摘要
借助复数理论讨论了高斯投影的复变函数表示。引入了等量纬度反解的直接展开式,借助计算机代数系统Mathematica推导出了子午线弧长与等量纬度之间的关系式,并将其拓展至复数域,导出了形式紧凑、结构简单的高斯投影正反解非迭代公式,并在此基础上给出了适合计算机计算的表达式及其相关系数在不同参考椭球下的数值形式。算例结果表明本文公式计算精度在10-6s以上,可供实际使用。
Gauss projection is discussed with the help of complex numbers theory. The direct expansion of the conformal latitude＇ s inverse solution is introduced in this paper. Expressions that illuminate the relationship between meridian arc and conformal latitude are derived with the help of computer algebra system Mathematica. After developing them into complex numbers domain,non-iterative formulae with a very concise form for Gauss projection＇ s forward and inverse transformations are also available. Based on these, expressions that can satisfy computer calculation requirement and their coefficients＇ numerical forms under different referenced ellipsoids are both given. Numerical examples show that the precision of these formulae is sufficiently accurate up to 10^-6 s and can satisfy practical use.
出处
《海洋测绘》
2009年第6期17-20,共4页
Hydrographic Surveying and Charting
基金
国家自然科学基金资助项目(40774002
40644020)
国家杰出青年科学基金资助项目(40125013)
关键词
高斯投影
复变函数
非迭代公式
计算机代数系统
Gauss projection
complex numbers
non-iterative formulae
computer algebra system
