  A large amount of quantitative geospatial data are collected and aggregated
in discrete enumeration units (e.g. countries or states). Smooth pycnophylactic
interpolation aims to find a smooth, nonnegative function such that the area
integral over each enumeration unit is equal to the aggregated data.
Conventionally, smooth pycnophylactic interpolation is achieved by a cellular
automaton algorithm that converts a piecewise constant function into an
approximately smooth function defined on a grid of coordinates on an equal-area
map. An alternative approach, proposed by Tobler in 1976, is to construct a
density-equalising map projection in which areas of enumeration units are
proportional to the aggregated data. A pycnophylactic interpolation can be
obtained from the Jacobian of this projection. Here, we describe a software
implementation of this method. Although solutions are not necessarily optimal
in terms of predefined quantitative measures of smoothness, our method is
computationally efficient and can potentially be used in tandem with other
methods to accelerate convergence towards an optimal solution.
