A new approach for designing orthophanic world maps

In order to produce a world map on which the continents closely resemble their appearance on the globe one must make sure that both the shape and the relative size of the individual land masses are well represented. In this paper a method is proposed to quantify the shape distortion and the relative distortion of area on a map projection. A new approach is suggested for producing so-called balanced map projections, which have an equal amount of area and shape distortion. Balanced map projections occupy a different position in distortion space than map projections that are commonly used for world maps. While, according to the calibration method that is applied, balanced map projections have an equal distortion of area and shape, popular map projections like the Winkel-Tripel and the Robinson projection have a shape distortion that is much higher than the distortion of area.