Reasoning about Gradual Changes of Topological Relationships

Spatial relationships between geographic objects are time-dependent and can change due to various phenomena. Water levels of rivers or lakes may rise causing flodding of buildings and roads near the shore line; contamination of soils may spread causing hazards for people living in affected areas; hurricanes may pass over islands or reach the continent; and market areas may expand so that they extend into adjacent political or administrative regions. In all these examples the objects changed their spatial relationships with respect to other spatial objects. A particularly important set of spatial relationships are , which are preserved under groups of continuous transformations. Models for changes of topological relationships are relevant to spatio-temporal reasoning in geographic space as they derive the most likely configurations and allow National Center for Geographic Information and Analysis and Department of Surveying Engineering, Boardman Hall, University of Maine, Orono, ME 04469, U.S.A. max,kaltaha @mecan1.maine.edu