We explore the use of cartogram projections for analysing spatial distribution of service facilities and the structure of road networks. We focus on the analysis of the regularity of the spatial structure, and investigate the effect of the human density raised to an exponent x on this structure. The spatial distribution of post office outlets in Switzerland is most regular at human density power 0.55, while the theory suggests an exponent of 2/3. The road network is most regular with an exponent of 1.0. We believe that cartograms can be useful for spatial analysis.