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中文摘要：
利用等距离纬度、等角纬度和等面积纬度这三种纬度和大地纬度间的正反解展开式，全面导出了它们之间变换的直接展开式，并将式中系数统一表示为椭球偏心率e的幂级数形式并展至e^10，解决了不同参考椭球下的变换问题。算例分析表明，直接展开式的计算精度优于10^-8”，满足地图投影精密计算的需要。
英文摘要：
Considering the traditional transformations between rectifying, conformal and authalic latitudes are comparatively fuzzy, the direct expansions of transformations between three kinds of latitudes are comprehensively derived with the help of computer algebra system Mathematica using the forward and inverse expansions of transformations between the three kinds of latitudes and geodetic latitude. Their coefficients are expressed in a power series of the ellipsoid＇s first eccentricity, e, and extended up to tenth-order terms of e, which could solve the transformation problem when different reference ellipsoids are used. Numerical examples show that the accuracies of these direct expansions are higher than 10-8＂, and could completely meet the needs of precise calculation in map projection.
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