Minimum distortion pointed-polar projections for world maps by applying graticule transformation

Abstract

ABSTRACTBoth the media and the geosciences often use small-scale world maps for demonstrating global phenomena. The most important demands on the projection of these maps are: (1) the map distortions have to be reduced as much as possible; (2) the outline shape of the mapped Earth must remind the viewer of the Globe. If the map theme to be illustrated requires neither equivalency (nor, which rarely happens, conformality) nor prescriptions for the map graticule, an aphylactic non-conical projection with simultaneously minimized angular and area distortions is advisable. In this paper, a graticule transformation by a parameterizable function helps to convert minimum distortion pointed-polar pseudocylindrical projections for world maps into general non-conical projections with further minimized distortions. The maximum curvature of the outline shape will be moderated at the same time in order to obtain a definitely pointed-polar character.