Map Calculus in GIS a proposal and demonstration(15)

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

and, in effect, implements the Lambda Calculus (Dominus, 1999). It is this property that

enabled the use of Perl to imitate the implementation of Map Calculus-enabled GIS. It

must be stated that the prototype uses very simple spatial functions (based on distance)

and allows only three arithmetic operations (addition, subtraction and multiplication)

between pairs of existing layers.

The implementation is based on two scripts, the first runs within Manifold and handles

the GUI, while the second runs outside acting as a server. This client/server architecture

was selected because it enables the installation of the server script on more powerful

machine than that of the client. Furthermore, the server script is more sophisticated and

contains some of the functionality that was mentioned in the previous sections. The

interface is made up of three separate forms, shown in Figure 2. The first interface

(Figure 2a) allows the user to create a new functional layer by selecting a spatial object

(point or pair of points) and selecting one of several basic spatial functions. This

interface is also used to delete a function from the database. The second interface (Figure

2b) allows the user to define map-algebra operations. The “Map Algebra” dialogue area

enables the creation of binary linear combinations of existing layers. Finally, the “display”

interface (Figure 2c) can be used to calculate the raster representation that is relevant to

the area currently displayed in the main window. The following part will demonstrate

some code segments that explain the implementation within the system. Some syntactic

“sugar” is used to make the code more readable.

The process of creating a layer is a simple one – the client sends a message to the server

that contains the layer identification (a name), the type, and a set of parameters that the

server must store in order to recalculate the function. In the case of a distance from a

point function, the stored data structure is defined as:

$new_layer->{layertype} = 1;

$new_layer->{layerid} = $LayerID;

$new_layer->{xcoord} = $x;

$new_layer->{ycoord} = $y;

As we are interested in Euclidean distance the only parameter that is needed is the

location of the point from which the measurement is carried out. A map-algebra layer is

defined by three parameters – the two layers that are used for calculation, and the

mathematical operation: