/*!

\page smoothing_page Smoothing

\n Smoothing is used to adjust the locations of element corners
(nodes) to reduce distortions in these elements.

<em>To apply smoothing to the elements of your mesh:</em>
<ol>

<li>In the \b Modification menu select the \b Smoothing item or click
<em>"Smoothing"</em> button in the toolbar.

\image html image84.png
<center><em>"Smoothing" button</em></center>

The following dialog will appear:

\image html smoothing.png
</li>
<li>In this dialog:

<ul>
<li>specify the IDs of the elements which will be smoothed:
<ul>
<li><b>Select the whole mesh, submesh or group</b> activating this
checkbox; or</li>
<li>choose mesh elements with the mouse in the 3D Viewer. It is
possible to select a whole area with a mouse frame; or</li> 
<li>input the element IDs directly in <b>ID Elements</b> field. The selected elements will be highlighted in the
viewer; or</li>
<li>apply Filters. <b>Set filter</b> button allows to apply a filter to the selection of elements. See more
about filters in the \ref selection_filter_library_page "Selection filter library" page.</li>
</ul>
</li>

<li>define the <b>Fixed nodes ids</b> that should remain at their location during
smoothing. If a mesh is built on a shape, the nodes built on its
geometric edges are always fixed. If the smoothing is applied to a part
of the mesh, the nodes of boundary elements are also
fixed. It is possible to additionally fix any other nodes. The fixed nodes can be
selected manually or by filters, just as the smoothed elements.</li>
<li>choose the <b>Smoothing Method:</b>
<ul>
<li>\b Laplacian smoothing pulls a node toward the center of
surrounding nodes directly connected to that node along an element
edge. 
<li>\b Centroidal smoothing pulls a node toward the
element-area-weighted centroid of the surrounding elements. </li>

Typically, the  Laplacian method will produce the mesh with the least element
distortion. It is also the fastest method. Centroidal smoothing usually
produces  a mesh with more uniform element sizes. Both methods
produce good results with "free" meshes.</li>
</ul>

\image html image83.gif

</li>
<li>specify the <b>Iteration limit</b>. Both smoothing methods
iterate through a number of steps to produce the resulting smoothed
mesh. At each new step the smoothing is reevaluated with the updated nodal locations. This
process continues till the limit of iterations has been
exceeded, or till the aspect ratio of all element is less than or equal to the
specified one.</li>
<li>specify the  <b>Max. aspect ratio</b> - the target mesh quality at which the
smoothing algorithm should stop the iterations.</li>
<li>activate <b>in parametric space</b> checkbox if it is necessary to
to improve the shape of faces in the parametric space
of geometrical surfaces on which they are generated, else the shape of
faces in the 3D space is improved. </li>   
</ul>
</li>
<li>Click \b Apply or <b> Apply and Close</b> button to confirm the operation.</li>
</ol>

\image html smoothing1.png "The initial mesh"

\image html smoothing2.png "The smoothed mesh"

<br><b>See Also</b> a sample TUI Script of a 
\ref tui_smoothing "Smoothing" operation.  

*/