基于条件变换的地图概括新定义

The New Definition of Cartographic Generalization Based on Conditioned Transformation

从较大比例尺地图A编较小比例尺地图B时必须进行地图概括。因此,地图概括中必然存在变换h:A→B。作为选取、夸大等地图概括形式实质上是点集之间在某种约束条件下的变换,不同的约束条件对应着不同的地图概括形式。根据这思路,提出了包括选取、夸大等11种地图概括形式的数学定义。由于依比例符号、不依比例符号和半依比例符号本质上属于地图概括,它的数学定义也可用同样的思路探讨。

Cartographic generalization must be needed in compilation from map A of larger scale to map B of smaller scale. Thus, there must exists transformation h ：A→B in the cartographic generalization. As cartographic generalization types, the selection, exaggeration, etc. are essentially transformations between point set under some binding conditions, and different binding conditions correspond to different types of cartographic generalizations. According to this thinking, the authors have examined the mathematical definition of eleven cartographic generalization types including selection, exaggeration, etc. Because scale symbol, non-scale symbol and semi- scale symbol essentially belong to cartographic generalization, their mathematical definition may also be examined by the same way.