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<h2>DESCRIPTION</h2>
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-<em>v.generalise</em>
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+<em>v.generalize</em>
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is a module for the generalization of GRASS vector maps. This module
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consists of algorithms for line simplification, line smoothing,
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network generalization and displacement (new methods may be added later).
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@@ -8,177 +8,207 @@ For more examples and nice pictures, see
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<em><a href="http://users.ox.ac.uk/~orie1848/tutorial.html">tutorial</a><br></em>
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<h2>NOTES</h2>
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-(Line) simplification is a process of reducing the complexity of vector features.
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-The module transforms a line into another line consisting of fewer vertices, that
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-still approximate the original line. Most of the algorithms described below
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-select a subset of points on the original line.
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+(Line) simplification is a process of reducing the complexity of vector
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+features. The module transforms a line into another line consisting of
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+fewer vertices, that still approximate the original line. Most of the
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+algorithms described below select a subset of points on the original line.
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<p>
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(Line) smoothing is a "reverse" process which takes as input a line and
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-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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+produces a smoother approximate of the original. In some cases, this is
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+achieved by inserting new vertices into the original line, and can total
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+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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-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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+Smoothing and simplification algorithms implemented in this module work
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+line by line, i.e. simplification/smoothing of one line does not affect
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+the other lines; they are treated separately. Also, the first and the
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+last point of each line is never translated and/or deleted.
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<h3>SIMPLIFICATION</h3>
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-<em>v.generalise</em> contains following line simplification algorithms:
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+<em>v.generalize</em> contains following line simplification algorithms:
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<ul>
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<li>Douglas-Peucker Algorithm</li>
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-<li>"Douglas-Peucker Reduction Algorithm"</li>
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+<li>Douglas-Peucker Reduction Algorithm</li>
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<li>Lang Algorithm</li>
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<li>Vertex Reduction</li>
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<li>Reumann-Witkam Algorithm</li>
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<li>Remove Small Lines/Areas</li>
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</ul>
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-Different algorithms require different parameters, but all the algorithms have
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-one parameter in common: the <b>threshold</b> parameter. In general, the degree
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-of simplification increases with the increasing value of <b>threshold</b>.<br>
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-
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-If the <b>-r</b> flag is passed, simplified lines that become shorter becomes shorter than the
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-<b>threshold</b> value are removed. Additionally, if the <b>type</b> parameter contains <b>area</b>
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-and a simplification algorithm is selected, then areas less than <b>threshold</b> are also removed.
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+Different algorithms require different parameters, but all the algorithms
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+have one parameter in common: the <b>threshold</b> parameter. In general,
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+the degree of simplification increases with the increasing value of
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+<b>threshold</b>.<br>
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<h4>ALGORITHM DESCRIPTIONS</h4>
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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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- information, please see: <A href="http://geometryalgorithms.com/Archive/algorithm_0205/algorithm_0205.htm">http://geometryalgorithms.com/Archive/algorithm_0205/algorithm_0205.htm</a>.</li>
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-<li> <i>Douglas-Peucker Reduction Algorithm</i> is essentially the same algorithm as the
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- algorithm above, the difference being that it takes additional <b>reduction</b> parameter
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- which denotes the percentage of the number of points on the new line with respect
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- to the number of points on the original line. Input parameters: <b>input</b>,
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+<li> <i>Douglas-Peucker</i> - "Quicksort" of line simplification, the
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+ most widely used algorithm. Input parameters: <b>input</b>,
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+ <b>threshold</b>. For more information, see: <br>
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+ <A href="http://geometryalgorithms.com/Archive/algorithm_0205/algorithm_0205.htm">http://geometryalgorithms.com/Archive/algorithm_0205/algorithm_0205.htm</a>.</li>
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+<li> <i>Douglas-Peucker Reduction Algorithm</i> is essentially the same
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+ algorithm as the algorithm above, the difference being that it takes
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+ an additional <b>reduction</b> parameter which denotes the percentage
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+ of the number of points on the new line with respect to the number
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+ of points on the original line. Input parameters: <b>input</b>,
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<b>threshold</b>, <b>reduction</b>.</li>
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-<li> <i>Lang</i> - Another standard algorithm. Input parameters: <b>input</b>, <b>threshold</b>, <b>look_ahead</b>.
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- For an excellent description, see: <A href="http://www.sli.unimelb.edu.au/gisweb/LGmodule/LGLangVisualisation.htm">http://www.sli.unimelb.edu.au/gisweb/LGmodule/LGLangVisualisation.htm</a>.</li>
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-<li> <i>Vertex Reduction</i> - Simplest among the algorithms. Input parameters: <b>input</b>, <b>threshold</b>.
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- Given a line, this algorithm removes the points of this line which are closer to each other than <b>threshold</b>.
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- More precisely, if p1 and p2 are two consecutive points, and the distance between p2 and p1 is less
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- than <b>threshold</b>, it removes p2 and repeats the same process on the remaining points.</li>
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-<li> <i>Reuman-Witkam</i> - Input parameters: <b>input</b>, <b>threshold</b>. This algorithm quite
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- reasonably preserves the global characteristics of the lines. For more information
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- see <A href="http://www.ifp.uni-stuttgart.de/lehre/vorlesungen/GIS1/Lernmodule/Lg/LG_de_6.html">http://www.ifp.uni-stuttgart.de/lehre/vorlesungen/GIS1/Lernmodule/Lg/LG_de_6.html</a>(german)</li>
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-<li> <i>Remove Small Lines/Areas</i> - removes the lines (strictly) shorter than threshold and areas (strictly) less than threshold.
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- Other lines/areas/boundaries are left unchanged. Input parameters: <b>input</b>, <b>threshold</b>
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+<li> <i>Lang</i> - Another standard algorithm. Input parameters:
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+ <b>input</b>, <b>threshold</b>, <b>look_ahead</b>.
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+ For an excellent description, see: <br>
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+ <A href="http://www.sli.unimelb.edu.au/gisweb/LGmodule/LGLangVisualisation.htm">http://www.sli.unimelb.edu.au/gisweb/LGmodule/LGLangVisualisation.htm</a>.</li>
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+<li> <i>Vertex Reduction</i> - Simplest among the algorithms. Input
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+ parameters: <b>input</b>, <b>threshold</b>.
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+ Given a line, this algorithm removes the points of this line which
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+ are closer to each other than <b>threshold</b>. More precisely, if
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+ p1 and p2 are two consecutive points, and the distance between p2
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+ and p1 is less than <b>threshold</b>, it removes p2 and repeats the
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+ same process on the remaining points.</li>
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+<li> <i>Reuman-Witkam</i> - Input parameters: <b>input</b>,
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+ <b>threshold</b>.
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+ This algorithm quite reasonably preserves the global characteristics
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+ of the lines. For more information, see: <br>
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+ <A href="http://www.ifp.uni-stuttgart.de/lehre/vorlesungen/GIS1/Lernmodule/Lg/LG_de_6.html">http://www.ifp.uni-stuttgart.de/lehre/vorlesungen/GIS1/Lernmodule/Lg/LG_de_6.html</a> (german).</li>
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</ul>
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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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+<i>Douglas-Peucker</i> and <i>Douglas-Peucker Reduction Algorithm</i>
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+use the same method to simplify the lines. Note that
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<div class="code"><pre>
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-v.generalise input=in output=out method=douglas threshold=eps
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+v.generalize input=in output=out method=douglas threshold=eps
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</pre></div>
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is equivalent to
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<div class="code"><pre>
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-v.generalise input=in output=out method=douglas_reduction threshold=eps reduction=100
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+v.generalize input=in output=out method=douglas_reduction threshold=eps reduction=100
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</pre></div>
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However, in this case, the first method is faster. Also observe that
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-<i>douglas_reduction</i> never outputs more vertices than <i>douglas</i>. And that,
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-in general, <i>douglas</i> is more efficient than <i>douglas_reduction</i>.
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-More importantly, the effect of
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+<i>douglas_reduction</i> never outputs more vertices than <i>douglas</i>,
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+and that, in general, <i>douglas</i> is more efficient than
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+<i>douglas_reduction</i>. 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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+v.generalize input=in output=out method=douglas_reduction threshold=0 reduction=X
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</pre></div>
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-
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is that 'out' contains approximately only X% of points of 'in'.
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<h3>SMOOTHING</h3>
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-The following smoothing algorithms are implemented in <em>v.generalise</em>
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+The following smoothing algorithms are implemented in <em>v.generalize</em>
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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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- <b>look_ahead</b> consecutive points. Input parameters: <b>input</b>, <b>look_ahead</b>.</li>
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-<li><i>McMaster's Sliding Averaging Algorithm</i> - Input Parameters: <b>input</b>, <b>slide</b>, <b>look_ahead</b>.
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- The new position of each point is the average of the <b>look_ahead</b> points around. Parameter <b>slide</b>
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- is used for linear interpolation between old and new position (see below).</li>
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-<li><i>McMaster's Distance-Weighting Algorithm</i> - Works by taking the weighted average of <b>look_ahead</b> consecutive points
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- where the weight is the reciprocal of the distance from the point to the currently smoothed point. And parameter <b>slide</b> is used
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- for linear interpolation between the original position of the point and newly computed position where value 0 means the original position.
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+<li><i>Boyle's Forward-Looking Algorithm</i> - The position of each point
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+ depends on the position of the previous points and the point
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+ <b>look_ahead</b> ahead. <b>look_ahead</b> consecutive points. Input
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+ parameters: <b>input</b>, <b>look_ahead</b>.</li>
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+<li><i>McMaster's Sliding Averaging Algorithm</i> - Input Parameters:
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+ <b>input</b>, <b>slide</b>, <b>look_ahead</b>.
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+ The new position of each point is the average of the <b>look_ahead</b>
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+ points around. Parameter <b>slide</b> is used for linear interpolation
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+ between old and new position (see below).</li>
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+<li><i>McMaster's Distance-Weighting Algorithm</i> - Takes the weighted
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+ average of <b>look_ahead</b> consecutive points where the weight is
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+ the reciprocal of the distance from the point to the currently
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+ smoothed point. The parameter <b>slide</b> is used for linear
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+ interpolation between the original position of the point and newly
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+ computed position where value 0 means the original position.
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Input parameters: <b>input</b>, <b>slide</b>, <b>look_ahead</b>.
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</li>
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-<li><i>Chaiken's Algorithm</i> - "Inscribes" a line touching the original line such that the points on this new line
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- are at least <i>threshold</i> apart. Input parameters: <b>input</b>, <b>threshold</b>. This algorithm
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- approximates the given line very well.</li>
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-<li> <i>Hermite Interpolation</i> - This algorithm takes the points of the given line as the control
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- points of hermite cubic spline and approximates this spline by the points approximately <b>threshold</b> apart.
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- This method has excellent results for the small values of <b>threshold</b>, but in this case it produces
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- a huge number of new points and some simplification is usually needed. Input parameters: <b>input</b>, <b>threshold</b>, <b>angle_thresh</b>.
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- <b>Angle_thresh</b> is used for reducing the number of the outputed points. It denotes the minimal
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- angle (in degrees) between two consecutive segments of line.</li>
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-<li> <i>Snakes</i> is the method of minimisation of the "energy" of the line. This method preserves the
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- general characteristics of the lines but smooths the "sharp corners" of the line. Input parameters <b>input</b>, <b>alpha</b>, <b>beta</b>.
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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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+<li><i>Chaiken's Algorithm</i> - "Inscribes" a line touching the original
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+ line such that the points on this new line are at least
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+ <i>threshold</i> apart. Input parameters: <b>input</b>,
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+ <b>threshold</b>. This algorithm approximates the given line very
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+ well.</li>
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+<li> <i>Hermite Interpolation</i> - This algorithm takes the points of
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+ the given line as the control points of hermite cubic spline and
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+ approximates this spline by the points approximately
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+ <b>threshold</b> apart. This method has excellent results for small
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+ values of <b>threshold</b>, but in this case it produces a huge
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+ number of new points and some simplification is usually needed.
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+ Input parameters: <b>input</b>, <b>threshold</b>, <b>angle_thresh</b>.
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+ <b>Angle_thresh</b> is used for reducing the number of the points.
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+ It denotes the minimal angle (in degrees) between two consecutive
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+ segments of a line.</li>
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+<li> <i>Snakes</i> is the method of minimisation of the "energy" of a
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+ line. This method preserves the general characteristics of the lines
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+ but smooths the "sharp corners" of a line. Input parameters
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+ <b>input</b>, <b>alpha</b>, <b>beta</b>.
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+ This algorithm works very well for small values of <b>alpha</b> and
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+ <b>beta</b> (between 0 and 5). These parameters affect the
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+ "sharpness" and the curvature of the computed line.</li>
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</ul>
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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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+One of the key advantages of <i>Hermite Interpolation</i> is the fact
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+that the computed line always passes through the points of the original
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+line, whereas the lines produced by the remaining algorithms never pass
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+through these points. In some sense, this algorithm outputs a line which
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+"circumscribes" the input line.
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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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-The output line always touches/intersects the centre of the input line segment between two
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-consecutive points. For more iterations, the property above does not hold, but the computed
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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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+On the other hand, <i>Chaiken's Algorithm</i> outputs a line which
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+"inscribes" a given line. The output line always touches/intersects the
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+centre of the input line segment between two consecutive points. For
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+more iterations, the property above does not hold, but the computed
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+lines are very similar to the Bezier Splines. The disadvantage of the
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+two algorithms given above is that they increase the number of points.
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+However, <i>Hermite Interpolation</i> can be used as another
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+simplification algorithm. To achieve this, it is necessary to set
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+<i>angle_thresh</i> to higher values (15 or so).
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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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+One restriction on both McMasters' Algorithms is that <i>look_ahead</i>
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+parameter must be odd. Also note that these algorithms have no effect if
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+<i>look_ahead = 1</i>.
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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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+Note that <i>Boyle's</i>, <i>McMasters'</i> and <i>Snakes</i> algorithm
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+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
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+the lines; they only translate the points, and do not insert any new points.
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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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+<i>Snakes</i> Algorithm is (asymptotically) the slowest among the
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+algorithms presented above. Also, it requires quite a lot of memory.
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+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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<h3>DISPLACEMENT</h3>
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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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+The displacement is used when the lines overlap and/or are close to each
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+other at the current level of detail. In general, displacement methods
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+move the conflicting features apart so that they do not interact and can
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+be distinguished.
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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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+This module implements an algorithm for displacement of linear features
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+based on the <i>Snakes</i> approach. This method generally yields very
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+good results; however, it requires a lot of memory and is not very efficient.
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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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+Displacement is selected by <b>method=displacement</b>. It uses the
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+following parameters:
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<ul>
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<li>
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-<b>threshold</b> - specifies critical distance. Two features interact if they are
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-closer than <b>threshold</b> apart.
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+<b>threshold</b> - specifies critical distance. Two features interact if
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+they are closer than <b>threshold</b> apart.
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</li>
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<li>
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-<b>alpha</b>, <b>beta</b> - These parameters define the rigidity of lines. For greater
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-values of <b>alpha</b>, <b>beta</b> (>=1), the algorithm does a better job at retaining the original
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-shape of the lines, possibly at the expense of displacement distance. If the values of <b>alpha</b>,
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-<b>beta</b> are too small (<=0.001), then the lines are moved sufficiently, but the geometry and topology of lines can
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-be destroyed. Most likely the best way to find the good values of <b>alpha</b>, <b>beta</b>
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+<b>alpha</b>, <b>beta</b> - These parameters define the rigidity of lines.
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+For larger values of <b>alpha</b>, <b>beta</b> (>=1), the algorithm
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+does a better job at retaining the original shape of the lines, possibly
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+at the expense of displacement distance. If the values of <b>alpha</b>,
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+<b>beta</b> are too small (<=0.001), then the lines are moved
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+sufficiently, but the geometry and topology of lines can be destroyed.
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+Most likely the best way to find the good values of <b>alpha</b>, <b>beta</b>
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is by trial and error.
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</li>
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<li>
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-<b>iterations</b> - denotes the number of iterations the interactions between
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-the lines are resolved. Good starting points for values of <b>iterations</b> are between 10 and 100.
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+<b>iterations</b> - denotes the number of iterations the interactions
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+between the lines are resolved. Good starting points for values of
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+<b>iterations</b> are between 10 and 100.
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</li>
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</ul>
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@@ -202,28 +232,30 @@ The behaviour of algorithm can be altered by the following parameters:
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with at least <b>degree_thresh</b> different lines.
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</li>
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<li>
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-<b>closeness_thresh</b> - is always in the range (0, 1]. Only the lines with
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-the closeness centrality value at least <b>closeness_thresh</b> apart are selected.
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-The lines in the centre of a network have greater values of this measure than
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-the lines near the border of a network. This means that this parameter can be used
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-for selecting the centre(s) of a network. Note that if closeness_thresh=0 then everything is selected.
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+<b>closeness_thresh</b> - is always in the range (0, 1]. Only the lines
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+with the closeness centrality value at least <b>closeness_thresh</b> apart
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+are selected. The lines in the centre of a network have greater values of
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+this measure than the lines near the border of a network. This means that
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+this parameter can be used for selecting the centre(s) of a network. Note
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+that if closeness_thresh=0 then everything is selected.
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</li>
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<li>
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-<b>betweeness_thresh</b> - Again, only the lines with a betweeness centrality
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-measure at least <b>betweeness_thresh</b> are selected. This value is always
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-positive and is larger for large networks. It denotes to what extent a line
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-is in between the other lines in the network. This value is great for the lines
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-which lie between other lines and lie on the paths between two parts of a network.
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-In the terminology of the road networks, these are highways, bypasses, main roads/streets, etc.
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+<b>betweeness_thresh</b> - Again, only the lines with a betweeness
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+centrality measure at least <b>betweeness_thresh</b> are selected. This
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+value is always positive and is larger for large networks. It denotes to
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+what extent a line is in between the other lines in the network. This
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+value is large for the lines which lie between other lines and lie on
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+the paths between two parts of a network. In the terminology of road
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+networks, these are highways, bypasses, main roads/streets, etc.
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</li>
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</ul>
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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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+All three parameters above can be presented at the same time. In that
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+case, the algorithm selects only the lines which meet each criterion.
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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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+Also, the outputed network may not be connected if the value of
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+<b>betweeness_thresh</b> is too large.
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<!-- TODO: example(s) -->
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