Overlay functions is one of the most frequently used functions in a GIS application. They combine two (or more) spatial data layers, comparing them position by position and treating areas of overlap - and of non-overlap - in distinct ways.
Standard overlay operators take two input data layers and assume that they are georeferenced in the same system and that they overlap in the study area. If either of these requirements is not met, the use of an overlay operator is pointless. The principle of spatial overlay is to compare the characteristics of the same location in both data layers and to produce a result for each location in the output data layer. The specific result to produce is determined by the user. It might involve a calculation or some other logical function to be applied to every area or location. With raster data, as we shall see, these comparisons are carried out between pairs of cells, one from each input raster. With vector data, the same principle of comparing locations applies but the underlying computations rely on determining the spatial intersections of features from each input layer.
Vector overlay operators are useful but geometrically complicated, and this sometimes results in poor operator performance. Raster overlays do not suffer from this disadvantage, as most of them perform their computations cell by cell, and thus they are fast. GISs that support raster processing - as most do - usually have a language to express operations on rasters. These languages are generally referred to as map algebra or, sometimes, raster calculus. They allow a GIS to compute new rasters from existing ones, using a range of functions and operators. Unfortunately, not all implementations of map algebra offer the same functionality.