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@@ -4,15 +4,63 @@
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<em>r.grow</em> adds cells around the perimeters of all areas
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in a user-specified raster map layer and stores the output in
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a new raster map layer. The user can use it to grow by one or
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-more than one cell, or like <em>r.buffer</em>, but with the
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+more than one cell (by varying the size of the <b>radius</b>
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+parameter), or like <em>r.buffer</em>, but with the
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option of preserving the original cells (similar to combining
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<em>r.buffer</em> and <em>r.patch</em>).
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+<h2>NOTES</h2>
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+The user has the option of specifying three different metrics which
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+control the geometry in which grown cells are created, (controlled by
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+the <b>metric</b> parameter): <i>Euclidean</i>, <i>Manhattan</i>, and
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+<i>Maximum</i>.
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+
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+<p>
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+
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+The <i>Euclidean distance</i> or <i>Euclidean metric</i> is the "ordinary" distance
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+between two points that one would measure with a ruler, which can be
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+proven by repeated application of the Pythagorean theorem.
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+The formula is given by:
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+
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+<div class="code"><pre>d(dx,dy) = sqrt(dx^2 + dy^2)</pre></div>
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+
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+Cells grown using this metric would form isolines of distance that are
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+circular from a given point, with the distance given by the <b>radius</b>.
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+
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+<p>
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+
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+The <i>Manhattan metric</i>, or <i>Taxicab geometry</i>, is a form of geometry in
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+which the usual metric of Euclidean geometry is replaced by a new
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+metric in which the distance between two points is the sum of the (absolute)
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+differences of their coordinates. The name alludes to the grid layout of
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+most streets on the island of Manhattan, which causes the shortest path a
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+car could take between two points in the city to have length equal to the
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+points' distance in taxicab geometry.
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+The formula is given by:
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+
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+<div class="code"><pre>d(dx,dy) = abs(dx) + abs(dy)</pre></div>
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+
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+where cells grown using this metric would form isolines of distance that are
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+rhombus-shaped from a given point.
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+
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+<p>
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+
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+The <i>Maximum metric</i> is given by the formula
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+
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+<div class="code"><pre>d(dx,dy) = max(abs(dx),abs(dy))</pre></div>
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+
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+where the isolines of distance from a point are squares.
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+
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<h2>SEE ALSO</h2>
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-<em><a href="r.buffer.html">r.buffer</a></em>,
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+<em><a href="r.buffer.html">r.buffer</a></em><br>
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<em><a href="r.patch.html">r.patch</a></em>
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+<p>
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+
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+<em><a href="http://en.wikipedia.org/wiki/Euclidean_metric">Wikipedia Entry: Euclidean Metric</a><br>
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+<em><a href="http://en.wikipedia.org/wiki/Manhattan_metric">Wikipedia Entry: Manhattan Metric</a>
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+
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<h2>AUTHORS</h2>
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Marjorie Larson,
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Eric Patton