A Voronoi-based map algebra

Abstract

Although the map algebra framework is very popular within the GIS community for modelling fields, the fact that it is solely based on raster structures has been severely criticised. Instead of representing fields with a regular tessellation, we propose in this paper using the Voronoi diagram (VD), and argue that it has many advantages over other tessellations. We also present a variant of map algebra where all the operations are performed directly on VDs. Our solution is valid in two and three dimensions, and permits us to circumvent the gridding and resampling processes that must be performed with map algebra. © 2006 Springer-Verlag Berlin Heidelberg.