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Modele struktur katastralnych

Lewandowicz E.

Roczniki Geomatyki

2013

T. 11, z. 2(59)

47--58

W artykule podjęto się pokazania różnych modeli struktur katastralnych uzyskanych z przekształcenia danych mapy ewidencyjnej. Realizacja praktyczna wiązała się z porządkowaniem pozyskanych danych z formy CAD do GIS i ich przekształceń na bazie danych geometrycznych, atrybutowych i topologicznych. Prezentowane wcześniej podobne opracowania (Lewandowicz 2009, 2011, Lewandowicz i inni 2013) bazowały na przekształceniach algebraicznych, a tym razem całe przekształcenia zostały przeprowadzone w systemie GIS, w oparciu o dostępne narzędzia związane z przekształcaniem danych, budowaniem relacji i powiązań, eksportów i edycji. W oparciu o przyjętą metodykę przekształceń, uzyskano modele struktur katastralnych w formie sieci obrazującej różne powiązania działek ewidencyjnych. Wizualizowane są one w postaci grafów, które przedstawiają struktury katastralne. Fragmenty grafów w formie gwiaździstej wskazują na optymalną, uporządkowaną strukturę. Zbudowane modele, uzupełnione danymi atrybutowymi, mogą być wykorzystywane w analizach sieciowych we wspomaganiu decyzyjnym w gospodarce gruntami i w zarządzaniu kryzysowym.

The paper intends to show different models of structures of cadastral data obtained from the transformation of the cadastral map. Practical realization was connected with organizing the data obtained from the CAD form into GIS and their transformation based on geometric, topological and attribute data. Presented earlier similar studies (Lewandowicz 2009, 2011, Lewandowicz et al. 2013) were based on algebraic transformations; this time the whole transformation was carried out in GIS based on available tools related to the transformation of data, building relationships and linkages, exports and editing. Based on the adopted methodology of transformations, cadastral models of structures were obtained in the form of a network illustrating other connections to the parcels. They are visualized in the form of graphs presenting cadastral data structure. Fragments of the graphs in starry form indicate optimal ordered structure. Constructed models supplemented by attribute information can be used in network analysis supporting decision-making in land management and crisis management.

Grafy jako narzędzie do definiowania relacji topologicznych pomiędzy danymi przestrzennymi

Lewandowicz E.

Roczniki Geomatyki

2004

T. 2, z. 2

160-171

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.