基于实数等角纬度的高斯投影变换

Gaussian Projection Transformation Based on Real Equiangular Latitude

摘要: 传统的高斯投影变换采用大地纬度作为变换参数。李厚朴、边少锋等研究了基于等角纬度的高斯投影复变换，金立新给出了实数域的非迭代法的反算变换式。基于非迭代法的高斯投影变换，正反算变换为2套各不相同的变换式及其变换系数，表达冗长。本文从数值计算的实用角度出发，正反算变换均采用正算式，反算变换利用正算式迭代计算。算法简明，程序精短，易于在Excel VBA上实现。基于等角纬度的高斯投影变换，变换精度与径差l无关。仅就考虑变换精度而言，无需进行分带投影。

Abstract: The traditional Gaussian projection transformation uses geodetic latitude as the transformation parameter. Li Houpu, Bian Shaofeng, and others studied Gaussian projection complex transformations based on equiangular latitude, and Jin Lixin provided the inverse transformation formula for non-iterative methods in the real number field. The Gaussian projection transformation based on non-iterative method involves two sets of different transformation equations and their transformation coefficients, which are expressed in a lengthy manner. This article starts from the practical perspective of numerical calculation, and both forward and inverse transformations are calculated using forward equations, while inverse transformations are iteratively calculated using forward equations. The algorithm is concise, the program is short, and it is easy to implement on Excel VBA. The Gaussian projection transformation based on equiangular latitude is independent of the transformation accuracy and radial difference l. In terms of transformation accuracy alone, there is no need for band projection.