摘要
通常地图投影反解变换有2种方法,即多项式拟合法和投影方程解析法。多项式法利用已知控制点的坐标对应关系,通过最小二乘法拟合求解地图投影反解变换的多项式函数,其优点是反解模型与地图投影无关,算法具有通用性,缺点是反算精度较低。解析法根据地图投影正算公式,在一定条件下通过解方程求得地图投影反解变换解析式,其优点是反解变换精度高,缺点是解法复杂。本文利用计算数学方法,根据地图投影变换的基本数学原理,提出了一种新的地图投影反解变换方法,双向迭代逼近法(BDIRA)。具有反解变换精度高、收敛速度快、算法通用和GIS软件编程实现方便等特点。
There are two common methods for map projection reverse transformation, namely, polynomial fitting method and analytical method of map projection equation. The polynomial fitting method is carried out by least squares fitting based on control points, it is universal but has lower reverse resolutions. The analytical method of map projection equation is carried out by solving map projection equations, it has high precision in inverse computaion but is very complex.The paper provides a new algorithm for map projection reverse transformation, namely, bi-directional iteration reverse algorithm (BDIRA), which integrates the advantages of two methods above, and meets the needs for most types of common map projections. The iteration of this algorithm for most map projections is convergent, so it is universal in some way. Another advantage of BDIRA is that its reverse errors can be controlled and simple to code in GIS Software developing.
出处
《测绘学报》
EI
CSCD
北大核心
2004年第2期179-185,共7页
Acta Geodaetica et Cartographica Sinica
基金
福建省自然科学基金资助项目(A99008)
福建省高新技术项目(99 H 42)
国家"十五"攻关项目(2001 BA 603B 02)
