\page smoothing_page Smoothing
-\n Smoothing is used to adjust the locations of element corners
-(nodes) to reduce distortions in these elements.
+\n Smoothing is used to improve quality of 2D mesh by adjusting the
+locations of element corners (nodes).
+
+\note Depending on the chosen method and mesh geometry
+the smoothing can actually decrease the quality of elements and even
+make some elements inverted.
<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.gif
+\image html image84.png
<center><em>"Smoothing" button</em></center>
-The dialog box contains the following fields which should be
-specified:
+The following dialog will appear:
\image html smoothing.png
+</li>
+<li>In this dialog:
<ul>
-<li><b>Id Elements</b> field allows to specify the elements which
-should be smoothed by selecting them in the 3D viewer (lock \b Shift
-button to select several elements).</li>
-<li><b>Select whole mesh, submesh or group</b> - smoothing is applied
-to the whole mesh or its part.</li>
-<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.</li>
-<li><b>Smoothing Method:</b>
+<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
<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>
+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><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>
+<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 the \b Apply or \b OK button to confirm the operation.</li>
+<li>Click \b Apply or <b> Apply and Close</b> button to confirm the operation.</li>
</ol>
-\image html smoothing1.png
+\image html smoothing1.png "The initial mesh"
-\image html smoothing2.png
+\image html smoothing2.png "The smoothed mesh"
<br><b>See Also</b> a sample TUI Script of a
\ref tui_smoothing "Smoothing" operation.
