The voronoi model and cultural space: applications to the social sciences and humanities

Abstract

The Voronoi model of space is becoming more and more important as a tool in the mathematical modelling of space for many application domains. In the Voronoi model, space is neither an empty void within which can be found occasional objects (the vector model), nor a lattice of arbitrary cells (the raster model). Rather, space is a continuous medium filled with proximity fields generated by objects. This representation of space has important implications for domains where geographic space is endowed with cultural characteristics or values. The Voronoi model of space concords fairly closely with the perceptual and linguistic spaces of humans and hence Voronoi zones around objects are meaningful. The Voronoi model of space is also a closer fit to qualitative data representation and analysis than other models. Finally, the Voronoi model permits nested hierarchical relations between entities which increases the richness of the querying capabilities. It is shown that the Voronoi model favors a rich qualitative database of the kind which will be found in culturally intensive application domains.