A complete solution of cartographic displacement based on elastic beams model and Delaunay triangulation
Keywords: Cartographic generalization, Displacement, Conflict, Elastic beams model, Delaunay triangulation, Skeleton, Proximity graph
Abstract. In map production and generalization, it is inevitable to arise some spatial conflicts, but the detection and resolution of these spatial conflicts still requires manual operation. It is become a bottleneck hindering the development of automated cartographic generalization. Displacement is the most useful contextual operator that is often used for resolving the conflicts arising between two or more map objects. Automated generalization researches have reported many approaches of displacement including sequential approaches and optimization approaches. As an excellent optimization approach on the basis of energy minimization principles, elastic beams model has been used in resolving displacement problem of roads and buildings for several times. However, to realize a complete displacement solution, techniques of conflict detection and spatial context analysis should be also take into consideration. So we proposed a complete solution of displacement based on the combined use of elastic beams model and constrained Delaunay triangulation (CDT) in this paper. The solution designed as a cyclic and iterative process containing two phases: detection phase and displacement phase. In detection phase, CDT of map is use to detect proximity conflicts, identify spatial relationships and structures, and construct auxiliary structure, so as to support the displacement phase on the basis of elastic beams. In addition, for the improvements of displacement algorithm, a method for adaptive parameters setting and a new iterative strategy are put forward. Finally, we implemented our solution on a testing map generalization platform, and successfully tested it against 2 hand-generated test datasets of roads and buildings respectively.