等距离球面高斯投影

针对传统高斯投影直接基于等角横切圆柱投影而带来的不能直接用球面坐标换算等问题,研究了一种运用等距离球面进行投影的高斯投影,即等距离球面高斯投影。借助等距离纬度正反解公式,推导了等距离球面高斯投影的正反解公式,分析了其经纬线变形情况;基于投影公式,计算和分析了等距离球面高斯投影的长度变形、角度变形、面积变形及子午线收敛角等参数;最后与传统高斯投影进行比较,说明了该投影的可用性。

A Kind of Gauss Projection Based on the Equidistant Sphere

A kind of Gauss projection based on the equidistant sphere is studied by reason of the problem of the impracticality of calculation by using the spherical coordinates for the traditional Gauss projection based on the horizontal elliptic cylinder. First, the direct and inverse solutions of the Gauss projection based on the equidistant sphere are derived by using the direct and inverse solutions of the rectifying latitude with respect to the geodetic latitude, which help to calculate the distortions of meridians and parallels. Then, the length distortion, angular distortion, area distortion, and convergence of meridians of the Gauss projection based on the equidistant sphere are analyzed. Finally, in comparison with the traditional Gauss projection as regards these distortion parameters, the Gauss projection based on the equidistant sphere is available in practice.