This paper describes a means for linking field and object representations of geographical space. The approach is based on a series of mappings, where locations in a continuous field are mapped to discrete objects. An object in this context is a modeler's conceptualization, as in a viewshed, highway corridor or biological reserve. An object can be represented as a point, line, polygon, network, or other complex spatial type. The relationship between locations in a field and spatial objects may take the form of one-to-one, one-to-many, many-to-one, or many-to-many. We present a typology of object fields and discuss issues in their construction, storage, and analysis. Example applications are presented and directions for further research are offered.