Siyka Zlatanova

Topological models and frameworks for 3D spatial objects

Topology is one of the mechanisms to describe relationships between spatial objects. Thus, it is the basis for many spatial operations. Models utilizing the topological properties of spatial objects are usually called topological models, and are considered by many researchers as the best suited for complex spatial analysis (i.e., the shortest path search). A number of topological models for two-dimensional and 2.5D spatial objects have been implemented (or are under consideration) by GIS and DBMS vendors. However, when we move to one more dimension (i.e., three-dimensions), the complexity of the relationships increases, and this requires new approaches, rules and representations. This paper aims to give an overview of the 3D topological models presented in the literature, and to discuss generic issues related to 3D modeling. The paper also considers models in object-oriented (OO) environments. Finally, future trends for research and development in this area are highlighted.

On 3D topological relationships

This paper presents an integrated study on the possible topological relationship between multidimensional simple objects in 0, 1, 2 and 3D space. The formal categorisation of spatial relationships is completed upon the 9-intersections 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.

3D spatial relationships model: a useful concept for 3D cadastre?

This paper contains some reflections about using 3D topology, and more generally some 3D concepts related to 3D cadastre. Firstly, we develop some conceptual views about 3D modelling and more specifically about the definition of 3D spatial objects. Secondly, we present a new framework for representing spatial relationships. The framework has different “complexity” levels and allows mixing simple and complex spatial relationships. Therefore, it is possible to consider different levels when querying spatial objects. Finally, some examples are presented in R 3 that demonstrate the applicability of the framework for cadastral objects.

The Dimensional Model: A Framework to Distinguish Spatial Relationships

A unique characteristic of GIS as compared to other information systems, is their capacity to manage spatial relationships, such as connections or interrelations among objects in the geometric domain. A number of frameworks use topology as a basic mechanism to define spatial relationships. The 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 objects and the dimensional relationships, i.e. the relationships existing between dimensional elements. The model addresses a substantial group of spatial relationships and provides a flexible framework to consider either generalised or specialised types of associations.