A combinatorial approach to cartograms

A homeomorphism from R2 to itself distorts metric quantities, such as distance and area. We describe an algorithm that constructs homeomorphisms with prescribed area distortion. Such homeomorphisms can be used to generate cartograms, which are geographic maps purposely distorted so its area distribution reflects a variable different from area, such as for example population density. The algorithm generates the homeomorphism through a sequence of local piecewise linear homomorphic changes. Sample results produced by the preliminary implementation of the method are included.