Relation between the extreme angular and areal distortion in cartographic representation

Summary

The paper presents the method of deriving representations, optimal from the point of view of global characteristics, for areal and extreme angular distortion (3), (7), if one is optional and the other characteristic is minimized at the same time. If a special minimization method (Section 5) is used for computer processing, the problem can be solved in the region of representation equations in the form of polynomials of the 3rd or 5th degree, while assuming symmetry relative to the equator and the central meridian. Thus, the method enables both the fundamental global characteristics to be regulated freely. Their dependence is illustrated in graphs (Figs 2 and 6) depending on the selected examples of representations of the whole globe. The latter shows that method is a contribution for cartographic practice as well.