高斯投影与墨卡托投影解析变换的复变函数表达式

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

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。

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.