地图图层系统为布尔代数系的证明及应用

The proof of cartographic layer system belonging to boolean algebra and its application

布尔代数系是适于电子计算机作逻辑运算的系统.任何地图实质上是有限个图层的集合.图层是电子地图系统和地理信息系统(GIS)数据基本存贮单元,是组织和管理数据的有效方式和有用手段.以点为基本元素的地图图像系统和以地图符号为基本元素的地图符号系统属于布尔代数系已经得到了证明.根据布尔代数的定义和充要条件,结合图层示例,论证了地图图层系统也是布尔代数系,这为地图图层系统在计算机的表示提供了计算机理论基础和数学工具.实例表明,不管是电子地图还是GIS中,都是利用图层来组织和管理地图数据库的.

Boolean algebra is the system where electronic computer can do logical operation. A map is the set of finite layers effectually. Layer is not only the basic storage unit of data in electronic map system, but also useful method and an efficient way in managing and organizing map data. Cartographic symbol system and cartographic image system belonging to Boolean algebra have been proved. Because layer suffices the necessary and sufficient conditions for Boolean algebra, cartographic layer system is Boolean algebra, which the computer theoretic base and mathematical tool of layer expressing in computer. Object-oriented layer stores and manages various useful data of space, attribute, symbol, annotation, legend. In electronic map and GIS layer is applied to organize data.