Spatial phenomena can be conceptually represented both discretely and continuously. Discrete phenomena refer to objects with well-defined boundaries and spatial dimensions and spatially invariant properties, such as buildings, parcels and streets. These geoobjects - in a more narrow sense - are modelled object-based and usually represented as vector data. With object-based data models, the geoobject itself is the starting point for the consideration. This has a geometry as an attribute to which thematic attribute values can be assigned. Thus, the vector data representation in the object-based data model assigns the corresponding attributes for the characterization of the thematic properties of the geoobject to the primitive point, line and polygon describing an object geometrically. For example, a point can be assigned a point number, a street name can be assigned to a street line defining a street center, or the parcel number or area size can be assigned to a polygon. In the raster data representation, thematic information is assigned to a single raster cell. The ISO 19107 standard deals with this in detail, see also C. Andrae (2009).
If, on the other hand, continuous phenomena that vary in space and cannot be clearly defined are considered, such as soil types, temperature distributions or terrain surfaces, the field-based model is used. For these, the cell in a data space is the starting point. An attribute value is linked directly or via a continuous function to each cell in the data space. Such continuous phenomena are called coverages. Not only do they specifically describe the geometry of the object itself, they also use a function to specify how neighboring positions and values relate to each other. They are more precisely specified in ISO 19123 Geoinformation - Coverage Geometry and Function Scheme or the OGC Abstract Specification Topic 6. Such fields can be described both discretely in the form of triangles, grid cells (raster data) or tesselations (such as thiessen polygons) and continuously in the form of functions (such as interpolation functions) that connect spatial positions with attribute values, e.g. for trend surfaces. Here it is assumed that a value can be specified for any location of such a field. Thus a value for such a phenomenon, i.e. a soil type, a temperature or a height value, applies only to a certain cell and may even vary over time.
The choice of describing an object as a discrete or continuous phenomenon not only influences the geometric modeling; it also implicitly determines topological relationships and the assignment of thematic and temporal properties to the object. It is possible to switch between discrete and continuous representations, depending on the question, the degree of detail, the method of recording and the ability to concretize. A good example of this is the description of a terrain surface in the form of a Digital Terrain Model (DTM), which can be represented on the one hand by regular grid cells in raster data form, but on the other hand also by triangles as vector data in the form of a triangular mesh.