Joint simplification of various types spatial objects while preserving topological relationships

Cartographic generalization includes the process of graphically reducing information from reality or larger scaled maps to display only the information that is necessary at a specific scale. After generalization, maps can show the main things and essential characteristics. The scale, use and theme of maps, geographical features of cartographic regions and graphic dimensions of symbols are the main factors affecting cartographic generalization. Geometric simplification is one of the core components of cartographic generalization. The topological relations of spatial features also play an important role in spatial data organization, queries, updates, and quality control. Various map transformations can change the relationships between features, especially since it is common practice to simplify each type of spatial feature independently (first administrative boundaries, then road network, settlements, hydrographic network, etc.). In order to detect the spatial conflicts a refined description of topological relationships is needed. Considering coverings and mesh structures allows us to reduce the more general problem of topological conflict correction to the problem of resolving topological conflicts within a single mesh cell. In this paper, a new simplification algorithm is proposed. Its peculiarity is the joint simplification of a set of spatial objects of different types while preserving their topological relations. The proposed algorithm has a single parameter — the minimum map detail size (usually it is equal to one millimeter in the target map scale). The first step of the algorithm is the construction of a special mesh data structure. On its basis for each spatial object a sequence of cells is formed, to which points of this object belong. If a cell contains points of only one object, its geometric simplification is performed within the bounding cell using the sleeve-fitting algorithm. If a cell contains points of several objects, geometric simplification is performed using a special topology-preserving procedure.