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

LI Houpu1,2 BIAN Shaofeng1 CHEN Liangyou3(1 Department of Navigation,Naval University of Engineering,717 Jiefang Road,Wuhan 430033,China)(2 Key Laboratory of Surveying and Mapping Technology on Island and Reef,State Bureau of Surveying and Mapping, 579 Qianwangang Road,Qingdao 266510,China)(3 75230 Troops,Huizhou 512100,China)  
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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