地图符号数学定义的研究

根据拓扑学和图论的有关定义及符号构形的知觉阈值,提出符号清晰描绘和表示的下极限--极限圆概念,通过地物在平面上投影的图上面积与极限圆的比较,推导了依比例符号、不依比例符号和半依比例符号的数学定义,从而使这三类地图符号的基本概念获得了精密的数学形式和定量描述。探讨了这三类地图符号的依存关系和相互转化的条件,使不依比例符号和半依比例符号随地图比例尺的缩小而数量倍增的规律得到了理论解释。

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

According to the scaled relation in the concerned catographic literatures,the cartographic symbols are classified into scale symbol,non-scale symbol and semi-scale symbol,whose mathematical definitions are produced in this paper.(1) The basic concepts applied in this paperThe internal point and external point in the topology;the trail and cycle in the graph theory;the consciousness thershold value of symbolic configuration in the map perception;the limit circle minO and the area S_xt of plane projection of surface feature on map,etc.(2) The definition of scale symbolicIf the boundary W_x of S_xt suffices the following condition:W_x={P|P∈ Ext minO∧S_xt=f(w_x)},then the S_xt calls the scale symbol with W_x as boundary.(3) The definition of Non-scale symbolicIf S_xt minO condition is sufficed and the median point of S_xt is the centre of limit circle min O,then the median point of S_xt is called the characteristic point of non-scale symbol and the cartographic symbol with it as localized centre is called the non-scale symbol. (4) The definition of semi-scale symbolicAfter the characteristic point and localized line of semi-scale symbol were definde i.e.the cartographic symbol with semi-scale symbol localized line as its central line and indication x surface feature is called the semi-scale symbol.The relation of three classes cartographic symbol and their transformation condition are discussed in this paper.