This paper provides a new representation for fields (continuous surfaces) in Geographical Information Systems (GIS), based on the notion of spatial functions and their combinations. Following Tomlin’s (1990) Map Algebra, the term “Map Calculus” is used

manage rasters larger then 2.147 gigabytes or about 23,000x23,000 cells of random

floating point numbers (ESRI, 2002).

Figure 1: Cost per gigabyte of stored information: 1988-2002 (source: NSF, 2002)

The storage and representation of function-based layers is, of course, incomplete without

the ability to visualise them. An important aspect of any modern GIS is its ability to

visualise surfaces and images rapidly and efficiently. In a Map Calculus-enabled GIS, this

can be achieved quite easily and, arguably, in a more transparent way then current

visualisation of raster layers. Due to the way in which computer displays are constructed,

a matrix of values must be created in the computer’s memory before sending it to the

screen. This requires that the GIS will calculate the value of (possibly complex) function

for each pixel of the screen. However, as this is done instantaneously, the GIS can use

parameters such as screen resolution and the current scale of the map that the user is

viewing to minimise the amount of calculations. For example, if a user uses a common

screen resolution of 1024x768, then the effective area of the map in a common GIS