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.
参考文献
[1]
|
胡毓钜, 龚剑文. 地图投影(第二版) [M]. 北京: 测绘出版社, 2006.
|
[2]
|
胡毓钜, 龚剑文. 地图投影图集(第三版) [M]. 北京: 测绘出版社, 2006.
|
[3]
|
祝国瑞. 地图学(第三版) [M]. 武汉: 武汉大学出版社, 2004.
|
[4]
|
钟业勋. 数理地图学[M]. 北京: 测绘出版社, 2007.
|
[5]
|
钟业勋, 胡毓钜. 圆柱投影, 圆锥投影和方位投影的统一数学模型及应用比较研究[J]. 地图, 1992(1): 12-17.
|
[6]
|
宁津生, 陈俊勇, 李德仁, 等. 测绘学概论[M]. 武汉: 武汉大学出版社, 2006.
|
[7]
|
程吉树, 陈水利. 点集拓扑学[M]. 北京: 科学出版社, 2008.
|
[8]
|
谷超豪. 数学词典[M]. 上海: 上海辞书出版社, 1992.
|
[9]
|
毋河海. GIS地图信息综合基本模型与算法[M]. 武汉: 武汉大学出版社, 2010.
|
[10]
|
李孝传, 陈玉清. 一般拓扑学导引[M]. 北京: 高等教育出版社, 1982.
|
[11]
|
钟业勋, 童新华, 韦清嫄. 地图投影的拓扑学原理[J]. 桂林理工大学学报, 2014, 34(3): 510-514.
|
[12]
|
罗淼, 严虹, 廖义琴. 几何学概论[M]. 北京: 清华大学出版社, 2011.
|
[13]
|
钟业勋, 胡宝清, 童新华, 等. 地图学概念的数学表述研究[M]. 北京: 科学出版社, 2015.
|