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.