几种世界地图投影的经纬网的数学变换

Mathematical Transformation of Latitude and Longitude Network on Several World Map Projections

正圆柱投影、伪圆柱投影和多圆锥投影的经纬网的构形不同,但它们都属于合同图形,都具有以中央经线λ0为对称轴的东、西向镜射变换和以赤道s0为对称轴的南、北向镜射变换的特点。都属于以中央经线和赤道交点O为中心的中心对称图形。根据非中央经线λi构形特点和空间结构,定义了外凸型曲经线网、离散型直经线网;根据非零纬线φj的构形特点和空间结构,定义了内凸同轴圆弧型纬线网、赤道平行线型纬线网。在此基础上,通过不同经纬网的组合,给出了正圆柱投影、伪圆柱投影和多圆锥投影的数学定义。根据集合运算的规则,阐释了不同类型地图投影间的数学变换。

The normal cylindrical projection,pseudo-cylindrical projection,and polyconic projection have different configuration of the longitude and latitude network,but they all belong to the contract graphics.And they all have the characteristics of symmetry transformation with the central me-ridianλ0 as the axis of symmetry when in the east-west direction,as the equator s0 as the axis of symmetry when in the north-south direction.Also,they all belong to a central symmetrical figure centered on the intersection O of the central meridian and the equator.According to the configu-ration features and spatial structure of the non-central meridiansλi,a convex curved longitude net and a discrete straight longitude net are defined in this paper.According to the configuration characteristics and spatial structure of the non-zero latitudesφj,the inner convex coaxial circular arc latitude net and the equatorial parallel latitude net are defined.On this basis,the mathematical definitions of normal cylindrical projection,pseudo cylindrical projection and polyconic projection are given by the combination of different latitude and longitude nets.According to the rules of set operations,the mathematical transformation between different types of map projections is explained in this paper.