Symbolize map distortion with inscribed circles in polygons

ABSTRACTFor the representation of geographic information, the distortion resulting from map projections and transformations is unwanted but unavoidable. Identical circles systematically arranged on the Earth's ellipsoid have been extensively used to symbolize the map distortion. Despite their effectiveness and popularity, these circles are not explicitly associated with any specific polygons in the map, thus possibly impairing their relevance if the map-readers are interested in particular regions. More importantly, for the map transformation specifically targeting polygons such as the area cartogram, placing the circles completely within the polygons becomes necessary because two neighboring polygons in an area cartogram could have distinctive distortion characteristics. This paper proposes new computer algorithms to enable a map-distortion symbolization approach based on inscribed circles entirely contained in polygons either on a projected 2D plane or on the Earth's ellipsoid. These inscribed circles in polygons (ICIP) are rendered as a series of maximum or equal-sized circles that are spatially exclusive, that is, without overlapping. Compared with the systematically arranged identical circles, the ICIP give cartographers certain flexibility and a new option for the map-distortion symbolization. Two area cartograms and three map projections are provided as examples to illustrate their usage and possible contribution in different mapping scenarios.