Formal description of topological relations between spatial objects with a hole

Abstract

Description and differentiation of topological relations are based on the changes of topological properties of spatial objects sets and their components before and after their intersection. There were many researches about special topological relations between two simple spatial objects, but the researches on topological relations of the spatial objects with a hole are relatively fewer. This paper uses the description frame of two spatial objects with holes, which is put forward by Egenhofer etc. Based on the 4ID, this paper put forward a new extended model which can describe special topological relations between the spatial objects with a hole. At the same time, the paper detrude 23 kinds of topological relations between a simple spatial object and a spatial object with a hole and 57 kinds of topological relations between two spatial objects which only with a hole.