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@@ -19,17 +19,15 @@ produces a smoother approximate of the original.
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In some cases, this is achieved by inserting new vertices into the original line, and can
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total up to 4000% of the number of vertices in the original. In such an instance,
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it is always a good idea to simplify the line after smoothing.
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-</p>
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<p>
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Smoothing and simplification algorithms implemented in this module work line by
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line, i.e. simplification/smoothing of one line does not affect the other lines;
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they are treated separately. Also, the first and the last point of each line is
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never translated and/or deleted.
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-</p>
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<h3>SIMPLIFICATION</h3>
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-<p>
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+
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<em>v.generalise</em> contains following line simplification algorithms:
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<ul>
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<li>Douglas-Peucker Algorithm</li>
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@@ -49,6 +47,7 @@ If the <b>-r</b> flag is passed, simplified lines that become shorter becomes sh
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and a simplification algorithm is selected, then areas less than <b>threshold</b> are also removed.
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<h4>ALGORITHM DESCRIPTIONS</h4>
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+
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<ul>
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<li> <i>Douglas-Peucker</i> - "Quicksort" of line simplification, the most widely used
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algorithm. Input parameters: <b>input</b>, <b>threshold</b>. For more
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@@ -71,7 +70,6 @@ and a simplification algorithm is selected, then areas less than <b>threshold</b
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Other lines/areas/boundaries are left unchanged. Input parameters: <b>input</b>, <b>threshold</b>
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</ul>
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-<p>
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<i>Douglas-Peucker</i> and <i>Douglas-Peucker Reduction Algorithm</i> use the same method
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to simplify the lines. Note that
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<div class="code"><pre>
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@@ -88,14 +86,13 @@ More importantly, the effect of
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<div class="code"><pre>
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v.generalise input=in output=out method=douglas_reduction threshold=0 reduction=X
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</pre></div>
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-<p>
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+
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is that 'out' contains approximately only X% of points of 'in'.
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-</p>
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<h3>SMOOTHING</h3>
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-<p>
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+
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The following smoothing algorithms are implemented in <em>v.generalise</em>
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-</p>
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+
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<ul>
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<li><i>Boyle's Forward-Looking Algorithm</i> - The position of each point depends on the
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position of the previous points and the point <b>look_ahead</b> ahead.
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@@ -122,12 +119,11 @@ The following smoothing algorithms are implemented in <em>v.generalise</em>
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This algorithm works very well for small values of <b>alpha</b> and <b>beta</b> (between 0 and 5). These
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parameters affects the "sharpness" and the curvature of the computed line.</li>
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</ul>
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-<p>
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+
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One of the key advantages of <i>Hermite Interpolation</i> is the fact that the computed line
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always passes through the points of the original line, whereas the lines produced by the
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remaining algorithms never pass through these points. In some sense, this algorithm outputs
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a line which "circumscribes" the input line.
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-</p>
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<p>
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On the other hand, <i>Chaiken's Algorithm</i> outputs a line which "inscribes" a given line.
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@@ -136,41 +132,34 @@ consecutive points. For more iterations, the property above does not hold, but t
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lines are very similar to the Bezier Splines. The disadvantage of the two algorithms given above is that
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they increase the number of points. However, <i>Hermite Interpolation</i> can be used as another
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simplification algorithm. To achieve this, it is necessary to set <i>angle_thresh</i> to higher values (15 or so).
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-</p>
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<p>
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One restriction on both McMasters' Algorithms is that <i>look_ahead</i> parameter must be odd. Also
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note that these algorithms have no effect if <i>look_ahead = 1</i>.
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-</p>
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<p>
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Note that <i>Boyle's</i>, <i>McMasters'</i> and <i>Snakes</i> algorithm are sometimes used in the signal processing to smooth the signals.
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More importantly, these algorithms never change the number of points on the lines; they only
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translate the points, and do not insert any new points.
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-</p>
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<p>
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<i>Snakes</i> Algorithm is (asymptotically) the slowest among the algorithms presented above. Also,
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it requires quite a lot of memory. This means that it is not very efficient for maps with the lines
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consisting of many segments.
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-</p>
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<h3>DISPLACEMENT</h3>
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-<p>
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+
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The displacement is used when the lines overlap and/or are close to each other at the current
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level of detail. In general, displacement methods moves the conflicting features apart so
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that they do not interact and can be distinguished.
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-</p>
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<p>
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This module implements algorithm for displacement of linear features based on
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the <i>Snakes</i> approach. This method generally yields very good results; however, it
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requires a lot of memory and is not very efficient.
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-</p>
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<p>
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Displacement is selected by <b>method=displacement</b>. It uses following parameters:
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-</p>
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<ul>
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<li>
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@@ -193,20 +182,19 @@ the lines are resolved. Good starting points for values of <b>iterations</b> are
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</li>
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</ul>
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-<p>
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+
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The lines affected by the algorithm can be specified by the <b>layer</b>,
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<b>cats</b> and <b>where</b> parameters.
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-</p>
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+
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<!-- TODO: example(s) -->
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<h3>NETWORK GENERALIZATION</h3>
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-<p>
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+
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Used for selecting "the most important" part of the network. This is based
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on the graph algorithms. Network generalization is applied if method=network.
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The algorithm calculates three centrality measures for each line in the
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network and only the lines with the values greater than thresholds are selected.
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The behaviour of algorithm can be altered by the following parameters:
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-</p>
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<ul>
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<li>
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@@ -229,27 +217,31 @@ which lie between other lines and lie on the paths between two parts of a networ
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In the terminology of the road networks, these are highways, bypasses, main roads/streets, etc.
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</li>
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</ul>
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-<p>
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+
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All three parameters above can be presented at the same time. In that case,
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the algorithm selects only the lines which meet each criterion.
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-</p>
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+
|
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<p>
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Also, the outputed network may not be connected if the value of <b>betweeness_thresh</b>
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is too large.
|
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-</p>
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+
|
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<!-- TODO: example(s) -->
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<h2>SEE ALSO</h2>
|
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|
-<em><a href="http://users.ox.ac.uk/~orie1848/tutorial.html">v.generalise Tutorial</a><br></em>
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-<em><a href="v.clean.html">v.clean</a><br></em>
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-<em><a href="v.dissolve.html">v.dissolve</a><br></em>
|
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+
|
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+<em>
|
|
|
+ <a href="v.clean.html">v.clean</a>,
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|
+ <a href="v.dissolve.html">v.dissolve</a>
|
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+</em>
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<br><br>
|
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|
+<a href="http://grass.osgeo.org/wiki/V.generalize_tutorial">v.generalize Tutorial</a> (from GRASS-Wiki)
|
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<h2>AUTHORS</h2>
|
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|
-Daniel Bundala, Google Summer of Code 2007, Student
|
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-<br>
|
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+
|
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+Daniel Bundala, Google Summer of Code 2007, Student<br>
|
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Wolf Bergenheim, Mentor
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<!-- TODO: references -->
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-<p><i>Last changed: $Date$</i>
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+<p>
|
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+<i>Last changed: $Date$</i>
|
Martin Landa