Abstract. This article considers the philosophical and experiential foundations of human perception of geographical phenomena and their abstraction and coding in geographical information systems. It examines the role of culture and language in describing geographical reality and explores the ways geographical data models reflect how people view the world. Differences between those who see the world as made of exact entities and smooth continuous surfaces, and those who prefer to view reality as a dynamic and complex are explored in terms of five aspects of spatial data, namely (i) objects versus fields, (ii) single scale versus multiple scales, (iii) Boolean versus multivalued logic, (iv) static versus dynamic descriptions and (v) determinism versus uncertainty. These five aspects are further divided into nine factors of geographical data which indicate the differences in the way people perceive spatial data. Eight “typical” GIS applications and four generic methods of handling spatial data are examined in terms of these nine factors to define a GIS “hyperspace”. The locations of the typical applications and the generic methods in this hyperspace show why no single generic approach to spatial data handling is sufficient for all possible applications. The analysis reinforces the authors' contention that spatial data analysis tools need to be chosen and developed to match the way users perceive their domains: these tools should not impose alien thought modes on users just because they are impressively “high tech”. The implications of this conclusion for choosing or developing spatial information systems, for data standardization and generalisation and for the further development of “GIS” as a discipline in its own right are presented as topics for further discussion.

Abstract: Practical needs in the realm of Geographic Information Systems (GIS) have driven the efforts to investigate formal and sound methods to describe spatial relations. After an introduction of the basic ideas and notions of topology, a novel theory of topological relations between sets is developed in which the relations are defined in terms of the intersections of the boundaries and interiors of two sets. By considering empty and non-empty as the values of the intersections, a total of sixteen topological spatial relations are described, each of which can be realized in RxR. This set is reduced to nine relations if the sets are restricted to spatial regions, a fairly broad class of subsets of a connected topological space having application to GIS. It is shown that these relations correspond to some of the standard set-theoretic and topological spatial relations between sets such as equality, disjointness, and containment in the interior.

The framework is independend of the existence of a distance function.

Abstract: Over the last ten years, a subfield of GIScience has been recognized that addresses the linkage between human thought regarding geographic space and the mechanisms of implementing these in computational models. This research area has developed an identity through a series of successful international conferences and the establishment of a journal. It has also been complemented through community activities such as an international standardization efforts and GIS interoperability. Historically, much of the advancement in computational methods has occurred at - or close to - the implementation level, as exemplified by the attention on the development of spatial access methods. Significant progress has been made at the levels of spatial data models and spatial query languages, although we note the lack of a comprehensive theoretical framework comparable to the relational data model in database management systems. The difficult problems that need future research efforts are the highly abstract level of capturing semantics of geographic information. A cognitive motivation is most promising as it shapes the focus on the user's needs and points of view, rather than on efficiency as in the case of a bottom-up system design. We also identify the need for new research in fields, models of qualitative spatial information, temporal aspects, knowledge discovery, and the integration of GIS with database management systems.

A spatial join takes two sets of spatial objects as input and produces a set of pairs of spatial objects as output, such that each pair fulfils the given spatial predicate. Examples include, “Find all houses that are less than 10Km from a lake” or “Find all buildings that are located within a wetland.”

Early proposals for multidimensional data structures, such as k-d tree or quadtrees, focused on memory-resident data and, therefore, do not take secondary storage management explicitly into account.