A generic model for planar geographical objects

Abstract The lack of a coherent theory underpinning geographical databases is a serious obstacle to research efforts in this field. This article attempts to construct part of such a theory, namely the formalization of the underlying object mode for geographical data whose spatial references are embedded in the plane. Questions of approximation and error analysis, while exposed and briefly discussed here, do not form a major part of the discussion. This work extends earlier work by giving a detailed construction of the classes and operations for spatial objects embedded in the plane. It goes on to provide an explicit link between this object model and its representation in computationally meaningful terms using classes of simplicial complexes and operations acting upon these classes.