AbstractMaps that correctly represent the geographic size and shape of regions, taking into account scaling and generalization, have the disadvantage that small regions can easily be overlooked or not seen at all. Hence, for some map use tasks where small regions are of importance, alternative map types are needed. One option is the so-called equal area unit maps (EAUMs), where every enumeration unit has the same area size, possibly also the same basic shape such as squares or hexagons. The geometrical distortion of EAUMs, however, leads to a more difficult search for regions as well as a falsification of topological relationships and spatial patterns. To describe these distortions, a set of analytical measures is proposed. But it turns out that the expressiveness of these measures is rather limited. To better understand and to model the influence of distortions, two user studies were conducted. The study on the search in EAUMs (also with the aim of reconstruct the search strategies of the users) revealed how important it is to consider the local topology (e.g. corner or border positions of regions) during the generation process. With regard to pattern identification, it could be shown that EAUMs significantly increase the detection rate of local extreme values. On the other hand, global lateral gradients or geostatistical hot spots often get blurred or even lost. As a consequence, a task-oriented selection of map types and further developments are recommended.
3D topological relationships of landforms and their spatial schema-based representation