The term cost distance is widely used within GIS and in this context has a dual meaning: (i) the notion of an alternative family of distance metrics; and (ii) a procedure for determining least cost paths across continuous surfaces, typically using grid representations. Within GIS the term is distinct from the computation of varying costs or times of travel across a network. The term cost in this connection is also a generic idea, not necessarily implying financial cost, but some composite measure that varies (i.e. is not constant) across the study region, and which needs to be taken into account when computing paths and distances.

An example serves to clarify this notion. Suppose that we wish to construct a section of road between two points, A(0,2) and B(4,2), where costs are constant over the region of interest. In this case the distance is simply 4 units and the path involved is a straight line in the plane (Figure 4‑51, bold line). Construction costs will simply be 4k units, where k is some constant (the cost per unit length of path construction). Now suppose that construction costs also depend on the cost of land acquisition, and that land costs vary in our study region in a simple manner — greater to the “north” of our region than to the “south”. In this situation it is cheaper to construct our road with a curve in it, taking advantage of the fact that land costs are lower to the south (nearer the x-axis in our model).

Figure 4‑51 Cost distance model

If costs increase in a precisely linear manner, the optimal (least cost) path will have a smooth curve form of the kind shown by the thinner line (a shape like a chain hanging between two posts). This case turns out to be solvable mathematically, as are cases where costs vary in radially symmetric manner (e.g. around a city centre), whereas almost every other example of varying costs cannot be solved precisely and we need to resort to computational procedures to find the least cost path.