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

3A 3B

3D 3C

Figure 3: (3A) A polyline, made of segments L1, L2 and L3, is used to demonstrate the capabilities of Map Calculus-enabled GIS. In this image, the distance function is calculated at a scale of about

1:4000. Once the user zooms in to a smaller area (3B), the system calculates the new values of the surface for that specific area, and, as the next image (3C) demonstrates there is no “pixelation” of the surface (note the scale bar). In 3D, the following composite function was calculated: (Dist L1 – Dist L2)+Dist L3. The resulting surface was calculated directly from the final function and not by creating intermediate surfaces.

Positioning function-based layers in the current

practice of GIS

When considering a significant departure from the established methods of field

representations in a GIS, there is a need to weigh the advantages and disadvantages of

the proposed approach and consider them in the light of existing experience. In this

section, a few aspects of traditional, raster-based representations are compared with

function-based representations. Raster representations are more general and can be