Event-based topology for dynamic planar areal objects

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. Further, the paper constructs a normal form, and proves that it is the ‘simplest’ form that can represent all the changes under consideration.