## table of contents

r.grow.distance(1grass) | GRASS GIS User's Manual | r.grow.distance(1grass) |

# NAME¶

**r.grow.distance** - Generates a raster map containing
distances to nearest raster features and/or the value of the nearest
non-null cell.

# KEYWORDS¶

raster, distance, proximity

# SYNOPSIS¶

**r.grow.distance**

**r.grow.distance --help**

**r.grow.distance** [-**mn**] **input**=*name*
[**distance**=*name*] [**value**=*name*]
[**metric**=*string*] [--**overwrite**] [--**help**]
[--**verbose**] [--**quiet**] [--**ui**]

## Flags:¶

## Parameters:¶

**input**=*name***[required]**-

Name of input raster map **distance**=*name*-

Name for distance output raster map **value**=*name*-

Name for value output raster 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 flag **-n** calculates the respective pixel distances to
the nearest NULL cell.

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

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.

The *Geodesic metric* is calculated as geodesic distance, to
be used only in latitude-longitude locations. It is recommended to use it
along with the *-m* flag in order to output distances in meters instead
of map units.

# EXAMPLES¶

## Distance from the streams network¶

North Carolina sample dataset:

g.region raster=streams_derived -p r.grow.distance input=streams_derived distance=dist_from_streams r.colors map=dist_from_streams color=rainbow

*Euclidean distance from the streams network in meters (map
subset)*

*Euclidean distance from the streams network in meters (detail, numbers
shown* *with d.rast.num)*

## Distance from sea in meters in latitude-longitude location¶

g.region raster=sea -p r.grow.distance -m input=sea distance=dist_from_sea_geodetic metric=geodesic r.colors map=dist_from_sea_geodetic color=rainbow

*Geodesic distances to sea in meters*

# SEE ALSO¶

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

*Wikipedia Entry:* *Euclidean Metric*

Wikipedia Entry: Manhattan Metric

# AUTHORS¶

Glynn Clements

# SOURCE CODE¶

Available at: r.grow.distance source code (history)

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