引用本文: 李胜全, 李厚朴, 边少锋. 拉格朗日投影与常用等角投影间解析变换的复变函数表示[J]. 武汉大学学报 ( 信息科学版), 2012, 37(11): 1382-1385.
LI Shengquan, LI Houpu, BIAN Shaofeng. Expressions of Analytical Transformations Between Lagrange and the Commonly Used Conformal Projections by Complex Numbers[J]. Geomatics and Information Science of Wuhan University, 2012, 37(11): 1382-1385.
 Citation: LI Shengquan, LI Houpu, BIAN Shaofeng. Expressions of Analytical Transformations Between Lagrange and the Commonly Used Conformal Projections by Complex Numbers[J]. Geomatics and Information Science of Wuhan University, 2012, 37(11): 1382-1385.

## Expressions of Analytical Transformations Between Lagrange and the Commonly Used Conformal Projections by Complex Numbers

• 摘要: 借助复变函数理论讨论了拉格朗日投影与常用等角投影间的解析变换问题,导出了拉格朗日投影正反解的复变函数表达式,在此基础上系统地建立了该投影与高斯投影、墨卡托投影和等角圆锥投影间解析变换的复变函数表示模型。这些复数变换公式是含参考椭球第一偏心率的符号形式,可解决不同参考椭球下的投影变换问题,与传统的实数变换公式相比,其结构更为简单,理论更为严密,便于实际使用。

Abstract: The problem of the analytical transformations between Lagrange and the commonly used conformal projections is discussed with the help of complex numbers theory.The forward and inverse expressions of Lagrange projection by complex numbers are derived,and the mathematical modes of the analytical transformations between Lagrange and Gauss,Mercator,Lambert conformal conic projections by complex numbers are systematically established.The formulae derived by the paper are in the symbolic form including the first eccentricity of the reference ellipsoid,so they could solve the transformation problems when different reference ellipsoids are used.Compared to traditional transformation formulae in the real number domain,they have more concise structure and stricter theory basis,and are more convenient for practical use.

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