Implementation and Improvement of Beams Displacement Algorithm in Automated Cartographic Generalization

The cartographic displacement algorithm based on the Beams model is a kind of global optimization algorithm that references the mechanics of materials. Using the model, the decay process of propagation in the displacement operation can be simulated, providing cartographically pleasing results with respect to the preservation of shape, spatial relations, and patterns of map object(s).However, the model lacks a detailed algorithm for implementation and a feasible method for setting the model's material parameters(i.e. elastic modulus, cross-sectional area, moment of intertia). Therefore, we focuses on the implementation and improvement of the algorithm. First, the basic mathematic model and solution method based on finite element method(FEM) are introduced. Second, from a point view of algorithm implementation, a detailed study of the key issues concerning the calculation and aggregation of the stiffness matrix and force vector are presented. Finally, to reduce the complexity of the parameters, we propose an adaptive parameter setting method to improve the algorithm. Supported by a constrained Delaunay triangulation(CDT), tests against a road network dataset and a building cluster dataset are carried out. The results illustrate that the improved algorithm is feasible and applicable to the displacement problems of linear object(s) and discrete polygon object clusters.