等面积纬度函数和等量纬度变换的直接解算公式

¹海军工程大学导航工程系,武汉市解放大道717号430033;²海军工程大学导航工程系,武汉市解放大道717号,430033;³75230部队,惠州市,512100

基金项目: 国家自然科学基金资助项目(40774002,40904018,41071295)；海军工程大学自然科学基金资助项目(HGDYDJJ009)；海岛(礁)测绘技术国家测绘局重点实验室开放研究基金资助项目(2010B04)

详细信息

The Direct Calculating Formulae for Transformations Between Authalic Latitude Function and Isometric Latitude

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 and Mapping, 579 Qianwangang Road,Qingdao 266510,China;³ 75230 Troops,Huizhou 512100,China

Funds: 国家自然科学基金资助项目(40774002,40904018,41071295)；海军工程大学自然科学基金资助项目(HGDYDJJ009)；海岛(礁)测绘技术国家测绘局重点实验室开放研究基金资助项目(2010B04)

摘要: 为实现等面积投影和等角投影间的直接变换,借助计算机代数系统Mathematica,推导出了等面积纬度函数和等量纬度变换的直接解算公式,并将式中系数统一表示为椭球第一偏心率的幂级数形式,可解决不同参考椭球下的变换问题。算例分析表明,本导出公式的计算误差分别小于10 m2和10-4(″),可供实际使用。
- 地图投影 /
- 等面积纬度函数 /
- 等量纬度 /
- 计算机代数系统
Abstract: In order to realize the direct transformations between authalic and conformal projections,the direct calculating formulae for transformations between authalic latitude function and isometric latitude are derived with the help of computer algebra system Mathematica.Their coefficients are expressed uniformly in a power series of the first eccentricity of the ellipsoid,and the transformation problem when different reference ellipsoids are used could be solved.Numerical examples show that errors of the two formulae is less than 10 m2 and 10-4″respectively,which could satisfy practical application.
- map projection /
- authalic latitude function /
- isometric latitude /
- computer algebra system