高斯投影变形解析分析  

Analytic Analysis of Gaussian Projection De-formation

作　　者：张思远 边少锋 周东权 

机构地区：[1]中国地质大学(武汉)地质探测与评估教育部重点实验室,湖北 武汉

出　　处：《测绘科学技术》2023年第2期55-66,共12页Geomatics Science and Technology

摘　　要：作为一种常用的等角投影方式,高斯投影被广泛用在大地测量学的各个应用领域中。传统的高斯投影方法将地球视为椭球体,其数学公式主要为经差的幂级数展开式,公式冗长且计算量大,计算精度不足,也不能很清晰地反映高斯投影的本质和投影变形规律。而将地球视为球体时,高斯投影与横墨卡托投影是等价的,因此高斯投影公式可表示为形式紧凑的闭合形式。针对传统方法中存在的问题,本文通过球面公式计算特殊点处的投影变形和一条6度带条带内的投影变形,以此分析高斯投影的投影变形规律。As a commonly used isometric projection, Gauss projection is widely used in various applications of geodesy. Regarding the earth as an ellipsoid, the traditional Gauss projection mathematical formu-la’s computation is too complex to clearly reflect the nature of Gauss’s projection and its distortion. When the Earth is considered a sphere, the Gauss projection is equivalent to the transverse Merca-tor projection, so the Gauss projection formula can be expressed as a compact closed form. In order to solve the problems in the traditional method, the projection deformation at a special point and the projection deformation in a 6-degree strip are calculated by the spherical formula in this paper, and the projection deformation rule of Gauss projection is analyzed.

关 键 词：高斯投影 幂级数展开式 投影变形 大地测量学 解析分析 等角投影 椭球体 数学公式 

分 类 号：TP3[自动化与计算机技术—计算机科学与技术]