椭球情形下等角和等面积正圆柱投影间的直接变换  

The Direct Transformations Between Conformal and Equal-Area Normal Cylindrical Projections Based on Earth Ellipsoid

作　　者：李厚朴[1] 李海波 唐庆辉[3] LI Hou-pu;LI Hai-bo;TANG Qing-hui(Department of Navigation,Naval University of Engineering,Wuhan 430033,Hubei Province,China;Troop 91710 of the People's Liberation Army,Helong 133506,Jilin Province,China;Troop 32022 of the People's Liberation Army,Wuhan 430070,Hubei Province,China)

机构地区：[1]海军工程大学导航工程系,湖北武汉430033 [2]中国人民解放军91710部队,吉林和龙133506 [3]中国人民解放军32022部队,湖北武汉430070

出　　处：《海洋技术学报》2019年第5期15-20,共6页Journal of Ocean Technology

基　　金：国家自然科学基金资助项目(41571441,41771487,41631072);湖北省杰出青年科学基金资助项目(2019CFA086)

摘　　要：为实现椭球情形下等角和等面积圆柱投影间的直接变换,借助具有强大符号运算功能的计算机代数系统Mathematica,推导出了等量纬度和等面积纬度函数间变换的直接展开式,并将公式系数统一表示为椭球第一偏心率e的幂级数形式,且统一展开至e10。在此基础上建立了等角和等面积正圆柱投影间的直接变换模型,可解决不同参考椭球下的投影变换问题。精度比对结果表明本文建立的直接变换模型相比于传统间接变换模型精度提高3~5个数量级,完全可以满足地图海图制图精密计算的需要。In order to realize the direct transformations between conformal and equal-area normal cylindrical projections,the direct expansions of transformations between isometric latitude and authalic latitude function are derived with the help of computer algebra system Mathematica which has the function of powerful symbolical operation.Their coefficients are expressed in a power series of the ellipsoid's first eccentricity and expanded to tenth order of e.Based on these formulae,the direct transformation models between conformal and equal-area normal cylindrical projections are established,which could solve problems that deal with transformations when different reference ellipsoids are used.The accuracy comparison results show that the accuracy of the direct transformation models increases up to 3 to 5 orders of magnitude compared to that of traditional indirect models,which could completely satisfy the requirement of the precise computation in cartography.

关 键 词：等角圆柱投影 等面积圆柱投影 等量纬度 等面积纬度函数 直接变换 

分 类 号：P282.1[天文地球—地图制图学与地理信息工程]