Geography Reference
In-Depth Information
FIGURE 8-17 A cost distance path tries to
avoid areas of high cost.
FIGURE 8-16 The cost distance path goes
from cell center to cell center.
rasters are calculated. In cost distance, the path proceeds from one cell center to the center of one of the
eight adjacent cells, always with the aim of minimizing the cost of getting to the source cell. In other words,
except for a few special cases (e.g., due north, straight southwest), the path generated by cost distance will
not be a straight line, but will zigzag so as to take in the cell centers along the way. See Figure 8-16.
The Euclidean distance direction is shown by a solid line. A possible path generated by cost distance is
shown by a dotted line, under conditions of a uniform cost raster. If the cost is not uniform, then the cost
distance path will be different. For example, look at Figure 8-17.
The EucDistance direction and path are represented by a solid line. A possible path generated by
CostDistance is represented by a dotted line, under the condition that high costs exist in the cells within
the outlined box.
Understanding How Total Costs Are Calculated
Calculating cost distance is somewhat involved. Take as an example a cell, size 10, that costs $1.15 per
unit distance to cross. What is the cost of traveling from the center of such a cell directly to its southern
edge? See Figure 8-18. The length of this segment is 5 (half the total distance of 10 across the cell). The
cost associated with the cell is 1.15 per unit of distance. The cost of this segment, then, is the product of
the distance and the cost per unit distance: 5 * 1.15
=
5.75.
When the path goes from cell corner to corner, the distance is longer than if the path goes from the side of
a cell to the opposite side. How much longer? Multiply the side-to-side distance by the square root of 2,
which is approximately 1.41421356237, which we will round to 1.414. See Figure 8-19.
For example, the cost to go diagonally across a 10 unit cell that had a toll of $1.15 would be
10 * 1.414 * 1.15
=
16.261
Each possible path from the source cell to each other cell is either calculated or considered in some way. That
can be a lot of paths. This type of calculation may take place several times for each cell, there can be hundreds
of thousands of cells, and the computer may make many attempts for each cell to find the least-cost path.
Search WWH ::
Custom Search