A conceptual framework for modelling spatial relations

Abstract

Various approaches lie behind the modelling of spatial relations, which is a heterogeneous and interdisciplinary field. In this paper, we introduce a conceptual framework to describe the characteristics of various models and how they relate each other. A first categorization is made among three representation levels: geometric, computational, and user. At the geometric level, spatial objects can be seen as point-sets and relations can be formally defined at the mathematical level. At the computational level, objects are represented as data types and relations are computed via spatial operators. At the user level, objects and relations belong to a context-dependent user ontology. Another way of providing a categorization is following the underlying geometric space that describes the relations: we distinguish among topologic, projective, and metric relations. Then, we consider the cardinality of spatial relations, which is defined as the number of objects that participate in the relation. Another issue is the granularity at which the relation is described, ranging from general descriptions to very detailed ones. We also consider the dimension of the various geometric objects and the embedding space as a fundamental way of categorizing relations.