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#### NAME

```       r.grow.distance  - Generates a raster map layer of distance to features in input layer.

```

#### KEYWORDS

```       raster, geometry

```

#### SYNOPSIS

```       r.grow.distance
r.grow.distance help
r.grow.distance   [-m]   input=name    [distance=name]     [value=name]    [metric=string]
[--overwrite]  [--verbose]  [--quiet]

Flags:
-m
Output distances in meters instead of map units

--overwrite
Allow output files to overwrite existing files

--verbose
Verbose module output

--quiet
Quiet module output

Parameters:
input=name
Name of input raster map

distance=name
Name for distance output map

value=name
Name for value output map

metric=string
Metric
Options: euclidean,squared,maximum,manhattan,geodesic
Default: euclidean

```

#### 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

```

#### SEEALSO

```        r.grow, r.buffer, r.cost, r.patch

Wikipedia Entry: Euclidean Metric
Wikipedia Entry: Manhattan Metric

```

#### AUTHORS

```       Glynn Clements

Last changed: \$Date: 2012-09-02 05:49:21 -0700 (Sun, 02 Sep 2012) \$

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