高斯投影与墨卡托投影解析变换的复变函数表达式

基金项目: 国家自然科学基金资助项目(40644020,40774002)；国家杰出青年科学基金项目(40125013)

详细信息

Expressions for Analytical Transformation Between Gauss and Mercator Projections by Complex Numbers

¹Department of Navigation,Naval University of Engineering,717 Jiefang Road,Wuhan 430033,China;²Institute of Geodesy and Geophysics,Chinese Academy of Sciences,340 Xudong Street,Wuhan 430077,China

Funds: 国家自然科学基金资助项目(40644020,40774002)；国家杰出青年科学基金项目(40125013)

摘要: 给出了高斯投影和墨卡托投影正反解的复变函数表达式,在此基础上推导出了这两种投影解析变换的复数形式的直接公式和间接公式,将其表示为含椭球第一偏心率e的符号形式,可解决两种投影在不同地球参考椭球下的变换问题。算例结果表明,复数变换公式的计算精度在0.000 1 m以上,可供实际使用。
- 地图投影 /
- 高斯投影 /
- 墨卡托投影 /
- 复变函数 /
- 解析变换
Abstract: Expressions for the forward and inverse solution of Gauss and Mercator projections by complex numbers are given in this paper.Based on these expressions,direct and indirect formulas of the analytical transformation between Gauss and Mercator projections are derived.These formulae are symbolical forms which include the first eccentricity e of the reference ellipsoide.Hence,they can solve problems that deal with transformations between Gauss and Mercator projections when different reference ellipsoids are used.The numerical investigation shows that these formulas are sufficiently accurate up to 0.000 1 m and can satisfy practical applications.
- map projection /
- Gauss projection /
- Mercator projection /
- complex numbers /
- analytical transformation