异面高斯投影变换与Excel VBA实现——以实数等角纬度为变换参数

Gaussian Projection Transformation of Different Surfaces and Its Implementation in Excel VBA—Using Real Isometric Latitude as Transformation Parameters

摘要: 随着我国工程建设的发展，对地球投影变换精度提出了更高的要求，尤其是高铁工程建设，其投影变换精度要求< 1 m/100 km。在传统标准椭球高斯投影变换的基础上，增加椭球膨胀计算模块，组构了异面高斯投影变换：反算、正算及换带。正反算变换均利用正算式计算，正算采用非迭代法，反算采用迭代法。参照大地纬度B表达的高斯变换式，本文给出了同一表达格式的基于等角纬度φ表达的高斯投影变换式。从实用角度出发，利用Excel VBA计算平台，以实数等角纬度为变换参数，采用大地坐标增量法及空间直角坐标法作为膨胀变换方法，开发了异面高斯投影变换宏，一键实现坐标的批量变换。椭球膨胀坐标偏位$\left(D_x,D_y\right)$ 主要由椭球长半轴增量$da$ 所贡献，且与$da$ 呈线性增长。

Abstract: With the development of engineering construction in our country, higher requirements have been put forward for the accuracy of earth projection transformation, especially for high-speed railway engineering construction, which requires a projection transformation accuracy of < 1 m/100 km. On the basis of the traditional standard ellipsoid Gaussian projection transformation, an ellipsoid dilation calculation module is added to construct different surface Gaussian projection transformations: inverse calculation, forward calculation, and strip transformation. Both forward and backward transformations are calculated using forward equations, with non iterative methods used for forward calculations and iterative methods used for backward calculations. Referring to the Gaussian transform expression of geodetic latitude B, this article presents a Gaussian projection transform expression based on equiangular latitude φ expression using the same expression format. From a practical perspective, using the Excel VBA computing platform, taking real isometric latitude as the transformation parameter, and adopting the geodetic coordinate increment method and spatial Cartesian coordinate method as the expansion transformation method, different surface Gaussian projection transformation macros were developed to achieve batch transformation of coordinates with one click. The offset $\left(D_x,D_y\right)$ of ellipsoidal expansion coordinates is mainly contributed by the increment $da$ of the ellipsoidal semi axis, and it increases linearly with $da$ .