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-<h1>Smoothing</h1>\r
-\r
-<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 \r
- corners (nodes) to reduce distortions in these elements.</p>\r
-\r
-<p> </p>\r
-\r
-<p class=TODO>To apply smoothing to the elements of your mesh:</p>\r
-\r
-<p> </p>\r
-\r
-<p class="whs2">1. Display a mesh or a submesh in the 3D \r
- viewer.</p>\r
-\r
-<p class="whs2">2. In the <span style="font-weight: bold;"><B>Modification \r
- </B></span>menu select the <span style="font-weight: bold;"><B>Smoothing </B></span>item \r
- 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 \r
- box contains the following fields which should be specified:</span></p>\r
-\r
-<p> </p>\r
-\r
-<p class="whs2"><img src="../pics/smoothing.png" x-maintain-ratio="TRUE" width="332px" height="396px" border="0" class="img_whs4"> </p>\r
-\r
-<ul type="disc" class="whs5">\r
- \r
- <li class=kadov-p><p class="whs6"><span \r
- style="font-weight: bold;"><B>Id Elements </B></span>field allows to specify \r
- the elements which should be smoothed by selecting them in the 3D viewer \r
- (lock <span style="font-weight: bold;"><B>Shift </B></span>button to select several \r
- elements).</p></li>\r
- \r
- <ul type="disc" class="whs5">\r
- \r
- <li class=kadov-p><p class="whs7">Select whole mesh, \r
- submesh or group - <span style="font-weight: normal;">smoothing is applied \r
- to the whole mesh or its part.</span></p></li>\r
- \r
- <li class=kadov-p><p><span style="font-weight: bold;"><B>Fixed nodes \r
- ids</B></span>: some nodes keep their location during smoothing. If a mesh \r
- is built on a geometry shape, the nodes built on geometrical edges are \r
- always fixed. If smoothing is applied to a part of a mesh then the boundary \r
- nodes of an elements set are also fixed. Any other nodes may be additionally \r
- fixed.</p></li>\r
- \r
- <li class=kadov-p><p><span style="font-weight: bold;"><B>Smoothing \r
- Method</B></span>:</p></li>\r
- \r
- <ul type="disc" class="whs5">\r
- \r
- <li class=kadov-p><p><span style="font-weight: bold;"><B>Laplacian</B></span> \r
- smoothing pulls a node toward the center of surrounding nodes directly \r
- connected to that node along an element edge. Centroidal smoothing pulls \r
- a node toward the element-area-weighted centroid of the surrounding elements. \r
- Typically, the Laplacian method will produce the mesh with the least element \r
- distortion. It is also the faster method. </p></li>\r
- \r
- <li class=kadov-p><p><span style="font-weight: bold;"><B>Centroidal</B></span> \r
- smoothing usually produces a mesh that has more uniform element sizes. \r
- Both methods produce good results with "free" meshes.</p></li>\r
- </ul>\r
- </ul>\r
-</ul>\r
-\r
-<p> </p>\r
-\r
-<p class="whs8"><img src="../image83.gif" width="527px" height="281px" border="0" class="img_whs9"></p>\r
-\r
-<ul type="disc" class="whs5">\r
- \r
- <li class=kadov-p><p class="whs6"><span \r
- style="font-weight: bold;"><B>Iteration limit: </B></span>both of the smoothing \r
- methods use an iterative procedure to converge toward a smoothed mesh. \r
- All nodes are smoothed according to one of the techniques shown above. \r
- Then the smoothing is reevaluated with the updated nodal locations. This \r
- process continues until the maximum number of iterations has been exceeded, \r
- or all elements has aspect ratio less or equal than the specified one.</p></li>\r
- \r
- <li class=kadov-p><p class="whs6"><span \r
- style="font-weight: bold;"><B>Max. aspect ratio</B></span>.</p></li>\r
-</ul>\r
-\r
-<p class="whs2"> </p>\r
-\r
-<p class="whs2">3. Click the <span style="font-weight: bold;"><B>Apply \r
- </B></span>or <span style="font-weight: bold;"><B>OK </B></span>button to confirm \r
- the operation.</p>\r
-\r
-<p class="whs2"> </p>\r
-\r
-<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>\r
-\r
-<p> </p>\r
-\r
-<p> <span style="font-weight: bold;"><B>See \r
- Also</B></span> a sample TUI Script of a <a href="../modifying_meshes.htm#bookmark8">Smoothing</a> \r
- operation. </p>\r
-\r
-<p> </p>\r
-\r
-<p> </p>\r
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+<!doctype HTML public "-//W3C//DTD HTML 4.0 Frameset//EN">
+
+<html>
+
+<head>
+<title>Smoothing</title>
+<meta http-equiv="content-type" content="text/html; charset=windows-1252">
+<meta name="generator" content="RoboHelp by eHelp Corporation www.ehelp.com">
+<link rel="stylesheet" href="../default_ns.css"><script type="text/javascript" language="JavaScript" title="WebHelpSplitCss">
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+if (navigator.appName !="Netscape")
+{ document.write("<link rel='stylesheet' href='../default.css'>");}
+//-->
+</script>
+<style type="text/css">
+<!--
+img_whs1 { border:none; width:30px; height:30px; float:none; border-style:none; }
+p.whs2 { margin-left:40px; }
+img_whs3 { border:none; width:24px; height:25px; border-style:none; }
+img_whs4 { border:none; width:332px; height:396px; float:none; border-style:none; }
+ul.whs5 { list-style:disc; }
+p.whs6 { margin-left:40px; font-weight:normal; }
+p.whs7 { font-weight:bold; }
+p.whs8 { margin-left:80px; }
+img_whs9 { border:none; width:527px; height:281px; border-style:none; }
+img_whs10 { border:none; float:none; width:353px; height:235px; border-style:none; }
+img_whs11 { border:none; width:351px; height:235px; float:none; border-style:none; }
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+ origWidth = innerWidth;
+ origHeight = innerHeight;
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+}
+onerror = null;
+//-->
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+{
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+ {
+ addTocInfo("MESH module\nModifying meshes\nSmoothing");
+addButton("show",BTN_IMG,"Show","","","","",0,0,"../whd_show0.gif","../whd_show2.gif","../whd_show1.gif");
+addButton("hide",BTN_IMG,"Hide","","","","",0,0,"../whd_hide0.gif","../whd_hide2.gif","../whd_hide1.gif");
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+<body><script type="text/javascript" language="javascript1.2">
+<!--
+if (window.writeIntopicBar)
+ writeIntopicBar(4);
+//-->
+</script>
+<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>
+
+<script type="text/javascript" language="javascript1.2">
+<!--
+if (window.writeIntopicBar)
+ writeIntopicBar(0);
+//-->
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+</html>
