长大线性工程归化纬度类高斯投影方法研究  

Research on the method of naturalized latitude class Gaussian projection for long linear engineering

作　　者：刘孟函 金立新 LIU Menghan;JIN Lixin(School of Surveying,Mapping and Geo-Information,Lanzhou Jiaotong University,Lanzhou 730070,China;Academician Expert Workstation of Gansu Dayu Jiuzhou Space Information Technology Co.,Ltd.,Lanzhou 730070,China;National and Local Joint Engineering Research Center for the Application of Geographical and National Conditions Monitoring Technology,Lanzhou Jiaotong University,Lanzhou 730070,China;Gansu Provincial Geographic and National Conditions Monitoring Engineering Laboratory,Lanzhou Jiaotong University,Lanzhou 730070,China;China Railway First Survey&Design Institute Group Ltd.,Xi’an 710043,China;Gansu Railway Survey&Enginteering Institute Co.,Ltd.,Lanzhou 730000,China)

机构地区：[1]兰州交通大学测绘与地理信息学院,兰州730070 [2]甘肃大禹九洲空间信息科技有限公司院士专家工作站,兰州730070 [3]地理国情监测技术应用国家地方联合工程研究中心,兰州730070 [4]甘肃省地理国情监测工程实验室,兰州730070 [5]中铁第一勘察设计院集团有限公司,西安710043 [6]甘肃铁道综合工程勘察院有限公司,兰州730000

出　　处：《测绘工程》2024年第4期29-38,共10页Engineering of Surveying and Mapping

基　　金：国家自然科学基金资助项目(41631072)。

摘　　要：对东西向长大线性工程而言,传统高斯投影受带宽影响导致控制距离较短且需要进行频繁的换带计算。为了解决这些问题,提出了一种基于复数归化纬度的斜轴高斯投影理论。首先,对类归化纬度进行了复平面的解析开拓,实现了将椭球面转化为平面的过程。其次,结合类归化纬度线弧长的表达式,推导出了其复数形式的弧长公式。此外,利用复变函数的知识,进一步得到了斜轴高斯投影面的坐标。最后,在实际工程应用中与传统高斯投影方法对比,证明此方法的优越性。For long east-west linear engineering,the traditional Gaussian projection is affected by bandwidth,which leads to short control distance and requires frequent band change calculation.To solve these problems,we propose a skew Gaussian projection theory based on complex normalized latitude.Firstly,the complex plane of the generalized latitude is extended analytically,and the process of transforming the ellipsoid into a plane is realized.Secondly,we derive the arc length formula in complex form by combining the expression of the arc length of the naturalized latitude line.In addition,the coordinates of the oblique Gaussian projection plane are obtained by using the knowledge of complex variable functions.Finally,compared with the traditional Gaussian projection method in practical engineering application,the superiority of this method is proved.

关 键 词：归化纬度 类高斯投影 长度比 子午线收敛角 

分 类 号：P282[天文地球—地图制图学与地理信息工程]