地图投影中三种纬度间变换直接展开式

基金项目: 国家973计划资助项目(2012CB719902);国家自然科学基金资助项目(40904018,41071295);国家自然科学基金青年科学基金资助项目(41201478);海岛(礁)测绘技术国家测绘地理信息局重点实验室资助项目(2010B04)

详细信息

Direct Expansions of Transformations Between Three Kinds of Latitudes Used in Map Projection

1 Department of Navigation, Naval University of Engineering, 717 Jiefang Road, Wuhan 430033, China;
2 Key Laboratory of Surveying and Mapping Technology on Island and Reef, State Bureau of Surveying, Mapping and Geoinformation, 579 Qianwangang Road, Qingdao 266510, China;
3 Navigation Guarantee Department of the Chiness Navy Headquarters, 19 West 3rd Ring Middle Road, Beijing 100841, China

摘要: 利用等距离纬度、等角纬度和等面积纬度这三种纬度和大地纬度间的正反解展开式,全面导出了它们之间变换的直接展开式,并将式中系数统一表示为椭球偏心率e的幂级数形式并展至e10,解决了不同参考椭球下的变换问题。算例分析表明,直接展开式的计算精度优于10-8″,满足地图投影精密计算的需要。
- 地图投影 /
- 等距离纬度 /
- 等角纬度 /
- 等面积纬度 /
- 直接展开式 /
- 计算机代数系统
Abstract: Considering the traditional transformations between rectifying,conformal and authalic latitudes are comparatively fuzzy,the direct expansions of transformations between three kinds of latitudes are comprehensively derived with the help of computer algebra system Mathematica using the forward and inverse expansions of transformations between the three kinds of latitudes and geodetic latitude.Their coefficients are expressed in a power series of the ellipsoid's first eccentricity,e,and extended up to tenth-order terms of e,which could solve the transformation problem when different reference ellipsoids are used.Numerical examples show that the accuracies of these direct expansions are higher than 10-8″,and could completely meet the needs of precise calculation in map projection.
- map projection /
- rectifying latitude /
- conformal latitude /
- authalic latitude /
- direct expansions /
- computer algebra system