椭球变换后的高斯投影正反算算法

GAUSS-KRUGER PROJECTION FORWARD AND REVERSE CALCULATION AFTER ELLIPSOID TRANSFORM

研究椭球变换后的高斯投影正算与反算问题,并研制了SuperCoor软件,计算实例结果证明了椭球变换后高斯正反算算法的正确性。从控制边长变形的角度看,3种椭球变换方法结果一致,而椭球膨胀法最为简洁。

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.