地图投影的拓扑学原理

Topologic principle in mapping projection

根据拓扑映射的定义,指出了"刺孔球面"(S2-{z})与二维平面R2的同胚性质。从有限闭区间及其彼此等势的拓扑学原理,推出f(A)为非空集。f(A)的边界是二维平面上的约当闭曲线,约当闭曲线的任意性,使得f(A)可以在拓扑变换下变形为任意的形状,构造多种多样的投影网格。以若干实例说明了拓扑映射ff1、f2的实现方法。

According to the definition of topological mapping,the quality of homeomorphism of sting-out sphere( S2- { z}) is put up with two-dimensional plane R2. The f( A) is deduced as a nonempty set according to the topologic principles of finite closed interval and equipollence to each other. The boundary of f( A) is a Jordan closed curve on 2D plan. With the randomicity of Jordan closed curve and different topologic transform rules,f( A) can be random shape and construct various projection grids. The new method of ff1,f2 function is showed by examples.