[GRASS-SVN] r31443 - grass/branches/develbranch_6/raster/r.grow2

[svn_grass at osgeo.org]

Author: epatton
Date: 2008-05-20 13:03:02 -0400 (Tue, 20 May 2008)
New Revision: 31443

Modified:
   grass/branches/develbranch_6/raster/r.grow2/description.html
Log:
Backported html updates from TRUNK: r31442

Modified: grass/branches/develbranch_6/raster/r.grow2/description.html
===================================================================
--- grass/branches/develbranch_6/raster/r.grow2/description.html	2008-05-20 17:01:47 UTC (rev 31442)
+++ grass/branches/develbranch_6/raster/r.grow2/description.html	2008-05-20 17:03:02 UTC (rev 31443)
@@ -4,15 +4,63 @@
 <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, or like <em>r.buffer</em>, but with the
+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.
+
 <h2>SEE ALSO</h2>
 
-<em><a href="r.buffer.html">r.buffer</a></em>,
+<em><a href="r.buffer.html">r.buffer</a></em><br>
 <em><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><br>
+<em><a href="http://en.wikipedia.org/wiki/Manhattan_metric">Wikipedia Entry: Manhattan Metric</a>
+
 <h2>AUTHORS</h2>
 
 Marjorie Larson,