New measures for analysis and comparison of shape distortion in world map projections

World maps can have quite different depictions of reality depending on the projection adopted, and this can influence our perception of the world. In this respect, shape is a significant property that needs to be considered, especially when representing large regions in general-purpose world maps. A map projection distorts most geometric properties (area, distance, direction/angle, shape, and specific curves) and usually preserves a single property or provides a compromise between different properties when transforming terrestrial features from globe to plane. The distortions are mainly classified based on area, distance and direction/angle and analyzed with Tissot’s theorem. However, this theorem offers a local (pointwise) solution, so the distortion assessment is valid at infinitesimal scale (i.e. for very small regions). For this reason, different approaches are required to analyze the distortions at finite scale (i.e. for larger regions). However, there are very few attempts at analyzing and comparing shape distortion of landmasses in world map projections owing to the fact that shape measurement is difficult and usually involves measuring different characteristics. Seeking to fill this gap, in this study, compactness and elongation distortion measures are introduced. In this regard, 16 world map projections are analyzed and compared with these distortion measures in a GIS environment, based on map datasets of continents and countries. An analysis of the effect of the levels of detail of the datasets is also presented.