An Extended K Function Method for Analyzing Distributions of Polygons with GIS

The objective of this paper is to develop a K function method for analyzing distributions of polygon-like entities in the real world by extending Ripley’s K function method. Many empirical studies using the K function method assume that entities are represented by points. If entities are small enough in comparison with a study area, this approximation may be acceptable. If not, polygon-like entities may not be approximated by points. To deal with polygon-like entities, this paper develops a K function method for analyzing distributions of polygons. First, the paper shows a method for extending the local K function of points to that of polygons. Second, the paper compares the result obtained from the K function of polygons with that of the points representing the polygons and shows a distinctive difference. Third, the paper formulates the cross K function method of polygons to analyze the relationship between two distributions of polygons of different kinds. Fourth, the paper implements the methods in GIS. Last, the paper applies the cross K function method of polygons to actual distributions of buildings of different uses in Aoyama, Tokyo.