An alternative method to constructing time cartograms for the visual representation of scheduled movement data

In a cartogram, the map elements are purposely modified with respect to an attribute. A time cartogram is a type of cartogram in which the geographic-distance between locations is replaced by a time-related attribute such as travelling-time, deforming the geography accordingly. This study concentrates on centred time cartograms that visualize travelling-times from a fixed starting location to other locations in the region. Several methods to construct time cartograms have been proposed, however these methods are not entirely satisfactory. In particular, none of them describes how to deform both the network and the map's boundaries based on travelling-times, which is necessary to maintain recognizability. In many cases, homeomorphism and topology are not maintained. The resultant maps from such methods are highly deformed and are difficult to read. Some of these methods are computationally demanding, while the procedures of others are not fully described. We present a method to construct time cartograms for the visual representation of scheduled movement data using the Dutch railways network as a case study. The method was developed by approaching the construction of time cartograms as a two-step process. In the first step, vector calculus is used to displace the train stations according to travelling-times from a fixed starting station. In the second step, moving-least-squares based affine deformation is applied to deform the railroads and the map's boundaries accordingly. To enhance understanding, concentric circles are drawn from the starting station to depict travelling-times. The method maintains homeomorphism and topology and yields time cartograms that are easily recognizable.