Abstract
Polygons are fundamental spatial objects used in GIS. They represent two-dimensional entities that are often in close relations in the real world. Market areas of competing supermarkets mutually invade each other. Expansion of an urban area often involves that of business and commercial districts in its inside. Such relations have drawn much attention of geographers, and have been analyzed in geography and other related fields. Standing in the same line, this paper proposes a new exploratory method of analyzing the relations among polygons. The objectives of analysis are to understand the whole structure of the relations among polygons and to detect local patterns in the relations. A focus is on the hierarchical relations among polygons since spatial hierarchy is an essential concept in geography. Using topological relations between a pair of polygons, this paper proposes graph representations that visualize the relations among more than two polygons. They allow us to analyze the relations among polygons at both global and local scales and to classify them in terms of the closeness of relations. The method is applied to analysis of the result of experiment in environmental psychology. Technical soundness of the method is discussed as well as empirical findings.
