Geography Reference
In-Depth Information
Problems of this sort may be solved with the Euclidean Distance tool, using as input a source
raster with multiple source cells.
Excluding Distances beyond a Certain Threshold
If the problem warrants it, you may limit the search for the closest source cell so that it does not
exceed a given value. To do this, you select an option that says “if you have to look further than
this to get to a source cell, just forget it.” Such a number may be called a limit, a cap, a cutoff
value, or a threshold.
Other Factors That Influence Cost
We began this discussion on proximity saying our primary concern was the cost associated with moving
(moving being defined in a very general sense) from one place to another. We also said that distance
between points on the Cartesian plane was a major factor in the cost, and we have spent much of the
preceding discussion discussing how to obtain that distance.
Frequently, however, distance is not the only, or even the principal, cost of moving from one place to
another. An extreme example is of a person living in New York City who wants to visit a second person
who lives nearby. Let's conjecture: the two people live in 33rd-floor apartments, toward the middle of
parallel long-block streets, and their apartments share a common back wall. They actually live only a
few feet from one another. But to travel from one apartment to the other requires two elevator rides,
encounters with doormen or buzzer systems, and a not-inconsiderable walk (or cab ride). Clearly, the
calculation of simple Euclidean distance is not the only tool we need to determine cost.
As a second example, suppose that you want to take a hike. In between your starting and ending
locations lie both swamp and dense forest. By taking a longer route, you can walk through pasture.
The time and difficulty of the route you take will be a function of both the distance and the difficulty of
making your way through various environments.
We can generalize these problems by creating a “cost surface.” We develop this cost surface so that each
raster cell contains a number that indicates the cost of going through a unit of distance in that cell. If it is
three times as hard to go through the forest as it is to go through the pasture, we might assign values of 1 in
the pasture cells and 3 in the forest cells. If a certain place in the swamp poses a threat of people being eaten
by alligators, we might assign a very high cost (say 10,000) to traversing the distances in the swamp cells.
A third example: While off-road vehicles are becoming increasingly popular, it is still less expensive to
travel by automobile from one city to another by using paved roads. The cost of traveling a straight line in
this case, in terms of speed, danger, and possible encounters with law enforcement officials, is prohibitive.
Consider Figure 8-14. The time to go from A to B is greatly reduced by going around the volcanic
mountain rather than over it. While the shortest path between points A and B is a straight line, it is not
the fastest path, because the cost for crossing over the mountain is much greater than going around it.
In short, Euclidean distance has the limitation of assuming that the cost of crossing distances in any cell
on the way to a source cell is the same as the cost of crossing distances in any other cell. You will learn
how to indicate that some cells are more expensive to cross than others. You will also learn how to find
the most inexpensive route (the least-cost path) even though it may not be the shortest.
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