On 3D Topological Relationships

Abstract

This paper presents an integrated study on possible topological relationship between multidimensional simple objects in 0,1,2 and 3 D space. The formal categorisation of spatial relationships is completed upon the 9intersections model. The focus is on the definition of a unified set of conditions for eliminating relationships that cannot be realised in reality. The negative conditions are formulated on the basis of dimension and co-dimension of objects, and connectivity of boundaries. The set of 25 conditions is sufficient for deriving all the possible relationships mentioned currently in the literature and for specifying the relationships between surface and surface in 3D space. Drawings of example configurations verify the obtained results in 3D space. 1 Introduction The topological spatial relationships gain an increasing attention in the last decade. The topic of research has shifted from issues related to the definition of a particular formalism to represent topological relation..