National Center for Geographic Information and Analysis Multiple Topological Representations

Humans use multiple mental models of the world to reason efficiently at different levels of abstraction. Current geographic information systems (GIS) normally use only a single model or representation of the world. If only a single level of abstraction is supported, the utility of the system is limited. Future GIS should support multiple representations at different levels of abstraction, so that adequate levels of abstraction can be found for a large range of scales. Queries that require little detail can then be processed as efficiently as those which require much detail. This paper proposes an approach to supporting multiple levels of abstraction in a GIS through multiple topological representations (MTR). The representations are linked by hierarchical relations between elementary spatial building blocks called cells. We introduce largest homogeneous cells (LHC's) to guarantee the hierarchical structure of these links. LHC's can easily be modelled in topological representations that use different kinds of cells. They therefore form an interface between an MTR and the underlying implementations of (single) topological representations. MTR's can represent arbitrary configurations of objects in any dimension.