利用算子微分理论和反演方法探求地图投影正解变换  

Searching for the Transformation of Map Projection Based on the Differential Theory of Operator and Inversion Method

作　　者：任留成[1,2] 吕泗洲[1] 

机构地区：[1]空军指挥学院战略战役系,北京100097 [2]中国科学院遥感应用研究所,北京100101

出　　处：《测绘科学技术学报》2013年第1期15-18,共4页Journal of Geomatics Science and Technology

基　　金：国家自然科学基金项目(41071287)

摘　　要：探求地图投影模型是一个很复杂的数学问题,涉及诸多数学理论和方法,解算步骤和过程一般都很繁琐。此处根据现代数学中的算子微分理论和微分几何理论,采用反演的方法对地图投影的正解变换进行了研究,简化了地图投影正解求解的过程和步骤。基本思路是先通过求解地图投影的反解变换,再根据反解变换求其相应的正解变换。并利用微分算子理论中的等角和等面积投影定理,分别验证了所探求的正反解是等角投影还是等面积投影。最后经过算例证明该方法的快捷性和有效性。Searching for the map projection model is a very complicated problem, because many mathematic the- ory and methods will be involved, the process and solving steps will be more trivial generally. Based on the differential theory of operator and differential geometry of modern mathematic, the method of inversion was applied to search for the transformation of map projection, the process and steps of obtaining map projection formula was simplified. The basic idea was to obtain the inverse transformation of map projection firstly, and then the transformation of map projection was got according to its inverse transformation. The theorems of preserving angles or areas were applied in order to verify the characteristics of preserving angles or areas of the transformation and inverse transformation of map projection gained. The validity and agility of this method was verified by some examples finally.

关 键 词：算子微分 反演方法 地图投影 正解变换 反解变换 

分 类 号：P282.1[天文地球—地图制图学与地理信息工程]