The user has the option of specifying five different metrics which control the geometry in which grown cells are created, (controlled by the metric parameter): Euclidean, Squared, Manhattan, Maximum, and Geodesic.
The Euclidean distance or Euclidean metric is the "ordinary" distance between two points that one would measure with a ruler, which can be proven by repeated application of the Pythagorean theorem. The formula is given by:
d(dx,dy) = sqrt(dx^2 + dy^2)
The Squared metric is the Euclidean distance squared, i.e. it simply omits the square-root calculation. This may be faster, and is sufficient if only relative values are required.
The Manhattan metric, or Taxicab geometry, is a form of geometry in which the usual metric of Euclidean geometry is replaced by a new metric in which the distance between two points is the sum of the (absolute) differences of their coordinates. The name alludes to the grid layout of most streets on the island of Manhattan, which causes the shortest path a car could take between two points in the city to have length equal to the points' distance in taxicab geometry. The formula is given by:
d(dx,dy) = abs(dx) + abs(dy)
The Maximum metric is given by the formula
d(dx,dy) = max(abs(dx),abs(dy))
The Geodesic metric is calculated as geodesic distance, to be used only in latitude-longitude locations. It is recommended to use it along with the -m flag in order to output distances in meters instead of map units.
If minimum_distance is given, all cells with a distance smaller than minimum_distance will be set to NULL.
If maximum_distance is given, all cells with a distance larger than maximum_distance will be set to NULL. The resultant output is equivalent to a buffer.
If both minimum_distance and maximum_distance are given, the result will be similar to a doughnut, a restricted belt for a given distance range. All cells outside this distance range will be set to NULL.
g.region raster=streams_derived -p r.grow.distance input=streams_derived distance=dist_from_streams r.colors map=dist_from_streams color=rainbow
g.region raster=sea -p r.grow.distance -m input=sea distance=dist_from_sea_geodetic metric=geodesic r.colors map=dist_from_sea_geodetic color=rainbow
Wikipedia Entry: Manhattan Metric
Available at: r.grow.distance source code (history)
Latest change: Thursday Feb 03 11:10:06 2022 in commit: 547ff44e6aecfb4c9cbf6a4717fc14e521bec0be
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