顾及拱高误差的墨卡托大地线快速展绘算法  

Rapid plotting algorithm for the Mercator geodetic line with regard to the arch height error

作　　者：董箭[1,2] 李彬彬 彭认灿[1,2] 刘波 刘国辉 DONG Jian;LI Binbin;PENG Rencan;LIU Bo;LIU Guohui(Department of Military Oceanography and Hydrography&Cartography,Dalian Naval Academy,Dalian,Liaoning 116018,China;Key Laboratory of Hydrographic Surveying and Mapping of PLA,Dalian Naval Academy,Dalian,Liaoning 116018,China;Cartographic Information Center of Navy General Staff,Tianjin 300450,China)

机构地区：[1]海军大连舰艇学院军事海洋与测绘系,辽宁大连116018 [2]海军大连舰艇学院海洋测绘工程军队重点实验室,辽宁大连116018 [3]海军参谋部海图信息中心,天津300450

出　　处：《测绘科学》2020年第9期43-51,共9页Science of Surveying and Mapping

基　　金：国家重点研发计划项目(2017YFC1405505);国家自然科学基金项目(41601498,41471380)。

摘　　要：针对大地线矢量展绘算法执行过程中存在的内插距离参数与展绘精度无法定量调控与自适应匹配问题,该文将顾及恒向线与大地线夹角的恒向线段推求方法应用扩展至大地线展绘误差的定量评估与控制过程。在建立大地线展绘长度误差及拱高误差定量评估模型的基础上,阐明了内插距离参数取值对大地线展绘精度与效率的影响规律;采用大地线展绘局部拱高误差约束限定大地线展绘整体长度误差的策略,建立了墨卡托投影条件下恒向线与大地线夹角及与大地线展绘拱高限差的数值关联,构建了大地线展绘拱高误差约束的内插距离参数定量调控模型;提出了一种墨卡托投影条件下拱高误差阈值限定的大地线快速展绘算法。实验结果表明:该算法可实现任意长度、经纬度范围的大地线快速展绘,且精度控制在指定阈值范围内。In view of the problem that the interpolated distance parameters and the plotting precision of the geodetic line plotting algorithm cannot be quantitatively regulated and adaptively matched,this paper extends the application of the solution method for constant line segment by considering the angle of the constant line and the geodetic line to the quantitative evaluation and control process of the error of the geodetic line plotting.On the basis of constructing the quantitative evaluation model of the length error and the arch height error of the geodetic line plotting,the influence law of the value of the interstitial distance parameter on the precision and efficiency of the geodetic line plotting is expounded.The numerical correlation between the angle of constant line and geodetic line under Mercator projection and the arch height error of the geodetic line plotting is demonstrated.With the strategy of limiting the overall length error of the geodetic line plotting by the local arch height error threshold limits is used,a quantitative control model of interpolated distance parameters within the geodetic line plotting arch height error threshold limits was also established.A rapid plotting algorithm of the geodetic line with arch height error threshold under Mercator projection is proposed in this paper.The experimental results show that the algorithm can realize the rapid plotting of geodetic lines in any length and any latitude and longitude range,and the precision is controlled within the specified threshold range.

关 键 词：大地线展绘 内插距离参数 拱高误差 定量调控 自适应匹配 

分 类 号：P229[天文地球—大地测量学与测量工程]