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-<h1>Smoothing</h1>
-
-<p><img src="../i_blue.jpg" x-maintain-ratio="TRUE" width="30px" height="30px" border="0" class="img_whs1"> Smoothing is used to adjust the locations of element
- corners (nodes) to reduce distortions in these elements.</p>
-
-<p> </p>
-
-<p class=TODO>To apply smoothing to the elements of your mesh:</p>
-
-<p> </p>
-
-<p class="whs2">1. Display a mesh or a submesh in the 3D
- viewer.</p>
-
-<p class="whs2">2. In the <span style="font-weight: bold;"><B>Modification
- </B></span>menu select the <span style="font-weight: bold;"><B>Smoothing </B></span>item
- or click <img src="../image84.gif" width="24px" height="25px" border="0" class="img_whs3"> button in the toolbar. The <span style="margin-left: 40px;">dialog
- box contains the following fields which should be specified:</span></p>
-
-<p> </p>
-
-<p class="whs2"><img src="../pics/smoothing.png" x-maintain-ratio="TRUE" width="332px" height="396px" border="0" class="img_whs4"> </p>
-
-<ul type="disc" class="whs5">
-
- <li class=kadov-p><p class="whs6"><span
- style="font-weight: bold;"><B>Id Elements </B></span>field allows to specify
- the elements which should be smoothed by selecting them in the 3D viewer
- (lock <span style="font-weight: bold;"><B>Shift </B></span>button to select several
- elements).</p></li>
-
- <ul type="disc" class="whs5">
-
- <li class=kadov-p><p class="whs7">Select whole mesh,
- submesh or group - <span style="font-weight: normal;">smoothing is applied
- to the whole mesh or its part.</span></p></li>
-
- <li class=kadov-p><p><span style="font-weight: bold;"><B>Fixed nodes
- ids</B></span>: 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.</p></li>
-
- <li class=kadov-p><p><span style="font-weight: bold;"><B>Smoothing
- Method</B></span>:</p></li>
-
- <ul type="disc" class="whs5">
-
- <li class=kadov-p><p><span style="font-weight: bold;"><B>Laplacian</B></span>
- smoothing pulls a node toward the center of surrounding nodes directly
- connected to that node along an element edge. Centroidal smoothing pulls
- a node toward the element-area-weighted centroid of the surrounding elements.
- Typically, the Laplacian method will produce the mesh with the least element
- distortion. It is also the faster method. </p></li>
-
- <li class=kadov-p><p><span style="font-weight: bold;"><B>Centroidal</B></span>
- smoothing usually produces a mesh that has more uniform element sizes.
- Both methods produce good results with "free" meshes.</p></li>
- </ul>
- </ul>
-</ul>
-
-<p> </p>
-
-<p class="whs8"><img src="../image83.gif" width="527px" height="281px" border="0" class="img_whs9"></p>
-
-<ul type="disc" class="whs5">
-
- <li class=kadov-p><p class="whs6"><span
- style="font-weight: bold;"><B>Iteration limit: </B></span>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.</p></li>
-
- <li class=kadov-p><p class="whs6"><span
- style="font-weight: bold;"><B>Max. aspect ratio</B></span>.</p></li>
-</ul>
-
-<p class="whs2"> </p>
-
-<p class="whs2">3. Click the <span style="font-weight: bold;"><B>Apply
- </B></span>or <span style="font-weight: bold;"><B>OK </B></span>button to confirm
- the operation.</p>
-
-<p class="whs2"> </p>
-
-<p class="whs2"><img src="../pics/smoothing1.png" x-maintain-ratio="TRUE" width="353px" height="235px" border="0" class="img_whs10"> <img src="../pics/smoothing2.png" x-maintain-ratio="TRUE" width="351px" height="235px" border="0" class="img_whs11"></p>
-
-<p> </p>
-
-<p> <span style="font-weight: bold;"><B>See
- Also</B></span> a sample TUI Script of a <a href="../modifying_meshes.htm#bookmark8">Smoothing</a>
- operation. </p>
-
-<p> </p>
-
-<p> </p>
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