Joint Simplification of Various Types of Spatial Objects While Preserving Topological Relations

Abstract

Cartographic generalization includes the selection of objects and phenomena, as well as their simplification (generalization), to be shown in the map while preserving the main typical traits, characteristics, and correlations by the criteria set by the user in the request. These criteria include the problem being solved and the scale of the displayed map. Various map transformations can change the relationships between objects, especially since it is common practice to simplify each type of spatial object independently (first the administrative boundaries, then the road network, populated localities, hydrographic network, etc.). The solution of topological conflicts is one of the key problems of generalizing digital map. A great deal of attention has been paid to the solution of this problem since the start of studies in this domain. The consideration of coverings and mesh structures confines the more general problem of managing topological conflicts to solve topological conflicts within a mesh cell. This study proposes a new geometric simplification algorithm. Its feature consists of the joint simplification of a set of spatial objects of various types while preserving their topological relations. The only parameter of the proposed algorithm is the minimal size of the detail shown in the map. Usually, this size is equal to one millimeter in the target map scale. Step one of the algorithm is the construction of a special mesh data structure. This structure is used to form, for each spatial object, a sequence of cells, to which points of this object belong. If a cell contains points of only one object, the object is geometrically simplified within the bounding cell using the sleeve-fitting algorithm. If a cell contains points of several objects, the geometric simplification is done using a special topology-preserving procedure.