黄鹄, 钟业勋. 依比例符号、不依比例符号和半依比例符号数学定义的改进[J]. 武汉大学学报 ( 信息科学版), 2006, 31(3): 244-246.
引用本文: 黄鹄, 钟业勋. 依比例符号、不依比例符号和半依比例符号数学定义的改进[J]. 武汉大学学报 ( 信息科学版), 2006, 31(3): 244-246.
HUANG Hu, ZHONG Yexun. Improving the Mathematical Definition of Scale Symbol,Non-scale Symbol and Semi-scale Symbol in the Map[J]. Geomatics and Information Science of Wuhan University, 2006, 31(3): 244-246.
Citation: HUANG Hu, ZHONG Yexun. Improving the Mathematical Definition of Scale Symbol,Non-scale Symbol and Semi-scale Symbol in the Map[J]. Geomatics and Information Science of Wuhan University, 2006, 31(3): 244-246.

依比例符号、不依比例符号和半依比例符号数学定义的改进

Improving the Mathematical Definition of Scale Symbol,Non-scale Symbol and Semi-scale Symbol in the Map

  • 摘要: 三维空间中的制图物体要投影到地球椭球面S上,故存在三维空间X到地球椭球面S的映射f:X→S;x及其投影f(x)的属性、尺寸、形状等特征,被制图者认识和了解是对x进行地图表示的前提,故存在椭球面S到主体认识结构Y的映射g:S→Y。x的观念模型gf(x)可以表示在二维平面Z上,故Y与Z间必然存在映射q:Y→Z。根据非退化区间为等势集合的定理,知f、g、q为双一一函数,从而使x、f(x)、gf(x)与qgf(x)一一对应。而f(x)与qgf(x)是否与地图比例尺1∶M相关、无关或半相关,决定着地图符号qgf(x)为依比例符号、不依比例符号或半依比例符号的归属。这三类地图符号相互转化及条件,证明了事物由量变到质变的辩证规律。

     

    Abstract: The mapping objects in the three-dimensional space need being projected on S surface of earth-ellipsoid,so there is the mapping f:X→S from three-dimensional space X to the S surface of earth-ellipsoid.It is the premise of showing x on map for the attribute,measurement,shape,etc.characters of x and its mapping f(x) on S are known and undersdood by the cartographer,so there is the mapping g:S→Y from the S surface of earth-ellipsiod to the body cognition construction Y.The idea model of x in Y gf(x) may show on two-dimensional plane Z,so there is the mapping q:Y→Z from the body(idea) construction Y to the two-dimensional plane Z.According to the theorem non-deteriorate inter-regional belonging to the equipollence set,we know that the f,g,q are bijective,this makes x,f(x),gf(x) and qgf(x) corresponding one to one.It decides the map symbol qgf(x) belonging to the scale symbol or non-scale symbol or semi-scale symbol respectively for the f(x) and qgf(x) with the map scale 1∶M are related,aren't related or semi-related.

     

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