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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>&nbsp;</p>

<p class=TODO>To apply smoothing to the elements of your mesh:</p>

<p>&nbsp;</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>&nbsp;</p>

<p class="whs2"><img src="../pics/smoothing.png" x-maintain-ratio="TRUE" width="332px" height="396px" border="0" class="img_whs4"> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</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 &quot;free&quot; meshes.</p></li>
		</ul>
	</ul>
</ul>

<p>&nbsp;</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">&nbsp;</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">&nbsp;</p>

<p class="whs2"><img src="../pics/smoothing1.png" x-maintain-ratio="TRUE" width="353px" height="235px" border="0" class="img_whs10"> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<img src="../pics/smoothing2.png" x-maintain-ratio="TRUE" width="351px" height="235px" border="0" class="img_whs11"></p>

<p>&nbsp;</p>

<p>&nbsp;&nbsp;<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. &nbsp;</p>

<p>&nbsp;</p>

<p>&nbsp;</p>

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