/*!

\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>Display a mesh or a submesh in the 3D viewer.</li>
<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 dialog box contains the following fields which should be
specified:

\image html smoothing.png

<ul>
<li><b>Id Elements</b> field allows to specify the elements which
should be smoothed
<ul>
<li>Check on <b>Select the whole mesh, submesh or group</b> option
<li>Choosing them manually with the mouse in the 3D Viewer. You can
click on an element in the 3D viewer and it will be highlighted</li>
<li>Applying Filters. The <b>Set filter</b> button allows to apply a
definite filter to selection of the elements. See more
about filters on the
\ref selection_filter_library_page "Selection filter library" page.</li>
</ul>
</li>
<b>Fixed nodes ids:</b> some nodes keep their location during
smoothing. If a mesh is built on a geometry shape, the nodes built on
geometrical edges are always fixed. If smoothing is applied to a part
of a mesh then the boundary nodes of an elements set are also
fixed. Any other nodes may be additionally fixed. Fixed nodes can be
selected manually or by filters too.</li>
<li><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 faster method.Centroidal smoothing usually
produces  a mesh that has more uniform element sizes. Both methods
produce good results with "free" meshes.</li>
</ul>

\image html image83.gif

</li>
<li><b>Iteration limit:</b> both of the smoothing methods use an
iterative procedure to converge toward a smoothed mesh. All nodes are
smoothed according to one of the techniques shown above. Then the
smoothing is reevaluated with the updated nodal locations. This
process continues until the maximum number of iterations has been
exceeded, or all elements has aspect ratio less or equal than the
specified one.</li>
<li><b>Max. aspect ratio</b> allows to define the quality at which the
smoothing algorithm should stop the iterations as the target of the
operation has been reached.</li>
<li>When <b>in parametric space</b> radio button is checked, the
algorithm tries 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 the \b Apply or \b OK 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.  

*/