摘要
借助复变函数理论讨论高斯投影的复变函数表示,与传统的高斯投影实数域表达式相比,本文导出的高斯投影正反解表达式形式紧凑,公式简单,特别是基于复变函数建立的尺度比和子午线收敛角公式能表示为闭合形式;当e=0时,高斯投影正反解公式均为简单准确的闭合表达式。最后,通过算例对导出的新公式进行验算。
Gauss projection is discussed with the help of complex number theory. Compared to traditional expressions of Gauss projection in the real number domain, a new expression derived in this paper has a very concise form both for the forward and inverse transformations between an ellipsoid and a plane. A single closed equation for both scale factor and meridian convergence is given based on complex numbers in particular. When the eccentricity is equal to zero, closed equations for the forward and inverse Gauss projection are also available. Numerical examples are attached to check the computations of this new formulation.
出处
《测绘学报》
EI
CSCD
北大核心
2008年第1期5-9,共5页
Acta Geodaetica et Cartographica Sinica
基金
国家自然科学基金项目(40644020)
国家杰出青年科学基金项目(40125013)
关键词
高斯投影
闭合形式
复变函数
Gauss projection
closed expressions
complex numbers
