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

Map Calculus in GIS

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This, of course, is a basic Euclidean distance function. However, the syntax \$x tells Perl

not to evaluate the variable x when constructing the string, but rather to postpone

evaluation to a later stage. Thus, for the point (14,-128), this code segment returns the

function:

sqrt(($x-(14))**2+($y-(-128))**2)

When the display function is activated, this segment of code is evaluated for every pair of

co-ordinates in the display area, assigning them as $x and $y. Finally, it is worth noting

the way in which composite layers are handled. This is done by recursively bringing up

the function that constructs the “Lambda Function” in the following way:

return constructFunc($layer2) . " $layer_id->{operation} " .

constructFunc($layer2);

Apart from the code, the server produces a raster layer according to the function of the

specific combination. The client then reads the file and it is possible to display the result

for the area currently displayed. This communication between client and server is grossly

inadequate in terms of speed, but it is good enough to demonstrate the visualisation

advantages of the approach. Figure 3 provides a demonstration of the output that is

expected from a Map Calculus-enabled GIS. Figures 3a-3c emulate the process of zoom-

in to a specific segment of the map and the creation of a finer raster for the area of

interest that the user has zoomed into. It is important to note that the two rasters that are

on display here contain exactly the same number of cells.