r.grow.distance(1)

NAME
r.grow.distance

DESCRIPTION
r.grow.distance generates raster maps representing the distance to the nearest non-null cell in the input map and/or the value of the nearest non-null cell.

NOTES
The user has the option of specifying four different metrics which control the geometry in which grown cells are created, (controlled by the metric parameter): Euclidean, Squared, Manhattan, and Maximum.

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: </div>
Cells grown using this metric would form isolines of distance that are
circular from a given point, with the distance given by the radius.

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:
</div>
where cells grown using this metric would form isolines of distance that are
rhombus-shaped from a given point.

The Maximum metric is given by the formula
</div>
where the isolines of distance from a point are squares.

EXAMPLE
Spearfish sample dataset
r.grow.distance input=roads distance=dist_from_roads

SEE ALSO
r.grow
r.buffer
r.cost
r.patch

Wikipedia Entry: Euclidean Metric
Wikipedia Entry: Manhattan Metric

AUTHORS
Glynn Clements

Last changed: $Date: 2008-11-20 11:59:22 +0100 (Thu, 20 Nov 2008) $

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