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## NAME

**r.grow** - Generates a raster map layer with contiguous areas grown by one cell.
## KEYWORDS

raster, geometry
## SYNOPSIS

**r.grow**

**r.grow help**

**r.grow** [-**q**] **input**=*name* **output**=*name* [**radius**=*float*] [**metric**=*string*] [**old**=*integer*] [**new**=*integer*] [--**overwrite**] [--**verbose**] [--**quiet**]
### Flags:

**-q**
- Quiet
**--overwrite**
- Allow output files to overwrite existing files
**--verbose**
- Verbose module output
**--quiet**
- Quiet module output

### Parameters:

**input**=*name*
- Name of input raster map
**output**=*name*
- Name for output raster map
**radius**=*float*
- Radius of buffer in raster cells
- Default:
*1.01*
**metric**=*string*
- Metric
- Options:
*euclidean,maximum,manhattan*
- Default:
*euclidean*
**old**=*integer*
- Value to write for input cells which are non-NULL (-1 => NULL)
**new**=*integer*
- Value to write for "grown" cells

## DESCRIPTION

*r.grow* adds cells around the perimeters of all areas
in a user-specified raster map layer and stores the output in
a new raster map layer. The user can use it to grow by one or
more than one cell (by varying the size of the **radius**
parameter), or like *r.buffer*, but with the
option of preserving the original cells (similar to combining
*r.buffer* and *r.patch*).
## NOTES

The user has the option of specifying three different metrics which
control the geometry in which grown cells are created, (controlled by
the **metric** parameter): *Euclidean*, *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 *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.
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.

## EXAMPLE

You can shrink inwards ("negative buffer") by preparing an inverse map first,
and then inverting the resulting grown map. For example:
# Spearfish sample dataset
MAP=fields
g.region rast=$MAP
r.mapcalc "inverse = if(isnull($MAP), 1, null())"
r.grow in=inverse out=inverse.grown
r.mapcalc "$MAP.shrunken = if(isnull(inverse.grown), $MAP, null())"
r.colors $MAP.shrunken rast=$MAP
g.remove inverse,inverse.grown

## SEE ALSO

*
r.buffer,
r.grow.distance
*
*
r.distance,
r.patch
*

*Wikipedia Entry: Euclidean Metric*

*Wikipedia Entry: Manhattan Metric*

## AUTHORS

Marjorie Larson,
U.S. Army Construction Engineering Research Laboratory
Glynn Clements

*Last changed: $Date: 2014-04-15 03:12:56 -0700 (Tue, 15 Apr 2014) $*

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