引用本文: 李厚朴, 边少锋, 陈良友. 等面积纬度函数和等量纬度变换的直接解算公式[J]. 武汉大学学报 ( 信息科学版), 2011, 36(7): 843-846.
LI Houpu, BIAN Shaofeng, CHEN Liangyou. The Direct Calculating Formulae for Transformations Between Authalic Latitude Function and Isometric Latitude[J]. Geomatics and Information Science of Wuhan University, 2011, 36(7): 843-846.
 Citation: LI Houpu, BIAN Shaofeng, CHEN Liangyou. The Direct Calculating Formulae for Transformations Between Authalic Latitude Function and Isometric Latitude[J]. Geomatics and Information Science of Wuhan University, 2011, 36(7): 843-846.

## The Direct Calculating Formulae for Transformations Between Authalic Latitude Function and Isometric Latitude

• 摘要: 为实现等面积投影和等角投影间的直接变换,借助计算机代数系统Mathematica,推导出了等面积纬度函数和等量纬度变换的直接解算公式,并将式中系数统一表示为椭球第一偏心率的幂级数形式,可解决不同参考椭球下的变换问题。算例分析表明,本导出公式的计算误差分别小于10 m2和10-4(″),可供实际使用。

Abstract: In order to realize the direct transformations between authalic and conformal projections,the direct calculating formulae for transformations between authalic latitude function and isometric latitude are derived with the help of computer algebra system Mathematica.Their coefficients are expressed uniformly in a power series of the first eccentricity of the ellipsoid,and the transformation problem when different reference ellipsoids are used could be solved.Numerical examples show that errors of the two formulae is less than 10 m2 and 10-4″respectively,which could satisfy practical application.

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