Spatial neighbors for topological spatial relations: the case of a circular spatially extended point

Abstract

This paper presents the conceptual neighborhood graphs with the transitions that exist between several topological spatial relations. The analyzed topological spatial relations include those that exist between a circular spatially extended point and a region, between a circular spatially extended point and a line, and between two circular spatially extended points. The conceptual neighborhood graphs were identified using the snapshot model. In this model, the identification of neighborhood relations is achieved looking at the topological distance existing between pairs of spatial relations. The obtained graphs are suitable for reasoning about gradual changes in topology. These changes can be associated with the motion of objects and/or deformations over time.