## 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).

If radius is negative,r.grow shrinks areas by removing cells around the perimeters of all areas.

## 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

In this example, the lakes map in the North Carolina sample dataset location is buffered:

    g.region raster=lakes -p
    # the lake raster map pixel resolution is 10m
    r.grow input=lakes output=lakes_grown_100m radius=10

Shrinking instead of growing:

    g.region raster=lakes -p
    # the lake raster map pixel resolution is 10m
    r.grow input=lakes output=lakes_shrunk_100m radius=-10

## SEE ALSO

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

Wikipedia Entry: Euclidean Metric
Wikipedia Entry: Manhattan Metric

## AUTHORS

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

Glynn Clements