摘要
针对长线工程中横轴椭圆柱等角投影在设计工程平面施工图时需要频繁分带和精度较低的问题,提出了以线路走向的椭球大椭圆线为新的中央子午线进行投影的大椭圆线椭球高斯投影,并研究大椭圆线椭球的参数理论模型。首先,推导了以归化纬度代替大地纬度为参数的子午线弧长公式;其次,根据二次曲线不变量理论、线性代数、微积分等知识推导出以平面方程系数为参数的大椭圆椭球基本几何参数的计算模型;然后,推导出基础椭球与大椭圆椭球之间大地坐标的直接转换模型;最后,以某一实际工程资料为基础,验证了推导的理论模型的正确性和优越性,以便在长线工程中普及应用。
Aiming at the problem that Gauss projection in the line engineering project needs to be frequently strapped and has low precision when designing the plane construction drawing of the project,this paper proposes a large elliptical Gaussian projection of an elliptical line projecting from the ellipsoid elliptical line of the route for the new central meridian,and analyzes the parametric theoretical model of the elliptic ellipsoid.Firstly,it derives the meridian arc length formula by using the naturalized latitude instead of the geodetic latitude as a parameter.Secondly,according to the quadratic curve invariant theory,linear algebra,calculus and other knowledge,it deduces the model of solving the basic geometric parameters of the large ellipse ellipsoid with the plane equation coefficient as the parameter.Furthermore,a direct conversion model of the geodetic coordinates between the base ellipsoid and the large ellipse ellipsoid is deduced.Finally,based on some actual engineering data,the correctness and superiority of the theoretical model deduced in this paper are verified to be popularized in long-term projects.
作者
冯黎刚
金立新
边少锋
李厚朴
FENG Ligang;JIN Lixin;BIAN Shaofeng;LI Houpu(Shanxi College of Communication Technology,Xi’an 710018,China;China Railway First Survey and Design Institute Group Co.Ltd,Xi’an 710043,China;General Engineering Survey Institute of Railways of Gansu,Lanzhou 730015,China;Department of Navigation,Naval University of Engineering,Wuhan 430033,China)
出处
《武汉大学学报（信息科学版）》
EI
CSCD
北大核心
2020年第2期219-225,232,共8页
Geomatics and Information Science of Wuhan University
基金
国家自然科学基金(41574009,41871376)
湖北省杰出青年科学基金(2019CFA086).
关键词
归化纬度
球心纬度
参数方程
大椭圆
高斯-克吕格投影
reduced latitude
geocentric latitude
parametric equation
large ellipse
Gauss-Kruger projec-tion
作者简介
第一作者:冯黎刚,硕士,主要从事大地测量与地球投影方面的研究。1426235296@qq.cm
