The objective of our study is, first, to provide a general framework for analyzing spatial relations observed in geographical phenomena, and second to develop a user-friendly toolbox of methods classified under this general framework. The implementation of this toolbox will be achieved in a GIS environment.
The toolbox consists of small boxes, which are labeled according to geometrical shapes of objects. We classify geographical objects by points, lines and areas (polygons), and in terms of these objects, we classify spatial relations into 6 relations: points-points, points-lines, points-polygons, lines-lines, lines-polygons, polygons-polygons.
1 Points-Points. Examples are: a spatial relationship between the distribution of railway stations and that of factories; that between distributions of two kinds of species (in ecology). A fairly many methods have been developed in geography and ecology, which are called association methods.
Strangely enough, methods for analyzing other spatial relations have been less developed in the related literature.
2 Points-Lines. An examples is a spatial relationship between the distribution of withered tress with respect to a network of express ways.
3 Points-Polygons. An example is a spatial relationship between the distribution of high-rise apartment buildings around big parks.
4 Lines-Lines. An example is a spatial relationship between a network of canals and that of roads.
5 Lines-Polygons. An example is a spatial relationship between the distribution of rice fields with respect to rivers.
6 Polygons-Polygons. An example is a spatial relationship between the distribution of race fields and that of wheat fields.
Methods for spatial relations, in particular, 2-6, should be developed. One possible and promising method would be the use of generalized Voronoi diagram, or more specifically, Voronoi diagrams for points, lines and polygons. A few initial attempts are shown in Okabe, Boots and Sugihara (1992).