Are topological relations dependent on the shape of spatial objects?

摘要

Topology is normally considered as independent of shape of spatial objects. This may not necessarily be true in describing relations between spatial objects in GIS. In this paper, we present proof that the topological relations between spatial objectsare dependent on the shape of spatial objects. That is, that the topological relations of non-convex sets cannot be deformed to the topological relations of convex sets. The significant theoretical value of this paper is on its findings that topology ofspatial objects is shape dependent. This indicates that when we want to describe topological relations between spatial objects in GIS, both topology and the shape of objects need to be considered. As a result, spatial data modeling, query and analysis based on the existing understanding of topology of spatial objects may need re-assessed.