<!doctype HTML public "-//W3C//DTD HTML 4.0 Frameset//EN"> <html> <head> <title>Aspect ratio 3D</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:416px; height:385px; border-style:none; } img_whs2 { border:none; width:30px; height:30px; float:none; border-style:none; } ul.whs3 { list-style:disc; } img_whs4 { border:none; width:258px; height:246px; border-style:none; float:left; } img_whs5 { border:none; width:133px; height:56px; border-style:none; } img_whs6 { border:none; width:425px; height:192px; border-style:none; } img_whs7 { border:none; width:89px; height:32px; border-style:none; } img_whs8 { border:none; width:569px; height:386px; float:none; border-style:none; } p.whs9 { margin-left:40px; } img_whs10 { border:none; width:24px; height:26px; border-style:none; } p.whs11 { margin-left:0px; } --> </style><script type="text/javascript" language="JavaScript"> <!-- if ((navigator.appName == "Netscape") && (parseInt(navigator.appVersion) == 4)) { var strNSS = "<style type='text/css'>"; strNSS += "p.whs11 {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 3D"); 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 3D</h1> <p><img src="image86.jpg" width="416px" height="385px" border="0" class="img_whs1"></p> <p> </p> <p><img src="i_blue.jpg" x-maintain-ratio="TRUE" width="30px" height="30px" border="0" class="img_whs2"> The Aspect Ratio 3D mesh quality criterion calculates the same parameter as the <a href="files/aspect_ratio.htm">Aspect ratio</a> criterion, but it is applied to 3D mesh elements: tetrahedrons, pentahedrons, hexahedrons, etc. </p> <p> </p> <ul type="disc" class="whs3"> <li class=kadov-p><p><img src="image20.gif" width="258px" height="246px" align="left" border="0" class="img_whs4">The <span style="font-weight: bold;"><B>Aspect Ratio</B></span> of a <span style="font-weight: bold;"><B>tetrahedron</B></span> 3D element is calculated by the formula:</p></li> </ul> <p> </p> <p> </p> <p><img src="image19.gif" width="133px" height="56px" border="0" class="img_whs5">,</p> <p> </p> <p>where <span style="font-weight: bold; font-style: italic;"><I><B>S</B></I></span><span style="font-weight: bold; font-style: italic; vertical-align: Sub;"><I><B>K</B></I></span> is the sum of surfaces of the faces of К and <span style="font-weight: bold; font-style: italic;"><I><B>V</B></I></span><span style="vertical-align: Sub; font-weight: bold; font-style: italic;"><I><B>K</B></I></span> is the volume of К :</p> <p> </p> <p><img src="image18.gif" width="425px" height="192px" border="0" class="img_whs6">T</p> <p> </p> <ul type="disc" class="whs3"> <li class=kadov-p><p>Other element types like quadrangle, pentahedron and hexahedron use the following formula:</p></li> </ul> <p><img src="image30.gif" width="89px" height="32px" border="0" class="img_whs7"> , where <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>i</B></I></span> represents 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> for all possible simplexes (of the same dimension as the element) that compose the element.</p> <p>For example, a hexahedron is split in 6 tetrahedrons, the <span style="font-weight: bold;"><B>Aspect ratio 3D</B></span> is calculated for each of them, then the greatest <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> is considered to be the <span style="font-weight: bold;"><B>Aspect ratio 3D</B></span> criterion for the whole hexahedron.</p> <p><img src="pics/image139.gif" x-maintain-ratio="TRUE" width="569px" height="386px" border="0" class="img_whs8"></p> <p> </p> <p class=TODO>To apply the Aspect Ratio 3D quality criterion to your mesh:</p> <p class=TODO> </p> <p class="whs9">1. Display your mesh in the viewer.</p> <p class="whs9"> </p> <p class="whs9">2. Choose <span style="font-weight: bold;"><B>Controls > Aspect Ratio 3D </B></span>or click <img src="image144.gif" width="24px" height="26px" border="0" class="img_whs10"> button of the toolbar. Your mesh will be displayed in the viewer with its elements colored according to the applied mesh quality control criterion:</p> <p> </p> <p class="whs11"><span style="font-weight: bold;"><B>See Also</B></span> a sample TUI Script of an <span style="font-weight: bold;"><B><a href="quality_controls.htm#bookmark11">Aspect Ratio 3D</B></span> quality control</a> operation. </p> <p> </p> <p> </p> <p> </p> <p> </p> <script type="text/javascript" language="javascript1.2"> <!-- if (window.writeIntopicBar) writeIntopicBar(0); //--> </script> </body> </html>