The Dimensional Model: A Framework to Distinguish Spatial Relationships

Abstract

The particularity of GIS compared to other information systems is the management of spatial relationships, i.e. the connections or interrelations between real objects in the geometric domain. A number of frameworks use topology as basic mechanism to define spatial relationships. OpenGIS consortium has adopted one of them, i.e. the 9-intersection model. In this paper, a new framework for representing spatial relationships -the Dimensional model -is introduced. The model was first developed for convex spatial objects and is now extended to topological n-manifolds. It is based on two major concepts, i.e. the dimensional elements of spatial object and the dimensional relationships being the relationships existing between dimensional elements. It represents a very large group of spatial relationships and provides a flexible framework to consider either generalised or specialised types of relationships.

Refining Topological Relations between Regions Considering Their Shapes

“…This paper developed a new model of projective relations based on the Dimensional Model [22] and the 9 + -intersection [15]. As a first step, this paper identified 30 projective relations between a region with a multi-order boundary and a region (i.e., projective region +mob -region relations) in R 2 , and schematized these 30 relations into a conceptual neighbourhood graph.…”

“…The Dimensional Model (DM) was formally defined according to affine geometry [21,22]. It was shown later that its definition satisfies projective geometry rules [23].…”

“…The 1 Let n be a positive integer. We denote by R n + the subset of tuples (α 1 ,...,α n ) with definition of the extended concept is beyond the scope of this article; see [21] or [22] for a comprehensive development. Strictly speaking, the object's "interior" concept in Euclidean topology, on which the original DM stands, is different from that in point-set topology [25], on which the 9-intersection stands.…”

“…For instance, projective geometry has been adopted to categorise spatial relations in a model called the Dimensional Model (DM) [21,22]. The motivation behind DM was to identify spatial relations between 3D objects more precisely.…”

The 9 + -Intersection: A Universal Framework for Modeling Topological Relations

“…Each topological part of a spatial object may be subdivided into multiple subparts based on their disconnection or qualitative difference (e.g., dimensions [18]). For instance, the boundary of a DLine is subdivided into two subparts; start-point and end-point [5].…”