子午线弧长和等面积纬度函数变换的直接展开式  

The Direct Expansions for Transformations Between Meridian Arc and Authalic Latitude Function

作　　者：李厚朴[1] 刘敏[2] 孔海英[2] 夏静欣[3] 

机构地区：[1]海军工程大学导航工程系,湖北武汉430033 [2]海军司令部航海保证部,天津300042 [3]海军出版社,天津300450

出　　处：《海洋测绘》2011年第1期17-19,共3页Hydrographic Surveying and Charting

基　　金：国家自然科学基金(40774002;40904018;41071295);国家杰出青年科学基金(40125013)

摘　　要：为实现等距离投影和等面积投影间的直接变换,借助计算机代数系统Mathematica,推导出了子午线弧长和等面积纬度函数变换的直接展开式,将式中系数统一表示为椭球偏心率的幂级数形式,可解决不同参考椭球下的变换问题。算例分析表明导出公式的精度分别高于10-3km2和10-4m,可供实际使用。In order to realize the direct transformations between rectifying and authalic projections,the direct expansions of transformations between meridian arc and authalic latitude function are derived with the help of computer algebra system Mathematica.Their coefficients are expressed uniformly in a power series of the ellipsoid＇s eccentricity,which could solve the problem of transformations when different reference ellipsoids are used.Numerical examples show that the precision of these formulae is higher than 10^-3km^2 and 10^-4m respectively,which could satisfy practical applications.

关 键 词：地图投影 子午线弧长 等距离纬度 等面积纬度函数 计算机代数系统 

分 类 号：P282.1[天文地球—地图制图学与地理信息工程]