Geografic-Information-System/raster/r.grow/r.grow.html

<h2>DESCRIPTION</h2>

<em>r.grow</em> 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 <b>radius</b>
parameter), or like <em>r.buffer</em>, but with the
option of preserving the original cells (similar to combining
<em>r.buffer</em> and <em>r.patch</em>).


<h2>NOTES</h2>
The user has the option of specifying three different metrics which
control the geometry in which grown cells are created, (controlled by
the <b>metric</b> parameter): <i>Euclidean</i>, <i>Manhattan</i>, and 
<i>Maximum</i>. 

<p>
The <i>Euclidean distance</i> or <i>Euclidean metric</i> 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: 

<div class="code"><pre>d(dx,dy) = sqrt(dx^2 + dy^2)</pre></div>

Cells grown using this metric would form isolines of distance that are
circular from a given point, with the distance given by the <b>radius</b>.

<p>
The <i>Manhattan metric</i>, or <i>Taxicab geometry</i>, 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:

<div class="code"><pre>d(dx,dy) = abs(dx) + abs(dy)</pre></div>

where cells grown using this metric would form isolines of distance that are
rhombus-shaped from a given point. 

<p>
The <i>Maximum metric</i> is given by the formula

<div class="code"><pre>d(dx,dy) = max(abs(dx),abs(dy))</pre></div>

where the isolines of distance from a point are squares.

<p>
If there are two cells which are equal candidates to grow into an empty space, 
<em>r.grow</em> will choose the northernmost candidate; if there are multiple 
candidates with the same northing, the westernmost is chosen. 


<h2>EXAMPLE</h2>

You can shrink inwards by preparing an inverse map first, and then
inverting the resulting grown map. For example:
<div class="code"><pre>
# 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
</pre></div>


<h2>SEE ALSO</h2>

<em>
<a href="r.buffer.html">r.buffer</a>,
<a href="r.grow.distance.html">r.grow.distance</a>
</em>

<p>
<em>
<a href="r.distance.html">r.distance</a>,
<a href="r.patch.html">r.patch</a>
</em>

<p>
<em><a href="http://en.wikipedia.org/wiki/Euclidean_metric">Wikipedia Entry: Euclidean Metric</a></em><br>
<em><a href="http://en.wikipedia.org/wiki/Manhattan_metric">Wikipedia Entry: Manhattan Metric</a></em>


<h2>AUTHORS</h2>

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

<p>
<i>Last changed: $Date$</i>