Building spatial models within GIS through Geo-Algebra

This paper describes Geo-Algebra, a mathematical framework for supporting geo-computational modelling in conjunction with GIS-based spatial data manipulation capabilities. Geo-Algebra overcomes the discrepancy between spatial modelling and GIS in the modes of representation as well as in their underlying concepts of space by using a common representational framework for (1) mathematical models expressing spatial relationships and (2) data models of georeferenced information. Geographic models of spatial structure and static as well as dynamic spatial interaction are formulated consistently within Geo-Algebra through a limited set of generic operations on map layers which are used simultaneously for GIS data manipulation and analysis. A significant advantage of Geo-Algebra over other approaches to integration, such as high-level computational languages, is the development of theoretical concepts of the most general kind which allows the derivation of general properties of these in a deductive manner. In particular, Geo-Algebra formalizes and extends the mathematical notion of Map into the novel concepts of relational and metarelational Maps. These extensions lead to the novel concepts of space bridging the absolute and relative, as well as static and dynamic views of space. Such theoretical concepts are also implemented in a dynamic simulation tool called Geocellular.