3D spatial models for geometric description of spatial objects

Abstract

Whilst thematic analysis and 2D spatial analysis are well studied, research on 3D spatial analysis is still at an intensive stage. Spatial relationships are the fundament of a large group of operations to be performed in Geographic Information System (GIS), e.g. inclusion, adjacency, equality, direction, intersection, connectivity, and their appropriate description and maintenance is inevitable. Similar to 2D variants, 3D GIS should be capable to perform metric (distance, length, area, volume, etc), logic (intersection, union, difference), generalisation, buffering, network (shortest way) and merging operations. Except metric operations, most of them require knowledge about spatial relationships. The third dimension increases drastically the number and complexity of all possible spatial relationships, compared with 2D GIS. A formalism for the detection of spatial relationships based on set topology notions has already been proposed by several authors, however the description of 3D spatial relationships is not sufficiently studied. The design of a spatial query language or the extending of existing languages, updating procedures to ensure topology consistency of database, etc., these are tasks that need further development. In this paper, the definition of a new spatial model will be given. It will be referred to as Geometric Domain Spatial Model. According to the proposed definition of an object, the geometry of each spatial object can be associated with four abstractions of geometric objects, i.e. point, line, surface and body.