The generalization of point clusters and its quality assessment based on a polarization approach

The paper introduces a polarization approach which can be applied as an algorithm to generalize point clusters or as a tool to assess the quality of other generalization algorithms. Based on the polarization approach, a two-dimensional spatial distribution regardless of its complexity can be converted into a simple spectrum line without information loss. The generalization or quality assessment procedure can then be conducted on the spectrum line in a straightforward manner. Due to the computing simplicity and the capability of preserving global as well as local characteristics of spatial distributions, the polarization approach can be implemented as a favorite tool in WebGIS. The process of polarization is composed of three steps: (1) determination of the origin of a polar coordinate system, (2) conversion of point features scattered over the mapping space into polar coordinates, (3) unfolding the polar coordinates on a spectrum line. By means of examples, the authors elucidate the working principle of generalization and quality assessment based on such a spectrum line.