Geography, Space, and Geographic Information Systems : Necessity and Development of a Generalized Algorithm for Computing Face Intersections

A Geographic Information System (GIS) is used to handle, analyse and visualize facts of the real world . These facts are assumed to be spatial in the sense that they are located at the earth s surface. The first chapter outlines that the recent success of applied GIS is based on this real world approach, which conforms to the tradition of geography as a scientific discipline. While most GIS-applications are pragmatically oriented in solving real-world-problems , each attempt to implement spatial theories of GIS ends up in the well known geographical dilemma that abstract space differs from real-world space; the former cannot be described in geographical terms and different spaces, thus, have nothing in common except that they are describable geometrically. Chapter two examines how abstract and real-world geometries are interrelated from a cognivite perspective, using a framework of different views from the cognitive sciences, such as cognitive psychology or cognitive semantics. It is shown how most of the geometrical and topological properties underlying human imagery and mental modeling can be mapped to the referenced physical conditions when navigating the earth s surface. In this sense GIS can be decoded as Geometrical Imagination System , i.e. a computer system for constructing diagrams corresponding to an earth s surface logic and metaphoric. If we accept GIS to be a spatialization technique providing comprehensive spatial abstractions for different actors, we can use GIS as a generic exploratory analysis tool. In this sense, common spatial data analysis functions implemented with GIS, such as overlay, buffering etc., can be applied to data analysis in general. To achieve this in case of the overlay function, the overlay algorithm must be generalized to handle any finite number of maps simultaneously. This algorithm is given in detail in chapter three. In chapter four, two example applications are given