/*!

\page smoothing_page Smoothing

\n Smoothing is used to improve quality of 2D mesh by adjusting the
locations of element corners (nodes). \note Depending on smoothing
method and mesh geometry smoothing can decrease quality of 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, sub-mesh or group</b> activating this
  check-box; 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 filters</b> button allows to apply a filter
  to the selection of elements. See more about filters in the 
  \ref filtering_elements "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 (a set of element), the nodes on
  boundary of the element set 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>

Laplacian method will produce the mesh with the least element
edge length. It is also the fastest method. Centroidal smoothing
produces a mesh with more uniform element sizes.</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> check-box if it is necessary 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 that is suitable for <b>planar meshes only</b>. </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.  

*/