GAUSS-KRUGER PROJECTION FORWARD AND REVERSE CALCULATION AFTER ELLIPSOID TRANSFORM
椭球变换后的高斯投影正反算算法

In order to reduce the side length and area distortion of projection, ellipsoid transformation and projection plane rising are needed for conversion between geodetic and projected coordinates. There are three methods for ellipsoid transformation, i.e., ellipsoid expanding, ellipsoid distortion and ellipsoid shift. Forward and reverse calculations of Gauss-Kruger projection on transformed ellipsoids are studied. SuperCoor software is developed to study the example data, and the results show that the formulas and algorithms presented are correct. From the perspective of controlling distortion of side length, the coordinate differences with three ellipsoid transformation methods are nearly the same and all can be used in practice. Among the three ellipsoid transformations, ellipsoid expanding model is the simplest. Thus, it should be considered as the first method to use in application.