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Topology and Geographical Information Systems

Ellul, C; Haklay, M; (2005) Topology and Geographical Information Systems. Presented at: RGS-IBG Annual Internatonal Conference 2005.

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Abstract

The first use of topology as a problem-solving tool has been attributed to Euler, who proved that the Konigsberg Bridge Problem is insoluble in 1735. Since then, topology has evolved as a branch of mathematics, and more recently as an area of functionality offered in Geographical and Spatial problem solving, allowing efficient implementation of adjacency, connectivity and containment analysis between two objects. This functionality is the corner stone of many algorithms in computational geography. The paper commences by reviewing and comparing two approaches to implementing such analysis in a GIS, namely calculating the relationships as required or pre-calculating the relationships and storing the results. The latter approach has been prevalent until recently, and the paper traces the different factors underpinning this fact, including both pointset and algebraic topology and the emergence of digital cartography.The importance of the concepts of ?interior?, ?exterior? and ?neighbourhood?, in relation to the implementation of topological analysis, are also discussed, and the requirement for topological frameworks highlighted.Finally, approaches to modelling topological relationships in a relational database are then reviewed, and it is concluded that the boundary-representation model provides an optimal mechanism to efficiently derive and maintain topological relationships, although graph representation may also be valid under some circumstances.

Type:Conference item (UNSPECIFIED)
Title:Topology and Geographical Information Systems
Event:RGS-IBG Annual Internatonal Conference 2005

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