A negative radius shrinks inwards instead of growing outwards.
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 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))
If there are two cells which are equal candidates to grow into an empty space, r.grow will choose the northernmost candidate; if there are multiple candidates with the same northing, the westernmost is chosen.
# North Carolina sample dataset g.region raster=lakes r.grow.shrink in=lakes out=lakes.shrunken radius=-2.01 r.colors lakes.shrunken rast=lakes
Wikipedia Entry: Euclidean Metric
Wikipedia Entry: Manhattan Metric
Glynn Clements
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