Hierarchical structures in map series

Abstract

Among the different operations in Geographic Information Systems (GIS), changing scale is crucial for the handling and analysis of multi-scale data. The term multi-scale is used to indicate that there are data of more than one level of detail in the database. In this research we investigate how to link map objects at different levels of detail that represent the same real-world entity. The observation method relies on careful observation of phenomena, similar to the method of reverse engineering in computer science. We propose a hierarchical data structure that supports and describes the behavior of map objects over four levels of detail. Each map is a level in a three-dimensional cube, the vertical axis represents the level of detail. The hierarchical data structure of the map cube model is a combination of three trees, representing three different types of hierarchies. It is a combination of the trans-hydro network, a tree of containers including the information on areas and elements, an area graph, and an element graph. We formalize the map cube model in the functional programming language Gofer with an object- oriented paradigm. Hierarchical data structures are best represented by trees or forests. In our model the trans-hydro network is represented by a filter hierarchy, the filter criterion is the relative importance of the link in the network. The container tree is an aggregation hierarchy - the more abstract the representation, the more containers are aggregated. The area graph is a collection of area trees; each tree represents a generalization hierarchy. The element graph is a collection of trees; each tree is constructed by several functions. Those functions are 'omit', 'typify', 'merge', and 'continue'. The first three functions correspond to the cartographic functions with the same name. Thus, the model incorporates all three types of hierarchies.