Improvement of moving least squares transformation in distance cartogram construction

Abstract

Distance cartograms are deformed maps in which the distance of each of the preselected point pairs in the geographic map is changed in step with a specified value. They are constructed through two steps: locating the points included in the preselected pairs, and locating other points. A technique of moving least squares transformation is used in the second step. In this letter, the above technique is improved to maintain homeomorphism in the cartogram. The weight function used in the transformation is modified. Experimental results show the effectiveness of the proposed approach. © 2019 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

Point Location Conversion in Distance Cartogram Construction Based on Vector Field Analysis

“…This section presents the experimental results of the proposed vector field (VF) method. First, simple artificial mapping models are used to compare the performance of the VF method with those of the following three methods previously proposed: the combination of the Delaunay triangulation and barycentric interpolation (DTBI) [2], the improved moving least squares transformation (IMLS) [4] and the triangle-similarity transformation (TS) [5]. Next, the map of the six prefectures of the northeastern area of Japan is used to evaluate the characteristics of the VF method.…”

“…To maintain the readability of the cartogram, the conversion must be smooth (i.e., continuous and differentiable) and homeomorphic [1], [2]. Although several methods to maintain the above properties have been proposed [4], [5], their performances are still insufficient as will be shown in Section 3.…”

Anamorphic Visualization of the Space-Time-Paradigm by Geodetic Network Adjustment

“…This method aims at minimizing the total square error by adjusting the locations (Navratil and Staudinger 2006). MLS has already been used in several research papers dealing with TTC (e.g., (Miura and Tajima 2019;Ullah and Kraak 2015;Wang et al 2018)). Though MLS is able to find the optimal solution for a given linear or linearized functional interrelationship, it requires further extensions to take into account the topology as well.…”

“…If yes, the nodes of conflict are moved again in order to restore the original topology. Miura and Tajima (2019) introduce a weighting function within MLS so that the configuration of the nodes in their geographic location is taken into account in the TTC as well. Although we focus on non-central TTCs, we should mention that MLS has also been applied in the generation of centrals TTCs of railroad networks by Ullah and Kraak (2015).…”