等面积纬度函数与常用纬度间的直接变换  

The direct transformation between authalic latitude function and common latitude

作　　者：李晓勇 李厚朴[1] 刘国辉 边少锋[1] LI Xiaoyong;LI Houpu;LIU Guohui;BIAN Shaofeng(College of Electrical Engineering,Naval University of Engineering,Wuhan 430043,China;Chart Information Center,Tianjin 300450,China)

机构地区：[1]海军工程大学电气工程学院,湖北武汉430043 [2]海图信息中心,天津300450

出　　处：《海洋测绘》2022年第2期78-82,共5页Hydrographic Surveying and Charting

基　　金：国家优秀青年科学基金(42122025);国家自然科学基金(41971416,42074010);湖北省杰出青年科学基金(2019CFA086)。

摘　　要：借助计算机代数系统Mathematica,推导出了分别以地心纬度、归化纬度、等角纬度、等距离纬度为变量的等面积纬度函数直接解算公式,并将式中的系数分别表示为椭球偏心率e和椭球第三扁率n的幂级数展开形式。算例分析表明,基于第三扁率n的幂级数展开式系数更为简单,精度更高,并且推导得出的直接展开式计算误差均小于0.2 m^(2)(与之相对应等面积纬度误差小于1.0×10^(-9′′)),可以满足地图投影精密计算的需要。With the help of computer algebra system Mathematica,the direct calculation formulas of the authalic latitude function are derived,which take geocentric latitude,reduced latitude,conformal latitude and rectifying latitude as variables.And the coefficients in the formulas are expressed as power series expansion of ellipsoid eccentricity e and ellipsoid third flattening n respectively.Example analysis shows that the coefficients of power series expansion based on the third flatness n are simpler and more accurate,and the calculation errors of the derived direct expansion are all less than 0.2 m^(2),which can meet the needs of precise calculation of map projection.

关 键 词：地图投影 等面积纬度函数 常用纬度 直接变换 符号表达式 计算机代数系统 

分 类 号：P282[天文地球—地图制图学与地理信息工程]