Implementation of an advanced Topological Structure in 2D GIS

Davood Parvinnezhad
M.A. in Geographical Information Systems (KNT University, Tehran, Iran)
Tabriz, Iran
Email: d_parvinnezhad@yahoo.com


Arash Rahmanizadeh
M.A. in Photogrammetry (Tehran University, Tehran, Iran)
Tabriz, Iran Email: aosakram@yahoo.com


Abstract
Spatial relations are the basis of many queries that Geographic Information Systems (GISs) perform, as such the topological relations deserves a focused attention from GIS researchers. Current commercial query languages do not sufficiently support such queries, since the languages only provide tools to compare equality or order of simple data types, such as integers or strings. The incorporation of spatial relationships over spatial domains into the syntax of a spatial query language is an essential extension beyond the power of traditional query languages.

Three different formal approaches exist for the definition of spatial relationships. The first one is based upon distance and direction in combination with the logical connectors AND, OR, and NOT. This approach has two severe deficiencies: (1) It is not possible to model inclusion or containment, unless ‘negative’ distances are introduced. (2) The lack of appropriate computer numbering systems for geometric applications impedes the immediate application of coordinate geometry and distance-based formalisms for spatial relationships.

The secondary approach is based on the representation of spatial data in the form of point sets. Binary relationships are described by comparing the ‘points’ of two objects with conventional set operators, such as equal, and less than or equal. A serious deficiency inherent to the point sets approach is that only a subset of topological relationships is covered with this formalism. While equality, inclusion, and intersection can be described, the point set model does not provide the necessary power to define neighborhood relationships.

The third approach is based on the intersection of the boundary, interior, and exterior of two objects to be compared and distinguishes only between “empty” and “non-empty” intersection. This method is superior to the other two formalisms because it describes topological relations by purely topological properties.

The 9-intersection model characterizes the topological relation between two point sets, A and B, by the set intersections of A’s interior , boundary , and exterior with the interior, boundary, and exterior of B. Hence, the 9-intersection model is better than the 4-intersection model in perfectly expressing the topological relationships between two objects. In 9-intersection model with each of these nine intersections being empty (0) or non-empty (1), the model distinguishes 512 different topological relations between two point sets, some of which cannot be realized, depending on the dimensions of the objects and the dimensions of their embedding space.
In this paper, the 9-intersection model is implemented using ActiveX and Dynamic Link Library (DLL) Technologies. The main characteristic of this package is to create advanced topological relationships between 2D objects in a GIS environment. A part of the City of Tehran information has been selected for assessing the software. Results of the test have shown the superiority of the proposed structure versus current commercial GIS software.