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-<h1>Aspect Ratio</h1>\r
-\r
-<p><img src="../i_blue.jpg" x-maintain-ratio="TRUE" width="30px" height="30px" border="0" class="img_whs1"> The <span style="font-weight: bold;"><B>Aspect Ratio</B></span> \r
- quality criterion for mesh elements reveals the degree of conformity of \r
- a mesh element to the regular element of its type (with all edges having \r
- the same length). The \r
- criterion can be defined as </p>\r
-\r
-<p class="whs2"><img src="../image142.gif" width="120px" height="56px" border="0" class="img_whs3">where <span style="font-weight: bold; font-style: italic;"><I><B>К</B></I></span> \r
- is the considered element of the mesh, <span style="font-weight: bold; font-style: italic;"><I><B>h</B></I></span><span \r
- style="vertical-align: Sub;\r
- font-weight: bold;\r
- font-style: italic;"><I><B>max</B></I></span> is the diameter of the element \r
- К (i.e. the length of the longest edge), <span style="font-weight: bold; font-style: italic;"><I><B>р</B></I></span><span \r
- style="vertical-align: Sub;\r
- font-weight: bold;\r
- font-style: italic;"><I><B>к</B></I></span> is the radius of the sphere \r
- inscribed in the element K, and <span style="font-weight: bold; font-style: italic;"><I><B>a</B></I></span> \r
- is a normalisation value chosen so that <span style="font-weight: bold; font-style: italic;"><I><B>Q</B></I></span><span \r
- style="vertical-align: Sub;\r
- font-weight: bold;\r
- font-style: italic;"><I><B>K</B></I></span> = 1 when К is an equilateral \r
- simplex. </p>\r
-\r
-<p class="whs2"> </p>\r
-\r
-<p>The value of <span style="font-weight: bold; font-style: italic;"><I><B>Q</B></I></span><span \r
- style="vertical-align: Sub;\r
- font-weight: bold;\r
- font-style: italic;"><I><B>K</B></I></span> varies between 1 and +oo and the \r
- closer it is to 1, the better the element К is. </p>\r
-\r
-<ul type="disc" class="whs4">\r
- \r
- <li class=kadov-p><p>The <span style="font-weight: bold;"><B>Aspect Ratio</B></span> \r
- of a <span style="font-weight: bold;"><B>triangle</B></span> 2D element consisting \r
- of 3 nodes is calculated by the formula:</p></li>\r
-</ul>\r
-\r
-<p> </p>\r
-\r
-<p class="whs2"><img src="../pics/image21.gif" x-maintain-ratio="TRUE" width="158px" height="110px" border="0" class="img_whs5"></p>\r
-\r
-<p class="whs2"><img src="../pics/image23.gif" x-maintain-ratio="TRUE" width="120px" height="48px" border="0" class="img_whs6"> ,</p>\r
-\r
-<p class="whs2"> </p>\r
-\r
-<p class="whs2">where <span style="font-weight: bold; font-style: italic;"><I><B>р</B></I></span><span \r
- style="vertical-align: Sub;\r
- font-weight: bold;\r
- font-style: italic;"><I><B>к</B></I></span> is the half perimeter of the \r
- element K and <span style="font-weight: bold; font-style: italic;"><I><B>S</B></I></span><span \r
- style="vertical-align: Sub;\r
- font-weight: bold;\r
- font-style: italic;"><I><B>K</B></I></span> is its surface.</p>\r
-\r
-<p class="whs2"> </p>\r
-\r
-<p class="whs2"><img src="../pics/image27.gif" x-maintain-ratio="TRUE" width="234px" height="96px" border="0" class="img_whs7"></p>\r
-\r
-<p class="whs8"> </p>\r
-\r
-<ul type="disc" class="whs4">\r
- \r
- <li class=kadov-p><p class="whs8">The <span style="font-weight: bold;"><B>Aspect \r
- Ratio</B></span> of a <span style="font-weight: bold;"><B>quadrangle</B></span> 2D \r
- element consisting of 4 nodes is the worst (i.e. the greatest) value from \r
- all triangles which can be built taking three nodes of the quadrangle. \r
- There are four triangles to consider: </p></li>\r
-</ul>\r
-\r
-<p class="whs9"><img src="../pics/image138.gif" x-maintain-ratio="TRUE" width="622px" height="412px" border="0" class="img_whs10"></p>\r
-\r
-<p class="whs9">Note, that the Aspect Ratio criterion is \r
- applicable to 2D mesh elements only. For 3D elements we use the <a href="../aspect_ratio_3d.htm">Aspect \r
- Ratio 3D</a> criterion. </p>\r
-\r
-<p class="whs11"> </p>\r
-\r
-<p class=TODO>To apply the Aspect Ratio quality criterion to your mesh:</p>\r
-\r
-<p class=TODO> </p>\r
-\r
-<p class="whs2">1. Display your mesh in the viewer.</p>\r
-\r
-<p class="whs2"> </p>\r
-\r
-<p class="whs2">2. Choose <span style="font-weight: bold;"><B>Controls \r
- > Aspect Ratio </B></span>or click <img src="../image37.gif" width="25px" height="24px" border="0" class="img_whs12"> button in the toolbar. \r
- Your mesh will be displayed in the viewer with its elements colored according \r
- to the applied mesh quality control criterion:</p>\r
-\r
-<p class="whs2"> </p>\r
-\r
-<p class="whs2"><img src="../image94.jpg" width="439px" height="313px" border="0" class="img_whs13"></p>\r
-\r
-<p class="whs2"> </p>\r
-\r
-<p class="whs8"><span style="font-weight: bold;"><B>See Also</B></span> \r
- a sample TUI Script of an <a href="../quality_controls.htm#bookmark8">Aspect \r
- Ratio quality control</a> operation. </p>\r
-\r
-<p> </p>\r
-\r
-<script type="text/javascript" language="javascript1.2">\r
-<!--\r
-if (window.writeIntopicBar)\r
- writeIntopicBar(0);\r
-//-->\r
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-</html>\r
+<!doctype HTML public "-//W3C//DTD HTML 4.0 Frameset//EN">
+
+<html>
+
+<head>
+<title>Aspect Ratio</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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+<!--
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+img_whs3 { border:none; width:120px; height:56px; border-style:none; }
+ul.whs4 { list-style:disc; }
+img_whs5 { border:none; width:158px; height:110px; float:none; border-style:none; }
+img_whs6 { border:none; width:120px; height:48px; float:none; border-style:none; }
+img_whs7 { border:none; width:234px; height:96px; float:none; border-style:none; }
+p.whs8 { margin-left:0px; }
+p.whs9 { margin-left:36px; }
+img_whs10 { border:none; width:622px; height:412px; float:none; border-style:none; }
+p.whs11 { margin-left:80px; }
+img_whs12 { border:none; width:25px; height:24px; border-style:none; }
+img_whs13 { border:none; width:439px; height:313px; border-style:none; }
+-->
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+if ((navigator.appName == "Netscape") && (parseInt(navigator.appVersion) == 4))
+{
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+ origHeight = innerHeight;
+ onresize = reDo;
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+//-->
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+{
+ if (window.setRelStartPage)
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+ document.location.reload();
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+<body><script type="text/javascript" language="javascript1.2">
+<!--
+if (window.writeIntopicBar)
+ writeIntopicBar(4);
+//-->
+</script>
+<h1>Aspect Ratio</h1>
+
+<p><img src="../i_blue.jpg" x-maintain-ratio="TRUE" width="30px" height="30px" border="0" class="img_whs1"> The <span style="font-weight: bold;"><B>Aspect Ratio</B></span>
+ quality criterion for mesh elements reveals the degree of conformity of
+ a mesh element to the regular element of its type (with all edges having
+ the same length). The
+ criterion can be defined as </p>
+
+<p class="whs2"><img src="../image142.gif" width="120px" height="56px" border="0" class="img_whs3">where <span style="font-weight: bold; font-style: italic;"><I><B>К</B></I></span>
+ is the considered element of the mesh, <span style="font-weight: bold; font-style: italic;"><I><B>h</B></I></span><span
+ style="vertical-align: Sub;
+ font-weight: bold;
+ font-style: italic;"><I><B>max</B></I></span> is the diameter of the element
+ К (i.e. the length of the longest edge), <span style="font-weight: bold; font-style: italic;"><I><B>р</B></I></span><span
+ style="vertical-align: Sub;
+ font-weight: bold;
+ font-style: italic;"><I><B>к</B></I></span> is the radius of the sphere
+ inscribed in the element K, and <span style="font-weight: bold; font-style: italic;"><I><B>a</B></I></span>
+ is a normalisation value chosen so that <span style="font-weight: bold; font-style: italic;"><I><B>Q</B></I></span><span
+ style="vertical-align: Sub;
+ font-weight: bold;
+ font-style: italic;"><I><B>K</B></I></span> = 1 when К is an equilateral
+ simplex. </p>
+
+<p class="whs2"> </p>
+
+<p>The value of <span style="font-weight: bold; font-style: italic;"><I><B>Q</B></I></span><span
+ style="vertical-align: Sub;
+ font-weight: bold;
+ font-style: italic;"><I><B>K</B></I></span> varies between 1 and +oo and the
+ closer it is to 1, the better the element К is. </p>
+
+<ul type="disc" class="whs4">
+
+ <li class=kadov-p><p>The <span style="font-weight: bold;"><B>Aspect Ratio</B></span>
+ of a <span style="font-weight: bold;"><B>triangle</B></span> 2D element consisting
+ of 3 nodes is calculated by the formula:</p></li>
+</ul>
+
+<p> </p>
+
+<p class="whs2"><img src="../pics/image21.gif" x-maintain-ratio="TRUE" width="158px" height="110px" border="0" class="img_whs5"></p>
+
+<p class="whs2"><img src="../pics/image23.gif" x-maintain-ratio="TRUE" width="120px" height="48px" border="0" class="img_whs6"> ,</p>
+
+<p class="whs2"> </p>
+
+<p class="whs2">where <span style="font-weight: bold; font-style: italic;"><I><B>р</B></I></span><span
+ style="vertical-align: Sub;
+ font-weight: bold;
+ font-style: italic;"><I><B>к</B></I></span> is the half perimeter of the
+ element K and <span style="font-weight: bold; font-style: italic;"><I><B>S</B></I></span><span
+ style="vertical-align: Sub;
+ font-weight: bold;
+ font-style: italic;"><I><B>K</B></I></span> is its surface.</p>
+
+<p class="whs2"> </p>
+
+<p class="whs2"><img src="../pics/image27.gif" x-maintain-ratio="TRUE" width="234px" height="96px" border="0" class="img_whs7"></p>
+
+<p class="whs8"> </p>
+
+<ul type="disc" class="whs4">
+
+ <li class=kadov-p><p class="whs8">The <span style="font-weight: bold;"><B>Aspect
+ Ratio</B></span> of a <span style="font-weight: bold;"><B>quadrangle</B></span> 2D
+ element consisting of 4 nodes is the worst (i.e. the greatest) value from
+ all triangles which can be built taking three nodes of the quadrangle.
+ There are four triangles to consider: </p></li>
+</ul>
+
+<p class="whs9"><img src="../pics/image138.gif" x-maintain-ratio="TRUE" width="622px" height="412px" border="0" class="img_whs10"></p>
+
+<p class="whs9">Note, that the Aspect Ratio criterion is
+ applicable to 2D mesh elements only. For 3D elements we use the <a href="../aspect_ratio_3d.htm">Aspect
+ Ratio 3D</a> criterion. </p>
+
+<p class="whs11"> </p>
+
+<p class=TODO>To apply the Aspect Ratio quality criterion to your mesh:</p>
+
+<p class=TODO> </p>
+
+<p class="whs2">1. Display your mesh in the viewer.</p>
+
+<p class="whs2"> </p>
+
+<p class="whs2">2. Choose <span style="font-weight: bold;"><B>Controls
+ > Aspect Ratio </B></span>or click <img src="../image37.gif" width="25px" height="24px" border="0" class="img_whs12"> button in the toolbar.
+ Your mesh will be displayed in the viewer with its elements colored according
+ to the applied mesh quality control criterion:</p>
+
+<p class="whs2"> </p>
+
+<p class="whs2"><img src="../image94.jpg" width="439px" height="313px" border="0" class="img_whs13"></p>
+
+<p class="whs2"> </p>
+
+<p class="whs8"><span style="font-weight: bold;"><B>See Also</B></span>
+ a sample TUI Script of an <a href="../quality_controls.htm#bookmark8">Aspect
+ Ratio quality control</a> operation. </p>
+
+<p> </p>
+
+<script type="text/javascript" language="javascript1.2">
+<!--
+if (window.writeIntopicBar)
+ writeIntopicBar(0);
+//-->
+</script>
+</body>
+</html>
