复变函数斜轴椭球变换法的衔接应用  

Connection and application of complex variable function ellipsoid transformation

作　　者：杨力 姚德新 YANG Li;YAO Dexin(School of Geomatics, Lanzhou Jiaotong University, Lanzhou 730070, Gansu;National-Local Joint Engineering Research Center of Technologies and Applications for National Geographic State Monitoring, Lanzhou 730070, China;Gansu Provincial Engineering Laboratory for National Geographic State Monitoring, Lanzhou 730070, China)

机构地区：[1]兰州交通大学测绘与地理信息学院,甘肃兰州730070 [2]地理国情监测技术应用国家地方联合工程研究中心,甘肃兰州730070 [3]甘肃省地理国情监测工程实验室,甘肃兰州730070

出　　处：《测绘工程》2021年第5期64-69,75,共7页Engineering of Surveying and Mapping

基　　金：兰州交通大学优秀平台支持(201806)。

摘　　要：针对转折大、高差大的长线工程,在长度投影变形不大于10 mm/km的条件下,为了衔接斜轴椭球变换前后的高斯平面坐标,建立高精度的工程控制网。文中利用高斯投影正解的非迭代复变函数解出高斯平面横纵坐标组成的复变量z关于参数(a,e,B,l)的偏导数,结合椭球变换大地坐标的变化量,推导椭球变换前后高斯平面坐标位移量的解析公式,构建了椭球变换前后高斯平面坐标衔接模型,并通过实际工程数据对模型进行精度分析,验证该理论模型正确性以及高斯平面坐标衔接的优越性,进一步丰富斜轴变换椭球高斯投影理论在长线工程中的应用。For long-line projects with large bends and large height differences,under the condition that the projected deformation is not greater than 10 mm/km,in order to connect the Gaussian plane coordinates before and after the ellipsoid transformation this paper establishes a high-precision plane control network by using the non-iterative complex variable function of the positive solution of the Gaussian projection to solve the partial derivative of z with respect to the parameters(a,e,B,l),where the complex variable z is composed of the abscissa and the ordinate of the Gaussian plane.In this paper,the analytical formula of the change amount of the Gaussian plane coordinate displacement before and after the ellipsoid transformation is deduced based on the change of the Geodetic coordinates before and after the ellipsoid transformation.Gaussian plane coordinate connection models before and after ellipsoid transformation are constructed,and the accuracy analysis of the model is carried out through actual engineering data,which verifies the correctness of the theoretical model and the superiority of Gaussian plane coordinate connection.Thus this can enrich the application of oblique axis transformation ellipsoidal Gaussian projection theory to the long-line engineering.

关 键 词：高斯投影复变函数正解 复变函数微分公式 椭球变换法 高斯平面坐标衔接 

分 类 号：U212.2[交通运输工程—道路与铁道工程]