| 1. | Gps is the technology which use the satellite to measure the 3d coordination of spatial points
Gps (全球定位系统)卫星定位技术利用人造地球卫星，确定地面点的空间位置。 |
| 2. | By taking these spatial points as initial guess , all exact real solutions withi n a certain range of variables are found using unrestraint optimization
以这些空间点为初始值，利用无约束优化，得到在一定值范围内的原方程组的全部精确实数解。 |
| 3. | This paper develops 3d graphics with opengl and draws three - dimensional entities visualization by spatial point set . thu three - dimensional effect and visualization of 3d entities figure are strengthened by light
摘要介绍了采用空间点集绘制实体的方法，生成真实感较强的三维实体图形的过程和三维实体的交互式旋转、缩放、多方位剖切等可视化显示。 |
| 4. | Secondly , this thesis purposes a new deformation correction method basing on neural net . it can get the mapping between spatial points and points in the image using this method after getting input , output and condition without considering other factors
最后将图像点的像素坐标输入给训练成功的bp网络,即可得到预期的空间位置,从而建立图像像素点与空间位置的映射关系。 |
| 5. | Now the 2d precision of spatial points is very great , but because by usual correlation fitting method we can transfer gps ellipsoidal height into normal height of the local geoid is considered as mathematical curve plane , it is not conform the fact of mountainous districts so the precision of elevation is so small that it is not satisfied with the requirement of leveling
目前，地面点的平面位置确定精度已相当高，但高程精度始终未能达到水准测量的要求，因为将gps大地高转化为水准正常高的拟合推估方法是将局部大地水准面视为数学曲面，常常与实际情况差异较大(特别在西部山区差异更大) 。 |
| 6. | In two - view case , a method is presented for calculation 2d projective transformation and construction the virtual elements by combination of spatial points and lines . so more 3d invariants of object ' s spatial structures can be extracted from real elements and virtual eleme nts . ( 3 ) the geometric characteristics of 2d symmetric objects " in perspective images are lucubrated
( 2 )扩展了2d射影变换矩阵的求解方法，将单纯利用点集对应的计算模式扩展到利用直线集、点线组合等多种类型来建立两个射影平面的对应关系；总结了平面上基于点、直线元素可求解的多种3d不变量；提出了双视图下由点、直线元素的多种对应关系求解2d射影变换来构造“虚元素”的方法，结合“实元素”和“虚元素”可以提取更多的空间3d不变量。 |
| 7. | Starting from the generativ e procedure of conjugate curves the generator 2 and generated curve 1 ar e re garded as two bunches of spatial point sets and the 1 is being considered a s a macroscopic expression in s1 coordinate space of points , satisfying the co n dition of conjugation during the course of relative movement , on 2
从共轭曲线的创成过程出发，将母曲线2和创成曲线1看作两簇空间点集，认为1是由相对运动过程中2上满足共轭条件的点在s1坐标空间中的宏观表现。 |
| 8. | For the special case one of original equations contains only two unknowns , these two variables can be sampled firstly , and then introduced into the other two 3 - variable equations . the real solutions obtained are spread along the cylindrical contour curve , so that a two dimensional graph which is easy to observe is generated . the corresponding spatial points of intersection are found through the points of intersection of the two curves in this graph
对于方程组中有一个二元方程的特殊情况，还可首先给该二元赋值，然后代入另外两个三元方程，将求得的实数解沿该二元方程的柱面轮廓线展开，得到便于观察的二维图形，通过该两条交线的交点找到其相应的空间交点。 |
