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Modele matematyczne związków topologicznych między obiektami przestrzennymi, ich implementacja w relacyjnych bazach danych oraz wykorzystanie do analiz przestrzennych danych geodezyjnych

Bielecka E.

Biuletyn Wojskowej Akademii Technicznej

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2010

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Vol. 59, nr 2

224-241

PL

W artykule przeanalizowano cztery systemy przeznaczone do zarządzania relacyjnymi bazami danych: Oracle 11g, PostgreSQL 8.3/PostGIS 1.3.3, SQL Server 2005 i 2008, MySQL, zwracając uwagę na zaimplementowane operatory topologiczne i ich zgodność ze specyfikacjami OGC. Nazwy i definicje stosowanych operatorów, poza bazą Oracle 11g, są zgodne ze standardami OGC i ISO. Jest to bardzo istotne ze względu na interoperacyjność relacyjnych baz danych, ponieważ gwarantuje poprawne i jednakowe rozumienie wyników relacji topologicznych uzyskanych za pomocą różnych narzędzi. Od kilkunastu lat wiele danych geodezyjnych jest udostępnianych użytkownikom tylko i wyłącznie w postaci cyfrowej. Zatem przekazanie klientowi zamówionych danych wymaga wyselekcjonowania z całego zbioru tylko tych, które spełniają wymagania określone w złożonym zapotrzebowaniu na dane. To z kolei nakłada na systemy bazodanowe zarządzające danymi geodezyjnymi pewne wymagania dotyczące wykonywania analiz przestrzennych, a mianowicie wspieranie minimum ośmiu operatorów topologicznych (equals - równość, disjoint - rozłączność, intersects - przecinanie, touches - styczność, crosses - krzyżowanie, within - zawieranie się w, contains - zawieranie i overlaps – nakładanie).

EN

Recently, developers of data base management system implement tools for spatial data analyses within a relational data base. The advantage of usage of a relational database system for storing spatial data have a great potential, especially in data mining. The article presents the results of analysis of the implemented spatial operators and their conformance with ISO and OGC standards in four relational DBMS: Oracle 11g, PostgreSQL 8.3 /PostGIS 1.3.3, SQL Server 2005 and 2008, MySQL. The names and definitions of implemented topological operators, except Oracle 11g data base, are in conformity with standards. This is of utmost importance for interoperability, because it assures correct and identical understanding of the results obtained using different tools. For several years, a lot of geodetic data have been delivered to users in digital form. Therefore data transfer from a database to a client requires selection from an entire data base to a set corresponding to user requirements. This puts on SDMS some additional conditions such as supporting eight topological relationships (equals, disjoint, intersects, touches, crosses, within, contains and overlaps) between spatial data.

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Modeling and manipulating fuzzy regions: strategies to define the topological relation between two fuzzy regions

Schmitz A., Morris A.

Control and Cybernetics

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2006

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Vol. 35, no 1

73-95

EN

Topological relations between geographic objects are among the most important kinds of relations to manage in Geographic Information Systems (GIS). However, it its very expensive in storage space to keep these relations explicitly stored. Therefore, the relations are usually not directly stored, but they are inferred from the geometry of the objects. Furthermore, the inference of the topological relations is very expensive in processing time, especially when managing complex geographic objects such as fuzzy regions, or regions with multiple alpha-cuts. In this paper we argue that the topological relations between two regions with multiple alpha-cuts can be defined using the topological relations between the crisp regions that compose these two regions. In addition, we present strategies to define the topological relation between two regions with multiple alpha-cuts, with the intent to minimize the number of overlays of crisp regions to be executed to define the topological relationship between the two regions.

3

Grafy jako narzędzie do definiowania relacji topologicznych pomiędzy danymi przestrzennymi

Lewandowicz E.

Roczniki Geomatyki

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2004

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T. 2, z. 2

160-171

EN

Graphs are abstract mathematical objects enabling to describe data in a simple form. The graph theory provides tools for solving specialized tasks, including typical problems related to spatial analysis: travelling salesman problem, path analysis, network flow. This paper discusses the possibility of applying graphs to determine topological data of a complex of geographical objects. A geometric graph has been constructed on the basis of a map fragment showing registration parcels. Its nodes represent boundary points, and edges - boundary lines. The neighborhood matrix describing this graph contains topological data, i.e. relationships between boundary points and lines. The neighborhood matrix describing this graph contains topological data, i.e. relationships between boundary points and lines. Traditionally, these data are saved as database records and associated with single objects.The above matrix contains all data concerning the whole complex of objects, which enables their processing. An algorithm transforming a graph representing boundary lines into a graph describing boundaries is proposed in the paper. This transformation involves reduction of 2-degree nodes, connected with summation of neighboring edges. In the transformed graph edges describe boundaries between two parcels. The data related to the administrative division of a country are specific, as they cover the spatial area completely, without any intervals, blanks or overlaps. These data should be illustrated using special planar graphs. A planar graph is a graph that can be embedded in a plane so that no edges intersect. An example may be a graph representing registration parcels. A geometric planar graph, in the form of a flat drawing, divides a set of points into regions (faces). Known algorithms can be used for obtaining cyclical graphs, describing each region separately, by means of nodes and edges. Such a description is possible even when the so called enclave is located within the parcel. Graphs illustrating this situation are presented in the paper. Enclaves may be represented as the so called islands. In such a case, a graph is composed of two subgraphs. Two independent graphs may be joined by the so called bridge, and two subgraphs . by an edge. In these two solutions concerning enclave representation it is possible to determine regions. The number of regions within a planar graph can be determined from the Euler.s formula, which defines the correlation between the number of regions, and the number of edges and nodes in a graph. Planar graphs describing regions may be transformed into dual graphs, where relationships between neighboring regions are presented in a simple way. In dual graphs nodes represent regions, and edges between nodes indicate that regions have a common edge. The degree of the node informs about the number of neighbors. If a parcel is described using a dual graph, a single matrix contains information on neighborhood relations within the whole complex of parcels. Traditionally, this information is contained in GIS databases in the form of single records corresponding to particular parcels. The theoretical bases of spatial data description applying graphs, presented in the paper, show that topological relationships within the whole complex of geographical objects can be recorded in a simple way. This in turn enables us to perform typical spatial analyses and to process topological data.