Advanced Topological Structure in GISAliReza Vafaeinezhad PhD Student of GIS in K.N.Toosi University vafaei78@yahoo.com Ali A. Alesheikh Assistant Professor in K.N.Toosi University alesheikh@kntu.ac.ir Davood Parvinnezhad M.Sc. Student of GIS in K.N.Toosi University D_parvinnezhad@yahoo.com Dept of Geodesy and Geomatics Eng. K.N.Toosi University of Technology Mirdamad cross, Valiasr st., Tehran, IRAN Abstract Queries in Spatial databases, such as Geographic Information Systems, image databases, or CAD/CAM systems, are often based upon the relationships among spatial objects. 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, because these languages provide only 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[1]. Unfortunately, currently used GIS softwares do not support advanced topological structures. As such, answering topological queries is time consuming, if not impossible. In this paper, currently used topological models are scientifically examined. 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. Results of the test have shown the superiority of the proposed structure versus current commercial GIS software. The world which we are living in it consists of 3D objects. Therefore, further researches are intended to extend the proposed model to properly answer 3D topological queries. 1- Introduction One capability that distinguishes GIS software from simple drawing packages is the ability to explore the spatial relationships between map features in different layers. spatial relationships are useful in GIS because many spatial modeling operations don't require coordinates, For example, to find an optimal path between two points requires a list of the lines or arcs that connect to each other and the cost to traverse each line in each direction. Coordinates are only needed for drawing the path after it is calculated. Spatial relationships include such as connectivity and adjacency (what is next to what), containment (what is enclosed by what) and proximity (how close something is to something else). GIS software enables researchers to ask questions like:
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[1]. 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[1]. 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 (The 9-intersection model). This method is superior to the other two formalisms because it describes topological relations by purely topological properties[1]. The 4-intersection and 9-intersection are two comprehensive models for binary topological spatial relations and applies to objects of type region, line, and point. The 4-intersection model characterizes the topological relation between two point sets, A and B, by the set intersections of A’s interior (Ao), and boundary (ðA) with the interior, and boundary of B[2]. The 9-intersection model The 9-intersection model characterizes the topological relation between two point sets, A and B, by the set intersections of A’s interior (Ao), boundary (ðA), and exterior(A- with the interior, boundary, and exterior of B (Eq. 1)[4].     Figure 1 The possible topological relationships between 2D features[5]. Implementation To use the 9-intersection model in GIS, a software package has been designed and implemented. The implementation flow-diagram and the applied interface for the software are represented in Figures 3, 4, respectively. The 9-intersection model has many critical problems especially when the co-dimensions between spatial objects are greater than 0, such as between line and polygon. Then in this package, we divide each of the relationship to some sub-relation cases for advanced description. For example, in Figure 2, the r063 relation is divided to some cases that represent it.  Figure2. Some cases of relations that represent one relation of 9-intersection model i.e. r063.  Figure 3 The flow-diagram of the software developed.  Figure 4 The interface of the software. One-layer topology
By running the software, three fields are added to an attributes table. These three fields contain “Pointid”, “X”, and “Y” as coordinates. An instance of the result for this status has been represented in Figure 5.  Figure 5 One-layer topology for point Once the software run, four fields are added to an attributes table. These fields contain “Lineid”, “Fromnode”, “Tonode”, and “Length”. The instance of running software for this case has been represented in Figure 6.  Figure 6 One-layer topology for line. Running the software, creates an additional table i.e. three fields contain “Polygonid”, “Perimeter”, and “Area”, are added to an attributes table and one new table that contains three fields for representing topological relations. This additional table used for cadastral cases. An instance of running software for this status has been represented in Figure 7.  Figure 7 One-layer topology for polygon. Two-layers topology Two-layers topology are described in 6 statuses as point-point, point-line, point-polygon, line-line, line-polygon, and polygon-polygon. In all of these cases and using the one-layer topology, one new table is created. This new table represents topology between two layers. The instances of running software for these statuses have been represented in Figures 8, 9, 10.  Figure 8 Two-layers topology for line-line.  Figure 9 Two-layers topology for line-polygon.  Figure 10 Two-layers topology for polygon-polygon. Conclusion Topological queries are posed frequently once a GIS is used. They require the information about the relationships between two spatial objects. Currently used software lacks the capability of presenting advanced topological structure. Recognizing this problem, the paper aimed at delving on the design and implementation of a advanced topological structure. A comprehensive review of the methods that can create such a structure has been presented in this paper. The methods are scientifically assessed. With the use of practical examples, the paper is then revealed the results of running prepared software for creating a advanced 2D topological structure. But the world which we are living in it consists of 3D objects. Therefore, further researches are intended to extend the proposed model to properly answer 3D topological queries. References
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