Research of models of topological relations of spatial objects

In map production it is necessary to keep the spatial relationships between map objects. Generalization is the simplification performed on geographical data when decreasing its representation scale. It is a common practice to simplify each type of spatial objects independently (administrative boundaries first, then road network, hydrographic network, etc.). During the process some spatial conflicts, which require manual correction, arise inevitably. The generalization automation still remains an open issue for data producers and users. Many researchers are working to achieve a higher level of automation. In order to detect the spatial conflicts a refined description of spatial relationships is needed.
The paper analyzes models of describing topological relationships of spatial objects: the nine intersections model, the topological chain model and the E-WID model. Each considered model allows to take into account some relations between objects, but does not allow to transfer them exactly. As a result, the task of developing a model of relations preserving topology is relevant. We have proposed an improved model of nine intersections, which takes into account the topological conflict that occurs when a point object is located next to a simplified line. Line simplification is one of the most requested actions in map production and generalization. When the mesh covered the map inside the cell there can be points, line segments and polygonal topological objects, which, if the cell is rather small, are polyline objects. Thus, the issue of simplification of topological objects within a cell is reduced to the issue of simplification of linear objects (polylines). The developed algorithm is planned to be used to solve the problem of consistent generalization of spatial data. The ideas outlined in this article will form the basis of a new index of spatial data that preserves their topological relationships.