On a Class of Map Transformations

This paper considers contiguity preserving map transformations (or cartograms) that have a preassigned arcal scale. Because for each such scale it is possible to construct infinitely many transformations, this paper investigates restrictions under which such cartograms are possible. It is shown that it is possible to construct transformations that preserve the location of boundaries and of any finite number of predefined points. However, these cartograms are often quite distorted. Different types of distortions and suitable measures are discussed.