Event‐based topology for dynamic planar areal objects

Abstract

Abstract Representation and reasoning about dynamic spatial phenomena requires at its foundation a formalism of spatial change. This paper extends our understanding of topological change, by providing a classification and analysis of events associated with changes in topological structures of spatial areal objects as they evolve through time. Tree structures are employed to represent topological relationships between regions and holes of areal objects. Basic and complex changes are specified using structure‐preserving mappings between trees. Furthermore, the paper constructs a normal form, and proves that it is the 'simplest' form that can represent all the changes under consideration. Keywords: EventsTopologyGraphsSpatio‐temporalDynamicFieldRegions Acknowledgements We thank Dr. John Stell and the anonymous reviewers for their insightful comments and suggestions. This material is based upon work supported by the National Science Foundation under grant numbers IIS‐0429644 and IIS‐0534429. Michael Worboys' work is also supported by the National Science Foundation under NSF grant numbers DGE‐0504494 and BCS‐0327615, and by the Ordnance Survey of Great Britain.