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.