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169 lines
5.1 KiB
HTML
169 lines
5.1 KiB
HTML
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<!doctype HTML public "-//W3C//DTD HTML 4.0 Frameset//EN">
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<html>
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<head>
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<title>Aspect ratio 3D</title>
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<meta http-equiv="content-type" content="text/html; charset=windows-1252">
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<meta name="generator" content="RoboHelp by eHelp Corporation www.ehelp.com">
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<link rel="stylesheet" href="default_ns.css"><script type="text/javascript" language="JavaScript" title="WebHelpSplitCss">
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</script>
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<style type="text/css">
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<!--
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img_whs1 { border:none; width:416px; height:385px; border-style:none; }
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img_whs2 { border:none; width:30px; height:30px; float:none; border-style:none; }
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if ((parseInt(navigator.appVersion) == 4) && (navigator.appName == "Netscape")) {
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onerror = null;
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<style type="text/css">
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div.WebHelpPopupMenu { position:absolute; left:0px; top:0px; z-index:4; visibility:hidden; }
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-->
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</style><script type="text/javascript" language="javascript1.2" src="whmsg.js"></script>
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<script type="text/javascript" language="javascript" src="whver.js"></script>
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<script type="text/javascript" language="javascript1.2" src="whproxy.js"></script>
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<script type="text/javascript" language="javascript1.2" src="whutils.js"></script>
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<script type="text/javascript" language="javascript1.2" src="whtopic.js"></script>
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</head>
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<body><script type="text/javascript" language="javascript1.2">
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if (window.gbWhTopic)
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{
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if (window.addTocInfo)
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{
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addTocInfo("MESH module\nQuality controls\nAspect ratio 3D");
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addButton("show",BTN_TEXT,"Show","","","","",0,0,"","","");
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}
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if (window.writeBtnStyle)
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writeBtnStyle();
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if (window.writeIntopicBar)
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writeIntopicBar(1);
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if (window.setRelStartPage)
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setRelStartPage("smesh.htm");
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else
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if (window.gbIE4)
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document.location.reload();
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//-->
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</script>
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<h1>Aspect ratio 3D</h1>
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<p><img src="image86.jpg" width="416px" height="385px" border="0" class="img_whs1"></p>
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<p> </p>
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<p><img src="i_blue.jpg" x-maintain-ratio="TRUE" width="30px" height="30px" border="0" class="img_whs2">This mesh quality criterion resembles to the Aspect ratio
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criterion, however, it is also applied to 3D mesh elements: tetrahedrons,
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pentahedrons, hexahedrons, etc. </p>
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<p>There are 2 simple formulas to evaluate directly the value of quality
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Qk for simplex in 2D and 3D. The formulas are :</p>
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<p><EFBFBD> For triangle :</p>
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<p> </p>
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<p><img src="image21.gif" width="158px" height="110px" border="0" class="img_whs3"></p>
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<p><img src="image23.gif" width="120px" height="48px" border="0" class="img_whs4"></p>
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<p>where :</p>
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<p> </p>
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<p><img src="image27.gif" width="234px" height="96px" border="0" class="img_whs5"></p>
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<p> </p>
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<p> </p>
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<p><EFBFBD> For tetrahedron :</p>
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<p> <img src="image20.gif" width="258px" height="246px" border="0" class="img_whs6"></p>
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<p> <img src="image19.gif" width="133px" height="56px" border="0" class="img_whs7"></p>
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<p>where :</p>
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<p><img src="image18.gif" width="425px" height="192px" border="0" class="img_whs8"> </p>
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<p>To calculate Sk , it is needed to sum the area of each of the 3 faces
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with the formula given with the triangle.</p>
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<p> </p>
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<p>For the other types of element like quadrangle, pentahedron and hexahedron
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the formula is the following :</p>
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<p><img src="image30.gif" width="89px" height="32px" border="0" class="img_whs9"> </p>
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<p>Where Qi are the quality of all the possible simplex (of same dimension
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as the element) that compose the element.</p>
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<p> </p>
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<p class="whs10"><span style="font-weight: bold;"><B>See Also</B></span>
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a sample TUI Script of an <a href="quality_controls.htm#bookmark11">Aspect
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Ratio quality control</a> operation. </p>
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<p> </p>
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<p> </p>
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<p> </p>
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<p> </p>
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<script type="text/javascript" language="javascript1.2">
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//-->
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</script>
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</body>
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</html>
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