基于极点到坐标原点的距离函数的常规地图投影分类体系

Classified System of Routine Map Projection Based on the Distant Function between the Pole to Coordinate Origin

摘要: 地球椭球面上的经线交于极点而纬线则相互平行。地图上的经纬网是地球椭球面上的经纬网的拓扑映射。投影网中极点到坐标原点的距离函数关联着7类常规地图投影的分类。距离等于零时对应着方位投影；距离为有限值时对应着圆锥投影和多圆锥投影;距离为无穷大时对应着圆柱投影。方位和伪方位投影的纬线为同心圆；圆锥和伪圆锥投影的纬线为同心圆弧；多圆锥投影的纬线为同轴圆弧；圆柱和伪圆柱投影的纬线为赤道的平行线。所有正常投影的经线均为直线，而伪型投影只有作为投影网对称轴的中央经线是直线，其余经线为中央经线的轴对称曲线。多圆锥投影的经线与伪型投影相同。极点到坐标原点的距离函数，与常规地图投影的分类具有等价关系，从而可以推出常规地图投影的一般定义。

Abstract: The longitudes of earth ellipsoid intersect at the poles and the latitudes are parallel to each other. The grid of longitudes and latitudes on the map is the topological map of the grid of longitudes and latitudes on earth ellipsoid. The distance function of the poles to the coordinate origin in the pro-jection grid is related to the classification of seven types of routine map projection. When the dis-tance is equal to zero, it is azimuthal projection; when the distance is finite, it is conic projection or polyconic projection; when the distance is infinite, it is cylindrical projection. The latitude of azi-muthal projection and pseudo-azimuthal projection are homocentric circles. The latitude of conic projection and pseudo-conic projection are homocentric circular arc. The latitude of polyconic projection is coaxial arc. The latitude of cylindrical projection and pseudo-cylindrical projection are parallel lines of the equator. All the longitudes of normal projection are straight, while for the pseudo-projection, only the central meridian of symmetry axis of a projection grid is a straight line and the remaining longitudes is the axisymmetric curve of the central longitudes. Meridian of polyconic projection is identical with the pseudo type projection. The distance function of the pole to the coordinate origin is equivalent to the classification of the routine map projection, so that the general definition of routine map projection can be deduced.