Topological Relationships between a Circular Spatially Extended Point and a Line: Spatial Relations and their Conceptual Neighborhoods

This paper presents the topological spatial relations that can exist in the geographical space between a Circular Spatially Extended Point and a Line and describes the use of those spatial relations in the identification of the conceptual neighbourhood graphs that state the transitions occurring among relations. The conceptual neighbourhood graphs were identified using the snapshot model and the smooth-transition model. In the snapshot model, the identification of neighbourhood relations is achieved looking at the topological distance existing between pairs of spatial relations. In the smooth-transition model, conceptual neighbours are identified analysing the topological deformations that may change a topological spatial relation. The graphs obtained were analysed as an alternative to map matching techniques in the prediction of the future positions of a mobile user in a road network.