复数高斯投影若干数学性质分析  

Analysis of some mathematical properties of complex Gaussian projection

作　　者：刘孟函 金立新[3,4] 刘士威 边少锋 李厚朴[5] LIU Menghan;JIN Lixin;LIU Shiwei;BIAN Shaofeng;LI Houpu(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;China Railway First Survey&Design Institute Group LTD,Xi'an 710043,China;Gansu Railway Survey&Enginteering Institute CO.,LTD.,Lanzhou 730000,China;Department of Navigation,Naval University of Engineering,WuHan 430033,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]甘肃大禹九洲空间信息科技有限公司院士专家工作站,甘肃兰州730070 [3]中铁第一勘察设计院集团有限公司,陕西西安710043 [4]甘肃铁道综合工程勘察院有限公司,甘肃兰州730000 [5]海军工程大学导航工程系,湖北武汉430033

出　　处：《海洋测绘》2023年第6期77-82,共6页Hydrographic Surveying and Charting

基　　金：国家自然科学基金(41631072)。

摘　　要：为进一步研究基于复变函数表示的高斯投影解析公式及相关理论和定理,在高斯投影复变函数表示的基础上,给出高斯投影正解复数平行圈半径、长度比和子午线收敛角的新公式。其次推导出高斯投影和墨卡托投影、高斯投影和等角球平面投影的变换关系。最后对复数高斯投影的数学本质进行了分析,进一步丰富了高斯投影的复变函数理论。In order to further study the related theories and theorems of complex Gaussian projection,in this paper on the basis of complex function representation of Gauss projection,the new formula is given about meridians convergence,length ratio and complex parallel circle radius.Secondly,the transformation relationship between Gaussian projection and Mercator projection and equiangular spherical plane projection are deduced.Finally,This paper analyzes the mathematical nature of the complex Gaussian projection.It further improves the complex number theory of Gaussian projection.

关 键 词：等量纬度 等角纬度 复数高斯投影 复数子午线弧长 复数平行圈半径 

分 类 号：P282[天文地球—地图制图学与地理信息工程]