测地坐标计算椭球面上凸多边形面积的算法  

Computation of Area for Convex Polygon on Earth Ellipsoid by Means of Geodesic Coordinate

作　　者：施一民[1] 朱紫阳[2] 

机构地区：[1]同济大学国家测绘局现代工程测量重点实验室,上海200092 [2]广东省国土资源厅测绘院,广东广州510500

出　　处：《同济大学学报（自然科学版）》2006年第4期504-507,共4页Journal of Tongji University:Natural Science

基　　金：国家自然科学基金资助项目(40471114);地球空间环境与大地测量教育部重点实验室开放基金资助项目(03-04-02)

摘　　要：推导出用三顶点的测地坐标计算地球椭球面上三角形面积的公式.公式表明,主项的表示式与按平面坐标求面积的计算式完全一致,而附加项的表示式亦有规律可循.因此,该公式的适用范围可由椭球面三角形推广至椭球面上任意凸多边形.与高斯平面上计算的面积相比,由于不受投影变形的影响,因而更接近于实际面积.这就为至今较难实施的椭球面的面积计算开拓了一个新的途径,有利于做出更客观的G IS空间量度与分析.实际数据的验算充分证实了该算法的正确性和有效性.The formula for area of triangle on ellipsoid by means of geodesic coordinate is derived in this paper. It shows that the primary term is identical with the formula for area of plane triangle by rectangular coordinate in three angular points, while the expression of remainder terms also has a rule to follow in form. The formula can also be applied to computing convex polygon on ellipsoid. Compared with the area on Gauss plane, there is no distortion in the area computation with this new approach, the result of which is closer to the true area. So a new algorithm of area on ellipsoid is developed, and one more objective space analysis is easy to acquire. The correctness and effectiveness of this method have been demonstrated by the application of data of a control network.

关 键 词：测地坐标 椭球面三角形 凸多边形 面积公式 

分 类 号：P226[天文地球—大地测量学与测量工程]