Compromise projections for world maps – an optimization approach using discrete global grid systems and principles from classical mechanics

Projections for world maps can only be a compromise between differentrequirements as it is impossible to construct a projection that preservesdistances, areas, and angles. Accordingly, choosing a suitable projection isdifficult – the wish list of requirements for such a projection is sometimeslong and in most cases impossible to fulfil. This article presents amechanism to translate such a wish list into a suitable compromiseprojection. For this purpose, an already known projection is initiallyselected and then subsequently optimized step by step, followingprinciples of classical mechanics and using a discrete global grid system.This mechanism is effective and can, in principle, easily be adapted toother possible requirements for a map projection. In particular, thismakes it possible to create projections that are optimized for the landareas and therefore exhibit less relevant distortion.