针对东西跨度较大的线路,借助最小二乘法建立斜轴参考椭球,以减小高斯投影横坐标;通过坐标系转换理论,推导出测区在各坐标系下的空间直角坐标,进而确定测区相对于斜轴参考椭球上的大地坐标;利用椭球变换法建立斜轴变形椭球以减小因高程引起的投影变形.以某铁路线为例,可知"斜轴变形椭球高斯投影方法"可大大减小投影后横轴方向分量,避免高斯投影分带现象,同时有效减小高程及其引起的投影变形.该方法数学模型严谨、运算过程清晰,便于编制相关软件,可投入工程使用.
For east-west spanning line, to reduce abscissa value of Gauss projection, the oblique reference ellipsoid was constructed by means of least square method. Via theory of coordinate system transformation, spatial rectangular coordinates of target region in each coordinate system were carried out, and then geodetic coordinates of target region on oblique reference ellipsoid were relatively given. Through ellipsoid transformation, oblique deformed ellipsoid was established to lessen distortion of projection caused by height. Taking one railway for example, it were shown that "An alteration of Gauss projection based on oblique deformed ellipsoid" could greatly deplete abscissa components, avoid zoning of Gauss projection and reduce height effectively, as well as the relevant distortion it caused. Strict mathematical model and clear operation process of the Gauss projection are convenient for programming of relative software, which can be applied in engineering.
[1] XIONG Jie. Ellipsoidal Geodesy[M]. Beijing: Publishing Housing of PLA, 1988. (熊介. 椭球大地测量学[M]. 北京: 解放军出版社, 1988.)
[2] YANG Qihe, SNYDER J P, TOBLER W R. Map Projection Transformation: Principles and Applications[M]. London: Taylor & Francis, 2000.
[3] LI Houpu, BIAN Shaofeng. The Expression of Gauss Projection by Complex Numbers[J]. Acta Geodaetica et Cartographica Sinica, 2008, 37(1): 5-9. (李厚朴, 边少锋. 高斯投影的复变函数表示[J]. 测绘学报, 2008, 37(1): 5-9.)
[4] SNYDER J P. Map Projections:A Working Manual[M]. Washington D C: Government Printing Office, 1987.
[5] GONG Yusheng, ZHANG Liping, ZHAO Haiying. Implementation of Gauss Projection Method in High Altitude Area[J].Journal of Liaoning Technical University: Natural Science, 2014, 33(1): 51-55. (宫雨生, 张丽萍, 赵海莹. 高海拔地区高斯投影方法与实现[J]. 辽宁工程技术大学学报: 自然科学版, 2014, 33(1): 51-55.)
[6] REN Xiaochun. Discussion on Horizontal Coordinate of Accurate Engineering Surveying for Ballastless Track of Passenger Dedicated Lines[J]. Railway Investigation and Surveying, 2008, 34(2): 1-4. (任晓春. 客运专线无碴轨道精密工程测量平面坐标系的探讨[J]. 铁道勘察, 2008, 34(2): 1-4.)
[7] ZHAO Junsheng. LIU Yanchun, WANG Keping, et al. Discussion on the Distortion of Distance in Gauss Projection[J]. Hydrographic Surveying and Charting, 2007, 27(3): 9-11. (赵俊生, 刘雁春, 王克平, 等. 关于高斯投影长度变形的探讨[J]. 海洋测绘, 2007, 27(3): 9-11.)
[8] YU Yajie, ZHAO Yingzhi, ZHANG Yuehua. The Establishment of Independent Coordinate System Based on the Ellipsoid Expansion Method[J]. Bulletin of Surveying and Mapping, 2011(12): 33-36. (于亚杰, 赵英志, 张月华. 基于椭球膨胀法实现独立坐标系统的建立[J]. 测绘通报, 2011(12): 33-36.)
[9] KUANG Jinzhu, XIA Shenzhou. Establish Regional Coordinate System with Gauss-Kruger Projection Calculation through Ellipsoid Transformation[J]. Surveying and Mapping of Geology and Mineral Resources, 2011, 27(4): 11-14. (况金著, 夏神州. 通过椭球变换建立区域坐标系的高斯投影算法[J]. 地矿测绘, 2011, 27(4): 11-14.)
[10] WANG Jiexian, WU Jicang, GAO Xiaobing. Oblique Mercator Projection and Its Applications on High Speed Railway Construction[J]. Geotechnical Investigation & Surveying, 2011, 39(8): 69-72. (王解先, 伍吉仓, 高小兵. 斜轴墨卡托投影及其在高铁建设工程中的应用[J]. 工程勘察, 2011, 39(8): 69-72.)
[11] LV Huiling. Application of Oblique Mercator Projection Method to Zhengxi Special Passenger Transport Line[J]. Journal of Geomatics, 2009, 34(1): 26-28. (吕慧玲. 斜轴墨卡托投影方法在郑西客专中的应用研究[J]. 测绘信息与工程, 2009, 34(1): 26-28.)
[12] LU Pengcheng, LIN Dongwei. Model for Oblique Mercator Projections as Well as Analysis on Its Applications[J]. Railway Investigation and Surveying, 2010, 36(4): 26-29. (陆鹏程, 林冬伟. 斜轴墨卡托投影模型及其应用分析[J]. 铁道勘察, 2010, 36(4): 26-29.)
[13] JIN Lixin, FU Hongping. Gaussian Projection Theory Based on Ellipsoid with Normal Section as the Central Meridian[M]. Xi'an: Xi'an Map Publishing House, 2012. (金立新, 付宏平. 法截面子午线椭球高斯投影理论[M]. 西安: 西安地图出版社, 2012.)
[14] ZENG Qixiong. Closed Formulae for Direct Solution of Geodetic Coordinates from Rectangular Space Coordinates[J]. Acta Geodaetica et Cartographica Sinica, 1981, 10(2): 83-95. (曾启雄. 空间直角坐标直接解算大地坐标的闭合公式[J]. 测绘学报, 1981, 10(2): 83-95.)
[15] WANG Hongsheng. Transformation of Space Rectangular Coordinates[J]. Acta Geodaetica et Cartographica Sinica, 1982, 11(1): 38-45. (汪鸿生. 空间直角坐标的变换[J]. 测绘学报, 1982, 11(1): 38-45.)
[16] SHEN Yunzhong, WEI Gang. Improvement of Three Dimensional Coordinate Transformation Model by Use of Interim Coordinate System[J]. Acta Geodaetica et Cartographica Sinica, 1998, 27(2): 161-165. (沈云中, 卫刚. 利用过渡坐标系改进3维坐标变换模型[J]. 测绘学报, 1998, 27(2): 161-165.)
[17] BIAN Shaofeng, CHAI Hongzhou, JIN Jihang. Geodetic Coordinate System and Datum[M]. Beijing: National Defence Industry Press, 2005. (边少锋, 柴洪洲, 金际航. 大地坐标系与大地基准[M]. 北京: 国防工业出版社, 2005.)
[18] BOWRING B R. The Accuracy of Geodetic Latitude and Height Equations[J]. Survey Review, 1985, 28(218): 202-206.
[19] BIAN Shaofeng, LI Zhongmei, LI Houpu. The Non-singular Formula of Gauss Projection by Complex Numbers in Polar Regions[J]. Acta Geodaetica et Cartographica Sinica, 2014, 43(4): 348-352. (边少锋, 李忠美, 李厚朴. 极区非奇异高斯投影复变函数表示[J]. 测绘学报, 2014, 43(4): 348-352.)
[20] FEI Yetai. Error Theories and Data Processing[M]. Beijing: China Machine Press, 2000. (费业泰. 误差理论与数据处理[M]. 北京: 机械工业出版社, 2000.)
[21] CHEN Junyong.Chinese Modern Geodetic Datum:Chinese Geodetic Coordinate System 2000 (CGCS2000) and Its Frame[J]. Acta Geodaetica et Cartographica Sinica, 2008, 37(3): 269-271. (陈俊勇. 中国现代大地基准: 中国大地坐标系统2000 (CGCS2000) 及其框架[J]. 测绘学报, 2008, 37(3): 269-271.)
