Cartographic line generalization based on radius of curvature analysis

Abstract

Cartographic generalization is one of the important processes of transforming the content of both analogue and digital maps. The process of reducing details on the map has to be conducted in a planned way in each case when the map scale is to be reduced. As far as digital maps are concerned, numerous algorithms are used for the generalization of vector line elements. They are used if the scale of the map (on screen or printed) is changed, or in the process of smoothing vector lines (e.g., contours). The most popular method of reducing the number of vertices of a vector line is the Douglas-Peucker algorithm. An important feature of most algorithms is the fact that they do not take into account the cartographic properties of the transformed map element. Having analysed the existing methods of generalization, the authors developed a proprietary algorithm that is based on the analysis of the curvature of the vector line and fulfils the condition of objective generalization for elements of digital maps that may be used to transform open and closed vector lines. The paper discusses the operation of this algorithm, along with the graphic presentation of the generalization results for vector lines and the analysis of their accuracy. Treating the set of verification radii of a vector line as a statistical series, the authors propose applying statistical indices of position of these series, connected with the shape of the vector line, as the threshold parameters of generalization. The developed algorithm allows for linking the generalization parameters directly to the scale of the topographic map that was obtained after generalization. The results of the operation of the algorithm were compared to the results of the reduction of vertices with use of the Douglas-Peucker algorithm. The results demonstrated that the proposed algorithm not only reduced the number of vertices, but that it also smoothed the shape of physiographic lines, if applied to them. The authors demonstrated that the errors of smoothing and position of vertices did not exceed the acceptable values for the relevant scales of topographic maps. The developed algorithm allows for adjusting the surface of the generalized areas to their initial value more precisely. The advantage of the developed algorithm consists in the possibility to apply statistical indices that take the shape of lines into account to define the generalization parameters.