A 27-Intersection Model for Representing Detailed Topological Relations between Spatial Objects in Two-Dimensional Space

Determining the spatial relations between objects is a primary function of a geographic information system (GIS). One important aspect of spatial relations is topological relations, which remain constant under topological transformations. Describing the geometry of a spatial object using the OpenGIS Simple Features Specification requires only simple features: the interior, boundary and exterior of a spatial object are defined. This paper proposes a comprehensive model, the 27-intersection model (27IM), which considers both the dimensions and the number of intersections. Some propositions are presented to exclude relations that the 27IM cannot implement. The 27IM describes six groups of topological relations: point/point, point/line, point/region, line/line, line/region and region/region. The formalism of the 27IM and the corresponding geometric interpretations between spatial objects are illustrated and then compared to the topological relations represented by the existing models, the nine-intersection model (9IM), the dimensionally-extended nine-intersection matrix (DE-9IM) and the separation number extended nine-intersection matrix (SNE-9IM). The results show that (1) the 27IM can represent the topological relations between two-dimensional spatial objects, (2) the 27IM can distinguish more topological relations than can the 9IM, DE-9IM or the SNE-9IM and that (3) the interoperability of the 27IM with the 9IM, DE-9IM and SNE-9IM is good.