摘要
借助复数理论讨论了高斯投影和兰勃特等角圆锥投影正反解的复变函数表示,推导出了这两种投影解析变换的复变函数表达式。该式为含参考椭球第一偏心率的符号形式,可解决两类投影在不同参考椭球下的变换问题,与传统的实数变换公式相比,其结构更为简单、理论更为严密。算例分析表明,导出公式的精度优于10-6 m,可供实际使用。
The forward and inverse expressions of Gauss and Lambert conformal conic projections were discussed with the help of complex number theory.The symbolical expressions of transformations between the two projections by complex numbers are derived.These expressions include the first eccentricity of the referenced ellipsoid,so they could solve the transformation problems when different reference ellipsoids are used.Compared to traditional transformation formulae in the real number domain,they have more concise structure and stricter theory basis.Numerical examples show that the accuracies of these expressions are higher than 10-6 m,and could satisfy practical applications.
出处
《舰船电子工程》
2013年第7期34-36,82,共4页
Ship Electronic Engineering
基金
973计划资助项目(编号:2012CB719902)
国家自然科学基金项目(编号:41071295
41201478)资助
关键词
等角投影
高斯投影
兰勃特等角圆锥投影
复变函数
解析变换
conformal projection
Gauss projection
Lambert conformal conic projection
complex numbers
analytical transformation
