Topological Relationships between Map Geometries

The importance of topological relationships between spatial objects is recognized in many disciplines. In the field of spatial databases, topological relationships have played an important role, providing mechanisms for spatial constraint specification and spatial indexing techniques. The use of spatial data in a map form has become popular, resulting in spatial data models such as topologies or, more generally, map geometries, which model collections of spatial objects that satisfy certain topological constraints. However, the topological relationships between map geometries remain unexplored. In this paper, we identify the set of valid topological relationships between map geometries, and then provide a mechanism by which they can be directly implemented on top of existing systems by using topological relationships between regions.