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.
g.region rast=streams_derived -p r.grow.distance input=streams_derived distance=dist_from_streams
Distance from sea in meters in latitude-longitude location:
g.region rast=sea -p r.grow.distance -m input=sea distance=dist_from_sea_geodetic metric=geodesic
Wikipedia Entry:
Euclidean Metric
Wikipedia Entry:
Manhattan Metric
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