## 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:

d(dx,dy) = sqrt(dx^2 + dy^2)

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:

d(dx,dy) = abs(dx) + abs(dy)

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

d(dx,dy) = max(abs(dx),abs(dy))

where the isolines of distance from a point are squares.
## EXAMPLE

Distance from the streams network (North Carolina sample dataset):
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

## SEE ALSO

*
r.grow,
r.buffer,
r.cost,
r.patch
*
*
Wikipedia Entry:
Euclidean Metric*

Wikipedia Entry:
Manhattan Metric

## AUTHORS

Glynn Clements
*Last changed: $Date$*