| 高斯投影与横墨卡托投影等价性证明 |
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| 引用本文： | 李忠美,于金星,李厚朴,边少锋.高斯投影与横墨卡托投影等价性证明[J].海洋测绘,2013,33(3):17-20. |
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| 作者姓名： | 李忠美 于金星 李厚朴 边少锋 |
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| 作者单位： | 1. 海军工程大学导航工程系,湖北武汉,430033
2. 海军海洋测绘研究所,天津,300061 |
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| 基金项目： | 973计划资助，国家自然科学基金项目 |
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| 摘 要： | 为探寻球面高斯与横墨卡托投影间的内在联系,将墨卡托投影中的圆柱旋转90°,与某一子午线相切,并根据球面三角形定理得到横墨卡托投影的一般表达式;考虑到高斯投影实数型级数展开式不易于进行公式变换,推导出球面高斯投影复变函数表示式;根据复变函数及常用初等函数的定义,从高斯投影复变函数表示出发,经过一系列数学分析过程,给出球面高斯投影与横轴墨卡托投影等价性的严格证明。
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| 关 键 词： | 高斯投影 横墨卡托投影 等价性 复变函数 |
The Verification of Equivalence Between Gauss and Transverse Mercator Projections |
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| LI Zhongmei,YU Jinxing,LI Houpu,BIAN Shaofeng.The Verification of Equivalence Between Gauss and Transverse Mercator Projections[J].Hydrographic Surveying and Charting,2013,33(3):17-20. |
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| Authors: | LI Zhongmei YU Jinxing LI Houpu BIAN Shaofeng |
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| Institution: | 1 (1.Department of Navigation,Naval University of Engineering,Wuhan 430033,China; 2.Naval Institute of Hydrographic Surveying and Charting,Tianjin 300061,China) |
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| Abstract: | In order to explore the internal relationship between Gauss and transverse Mercator projections on the sphere,the cylinder in normal Mercator projection is rotated right to touch the sphere at one meridian,and the formula of transverse Mercator projection is obtained on the basis of spherical triangle theorems. Considering transformation of power series expansion is not easy to be realized,expression of Gauss projection by complex numbers is derived. Based on the definition of complex variables and regular elementary functions, strict verification of equivalence between Gauss and transverse Mercator projections on the sphere is carried out via a series of mathematical analysis. |
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| Keywords: | Gauss projection transverse Mercator projection equivalence complex numbers |
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