<!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"> <!-- 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: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; } --> </style><script type="text/javascript" language="JavaScript"> <!-- if ((navigator.appName == "Netscape") && (parseInt(navigator.appVersion) == 4)) { var strNSS = "<style type='text/css'>"; strNSS += "p.whs8 {margin-left:1pt; }"; strNSS +="</style>"; document.write(strNSS); } //--> </script> <script type="text/javascript" language="JavaScript" title="WebHelpInlineScript"> <!-- function reDo() { if (innerWidth != origWidth || innerHeight != origHeight) location.reload(); } if ((parseInt(navigator.appVersion) == 4) && (navigator.appName == "Netscape")) { origWidth = innerWidth; origHeight = innerHeight; onresize = reDo; } onerror = null; //--> </script> <style type="text/css"> <!-- div.WebHelpPopupMenu { position:absolute; left:0px; top:0px; z-index:4; visibility:hidden; } p.WebHelpNavBar { text-align:right; } --> </style><script type="text/javascript" language="javascript1.2" src="../whmsg.js"></script> <script type="text/javascript" language="javascript" src="../whver.js"></script> <script type="text/javascript" language="javascript1.2" src="../whproxy.js"></script> <script type="text/javascript" language="javascript1.2" src="../whutils.js"></script> <script type="text/javascript" language="javascript1.2" src="../whtopic.js"></script> <script type="text/javascript" language="javascript1.2"> <!-- if (window.gbWhTopic) { if (window.setRelStartPage) { addTocInfo("MESH module\nQuality controls\nAspect ratio"); 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"); } if (window.setRelStartPage) { setRelStartPage("../index.htm"); autoSync(1); sendSyncInfo(); sendAveInfoOut(); } } else if (window.gbIE4) document.location.reload(); //--> </script> </head> <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>