A coverage describes some geographic phenomenon distributed over an arbitrary region of space. In terms of behaviour, it maps a position in space to a value (as described in the discussion of spatial function below). A Landsat satellite image can be considered a coverage of the reflectance of various wavelengths from a section of the earth's surface. Barometric pressure across a given area is usually treated as a coverage. Data describing land use across a broad area may also be considered a coverage.
The most distinguishing aspect of a coverage is that it has a spatial function, responsible for the mapping from a position to a value. A spatial function is a function defined on positions in space. It can be used to model: either continuous phenomena like barometric pressure or altitude, or discrete phenomena like land use or soil type. Its domain (i.e., input into the function) is always a spatial object, but its range (i.e., output from the function) can be anything, from a number to a spatial object to a geographic object. The function may be very simple, such as an assignment of image values to grid positions in the case of a raster. Alternatively, the function may be sophisticated, involving for example the interpolation of values at arbitrary locations.
In a mathematical context, a coverage is equivalent to the graph of a function. For example, a graph of a quadratic equation provides a y value for any arbitrary x value. Similarly, a spatial function provides a value for any arbitrary location in space, where the location may be a single point or a larger region. A given spatial function may provide the land use at a specified point. The input for another function may consist of an area of interest and a tree species of interest; the output may be Douglas Fir dominated forest stands, and include complete attribute descriptions. Alternatively, the function may be designed to return only the places of occurrence of those stands, that is, only their corresponding spatial objects.
SAIF does not provide direct support for methods or functions. Nevertheless, coverage types can be described in SAIF by Emphasizing the structural aspects of the data.