\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>
<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><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 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>
+ 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, 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>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
<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>
+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> 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>
+<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>
