提取空间拟合椭圆模型的中心坐标算法  

Algorithm for extracting center position of fitted space ellipse model

作　　者：范昌胜[1] 李斌[1] 陈新庄[2] FAN Chang-sheng;LI Bin;CHEN Xin-zhuang(School of Engineering and Architecture,Shaanxi Vocational and Technical College,Xi'an 710119,P.R.C.;Department of Applied Mathematics,School of Science,Northwestern Polytechnic University,Xi'an 710072,P.R.C.)

机构地区：[1]陕西工商职业学院工程与建筑学院,陕西西安710119 [2]西北工业大学理学院应用数学系,陕西西安710072

出　　处：《西南民族大学学报（自然科学版）》2020年第1期41-48,共8页Journal of Southwest Minzu University(Natural Science Edition)

基　　金：陕西省教育厅2017年专项科学研究计划课题(17JK0059);陕西省教育厅2017年重点科学研究计划(17JZ011)。

摘　　要：采用古塔每一层8个观测点的坐标,给出了解决各层中心位置坐标的通用方法.先用一个平面对原始观测数据进行空间平面拟合,把原本三维的问题降低到二维来考虑,使得原本的空间曲面问题简化成了平面问题.然后在该平面上建立局部坐标系,通过坐标变换得到观测点在局部坐标系下的坐标.再利用椭圆曲线拟合这8个观测点,得到椭圆的方程,椭圆的中心即为该塔层的中心.最后利用坐标逆变换得到在原始坐标系下的中心坐标.仿真实验和实验表明,该算法可以用来解决空间建筑物的中心位置进行标定的问题.算法比其它的算法具有速度快和推广价值高等优点.The coordinates of 8 observation points in each layer of the ancient tower are used to give a general method for solving the coordinates of the center position of each layer.Firstly,the spatial plane fitting of the original observation data is performed by a plane,and the original three-dimensional problem is reduced to two-dimensional,so that the original spatial surface problem is simplified into a planar problem.Then,a local coordinate system is established on the plane,and coordinates of the observation point in the local coordinate system are obtained by coordinate transformation.Then the elliptic curve is used to fit the eight observation points to obtain the elliptic equation.The center of the ellipse is the center of the tower layer.Finally,the coordinate of the original coordinate system is obtained by inverse coordinate transformation.Simulation experiments and experiments show that the algorithm can be used to solve the problem of calibration of the center position of space buildings.The algorithm of this paper has the advantages of faster speed and higher promotion value than other algorithms.

关 键 词：坐标变换 拟合方程 最小二乘法 空间椭圆曲线 中心提取 

分 类 号：TP391.9[自动化与计算机技术—计算机应用技术]