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| 常用等角投影及其解析变换的复变函数表示 | |
| 引用本文： | 李厚朴,边少锋,李海波.常用等角投影及其解析变换的复变函数表示[J].测绘科学技术学报,2012(2):109-112,117. |
| 作者姓名： | 李厚朴 边少锋 李海波 |
| 作者单位： | 1. 海军工程大学导航工程系,湖北武汉430033 2. 海岛礁测绘技术国家测绘地理信息局重点实验室,山东青岛266510 3. 部队,吉林和龙133506 |
| 基金项目： | 国家自然科学基金项目(41071295;40904018);海军工程大学自然科学基金项目(HGDYDJJ009);海岛(礁)测绘技术国家测绘地理信息局重点实验室项目(2010B04);水下测控技术重点实验室延伸性发展基金项目(Ys0C261102) |
| 摘 要： | 借助复变函数理论讨论了常用等角投影及其解析变换的复变函数表示;给出了高斯投影、墨卡托投影和等角圆锥投影正反解的复变函数表示模型;在此基础上系统地推导出了高斯投影、墨卡托投影和等角圆锥投影间解析变换的复变函数表达式.这些复数变换公式是含参考椭球第一偏心率的符号形式,可解决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. |
| 关 键 词： | 等角投影 高斯投影 墨卡托投影 等角圆锥投影 解析变换 复变函数 |
Expressions of Commonly Used Conformal Projections and Their Analytical Transformations by Complex Numbers |
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| LI Houpu,BIAN Shaofeng,LI Haibo.Expressions of Commonly Used Conformal Projections and Their Analytical Transformations by Complex Numbers[J].Journal of Zhengzhou Institute of Surveying and Mapping,2012(2):109-112,117. | |
| Authors: | LI Houpu BIAN Shaofeng LI Haibo |
| Institution: | 1.Department of Navigation,Naval University of Engineering,Wuhan 430033,China; 2.Key Laboratory of Surveying and Mapping Technology on Island and Reef, State Bureau of Surveying,Mapping and Geoinformation,Qingdao 266510,China; 3.91710 Troops,Helong 133506,China) |
| Abstract: | The expressions of commonly used conformal projections and their analytical transformations were thoroughly discussed with the help of complex numbers theory.The mathematical models of the forward and inverse solutions of Gauss,Mercator and conformal conic projections by complex numbers were given.Based on these models,the expressions of analytical transformations between Gauss,Mercator and conformal conic projections by complex numbers were systematically derived.These formulas by complex numbers are in the symbolic form including the first eccentricity of the reference ellipsoid,so they can solve the transformation problems when different reference ellipsoids are used.Compared with traditional transformation formulas in the real number domain,they have more concise structure and stricter theory basis. |
| Keywords: | conformal projection Gauss projection Mercator projection conformal conic projection analytical transformation complex numbers |
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