基于协调过程的地图政区自动着色

Adjustable Coloring Process for Administrative Units on a Map

地图制图中行政区划通常用颜色来区分,本文以Heawood定理及其证明过程为基础,提出一个基于协调某些已着色区域,用限定色数对政区进行自动着色的方法。它在只要求区分相邻色块的情况下,用最多5种颜色就可完成着色过程。并且在此方法中,根据制图中图面颜色平衡的要求,引进颜色的权重及相应的着色步骤。通过分析地图行政单元的区划特点以及制图中表示行政单元的要求,指出对政区这一类地图着色,在存在分离区域的情况下,不能保证按给定色数完成自动着色过程。

Administrative units are often distinguished by using different colors in cartography. Based on Heawood Theorem and its proving steps, this paper forwards a method in which administrative units may be automatically colored in given number of colors by adjusting some colored units. This coloring process can color any administrative units without separated areas in at most five colors. In addition, color weights are introduced in this process to meet the requirement of balancing different color areas no a map. By analysing graphic features of adminostrative units and earto graphic requiremts, this paper finally points out that no available process can assign given number of colors for any administrative units with separted areas so that any two neighbor units have different colors.