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Introducing Geographic Information Systems with ArcGIS: A Workbook Approach to Learning GIS, 3rd Edition by Michael D. Kennedy

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Buffering with Spatial Analyst (Maybe)
Recall that the site for the Wildcat_Boat facility has to be within 300 meters of a sewer line, and the site must be at least 20 meters away from any stream. Both the sewer lines and the streams are represented in raster by square cells that are 2 meters on a side, connected either at a side or a corner. To make a raster-style buffer representation of these linear entries, we need to fatten up the zones. There is a Spatial Analyst tool, Expand, which is reputed to be the raster equivalent of the vector procedure Buffer. You can find it at ArcToolbox > Spatial Analyst Tools > Generalization.
The problem with Expand is that it adds on the number of cells regardless of whether they touch side to side or corner to corner. If they touch side to side, and you have specified a cell size of 2 meters, you get 2 meters, on each side. If they touch corner to corner, however, as they would when buffering a diagonal line, the increment is about 2.828 meters (the length of the diagonal of the square which is twice the square root of 2). So, the moral of this story is that Expand is not a good equivalent for making a buffer. You can expand the width of Streams_rr2m by 10 cells to verify this fact. You’ll find that when a line runs horizontally or vertically, the distance from the center of the stream to the edge of the raster zone is about 21 meters. When the line is diagonal, the “buffer” is more like 29 meters. Please see Figure 8-41, noting the difference ...

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