内所有地震道进行坐标旋转，旋转后的转换波道集在炮检距、纵横波速度已知的条件下，用迭代方法计算三维转换点的平面坐标，并绘制在平面上。

The meshwork results are obtained from the later pictures. They clearly show the structure of four-dimension reseau and some meshwork results of shell data. The reason why the whole results are not achieved is that there are too many circumstances in which five or more dots share the same orb. In this case, the principle Delaunay is not in point any more, then the process of establishing meshwork will be intermitted.

后面的4幅图是后来所作的工作，得到了1个正方体4顶点以及其中心点的建网结果，从这里能清楚地看到4面体网格的结构，还有对贝壳数据点云的部分建网结果，之所以没有完成整个贝壳数据的建网是因为数据中存在较多的5点或5点以上共球的情况，这种情况下Delaunay准则不再适用，建网会中断，所以只完成了1个部分。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失