地球椭球面图斑面积计算方法探讨  

Discussion on calculation method of earth ellipsoid patch area

作　　者：史守正 石忆邵[1] SHI Shouzheng;SHI Yishao(College of Surveying and Geo-Informatics,Tongji University,Shanghai 200092,China;College of Environmental Science and Engineering,Suzhou University of Science and Technology,Suzhou,Jiangsu 215009,China)

机构地区：[1]同济大学测绘与地理信息学院,上海200092 [2]苏州科技大学环境科学与工程学院,江苏苏州215009

出　　处：《测绘科学》2019年第11期164-169,175,共7页Science of Surveying and Mapping

摘　　要：针对地球椭球面图斑连线类型的非唯一性、椭球面梯形面积计算公式的多样性以及任意图斑面积计算精度控制的复杂性等问题,该文基于理论探讨与实例计算相结合的方法,明确了土地面积量算中适宜采用的椭球面图斑类型,测定了各椭球面梯形面积公式的计算精度,给出了任意图斑面积计算精度控制的新思路。研究表明:采用等角航线作为地球椭球面两界址点之间连线的等角航线图斑更适宜于土地面积量算工作;取至e10项的乘积项椭球面梯形面积公式不仅精度高于其他两个理论上等价的近似公式,而且也高于精确计算公式;把割、补三角形看做特殊的椭球面大梯形,借助递归算法,提出了椭球面大梯形面积计算的新公式,这为椭球面上任意图斑面积计算及精度控制提供了新思路。Aiming at the non-uniqueness of two-point connection types on earth ellipsoid,the diversity of the calculation formulas for ellipsoid trapezoidal area,and the complexity of the accuracy control in arbitrary patch area calculation,based on the combination of theoretical discussion and case calculation,the type of ellipsoidal patch suitable for land area measurement is clarified,the accuracy of the ellipsoid trapezoidal area formulas is determined,and a new idea of the accuracy control in patch area calculation is given.The research show that the rhumb line patch is more suitable for the land area measurement work than other types of patches;the area calculation accuracy obtained by the product approximate formula taken to e10 items is not only higher than the other two theoretically equivalent approximation formulas,but also higher than the exact formula.The cut and complement triangles are regarded as special ellipsoidal large trapezoids,then a new area calculation formula of the ellipsoidal large trapezoid is given with the help of recursive algorithm,which provides a new idea for the arbitrary patch area calculation and the accuracy control on the ellipsoid surface.

关 键 词：地球椭球面 图斑 等角航线 面积公式 计算实例 递归算法 

分 类 号：P282[天文地球—地图制图学与地理信息工程]