Towards a general theory of geographic representation in GIS

Geographic representation has become more complex through time as researchers have added new concepts, leading to apparently endless proliferation and creating a need for simplification. We show that many of these concepts can be derived from a single foundation that we term the atomic form of geographic information. The familiar concepts of continuous fields and discrete objects can be derived under suitable rules applied to the properties and values of the atomic form. Fields and objects are further integrated through the concept of phase space, and in the form of field objects. A second atomic concept is introduced, termed the geo-dipole, and shown to provide a foundation for object fields, metamaps, and the association classes of object-oriented data modelling. Geographic dynamics are synthesized in a three-dimensional space defined by static or dynamic object shape, the possibility of movement, and the possibility of dynamic internal structure. The atomic form also provides a tentative argument that discrete objects and continuous fields are the only possible bases for geographic representation.