The Analytical Expressions of the Constraints in Cartographic Generalization

Optimization approaches applied in cartographic generalization seek to a sound solution based on a series of pre-defined constraints. In this paper, five types of constraints in the cartographic generalization are distinguished: position, simplification, shape characteristic, spatial relations and spatial distribution. Several observations in terms of measures for constraints are introduced. Accordingly to least squares adjustment theory, the analytical expressions (namely observation equations and conditional equations about residuals) of part graphic constraints are established. Furthermore, the simple example is given, the method of least square based on constraint is used to simplify building ground plan. The practice shows that the constraint method is feasible and effective.