2004-06-18 14:55:35 +06:00
<!doctype HTML public "-//W3C//DTD HTML 4.0 Frameset//EN">
< html >
< head >
< title > Aspect Ratio< / title >
2005-11-28 14:57:47 +05:00
< 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" >
2004-06-18 14:55:35 +06:00
<!--
if (navigator.appName !="Netscape")
{ document.write("< link rel = 'stylesheet' href = '../default.css' > ");}
//-->
< / script >
< style type = "text/css" >
<!--
2005-11-28 14:57:47 +05:00
img_whs1 { border:none; width:30px; height:30px; float:none; border-style:none; }
2006-05-06 14:51:48 +06:00
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; }
2004-06-18 14:55:35 +06:00
-->
2005-11-28 14:57:47 +05:00
< / style > < script type = "text/javascript" language = "JavaScript" >
2004-06-18 14:55:35 +06:00
<!--
if ((navigator.appName == "Netscape") & & (parseInt(navigator.appVersion) == 4))
{
var strNSS = "< style type = 'text/css' > " ;
2006-05-06 14:51:48 +06:00
strNSS += "p.whs8 {margin-left:1pt; }";
2004-06-18 14:55:35 +06:00
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" >
<!--
2005-11-28 14:57:47 +05:00
div.WebHelpPopupMenu { position:absolute; left:0px; top:0px; z-index:4; visibility:hidden; }
2006-06-01 17:39:17 +06:00
p.WebHelpNavBar { text-align:right; }
2004-06-18 14:55:35 +06:00
-->
2005-11-28 14:57:47 +05:00
< / style > < script type = "text/javascript" language = "javascript1.2" src = "../whmsg.js" > < / script >
2004-06-18 14:55:35 +06:00
< 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 >
2006-06-01 17:39:17 +06:00
< script type = "text/javascript" language = "javascript1.2" >
2004-06-18 14:55:35 +06:00
<!--
if (window.gbWhTopic)
{
2006-06-01 17:39:17 +06:00
if (window.setRelStartPage)
2004-06-18 14:55:35 +06:00
{
2005-11-28 14:57:47 +05:00
addTocInfo("MESH module\nQuality controls\nAspect ratio");
2006-06-01 17:39:17 +06:00
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");
2004-06-18 14:55:35 +06:00
}
if (window.setRelStartPage)
{
2006-06-01 17:39:17 +06:00
setRelStartPage("../index.htm");
2004-06-18 14:55:35 +06:00
2005-11-28 14:57:47 +05:00
autoSync(1);
2004-06-18 14:55:35 +06:00
sendSyncInfo();
sendAveInfoOut();
}
2006-06-01 17:39:17 +06:00
2004-06-18 14:55:35 +06:00
}
else
2005-11-28 14:57:47 +05:00
if (window.gbIE4)
document.location.reload();
2004-06-18 14:55:35 +06:00
//-->
< / script >
2006-06-01 17:39:17 +06:00
< / head >
< body > < script type = "text/javascript" language = "javascript1.2" >
<!--
if (window.writeIntopicBar)
writeIntopicBar(4);
//-->
< / script >
2004-06-18 14:55:35 +06:00
< 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 >
2006-05-06 14:51:48 +06:00
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 >
2004-06-18 14:55:35 +06:00
< p > < / p >
2006-05-06 14:51:48 +06:00
< p class = "whs2" > < img src = "../pics/image21.gif" x-maintain-ratio = "TRUE" width = "158px" height = "110px" border = "0" class = "img_whs5" > < / p >
2005-12-12 20:29:54 +05:00
2006-05-06 14:51:48 +06:00
< p class = "whs2" > < img src = "../pics/image23.gif" x-maintain-ratio = "TRUE" width = "120px" height = "48px" border = "0" class = "img_whs6" > ,< / p >
2005-12-12 20:29:54 +05:00
2006-05-06 14:51:48 +06:00
< p class = "whs2" > < / p >
2005-12-12 20:29:54 +05:00
2006-05-06 14:51:48 +06:00
< 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 >
2004-06-18 14:55:35 +06:00
2006-05-06 14:51:48 +06:00
< p class = "whs2" > < / p >
2004-06-18 14:55:35 +06:00
2006-05-06 14:51:48 +06:00
< p class = "whs2" > < img src = "../pics/image27.gif" x-maintain-ratio = "TRUE" width = "234px" height = "96px" border = "0" class = "img_whs7" > < / p >
2004-06-18 14:55:35 +06:00
2006-05-06 14:51:48 +06:00
< p class = "whs8" > < / p >
2004-06-18 14:55:35 +06:00
2006-05-06 14:51:48 +06:00
< 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 >
2004-06-18 14:55:35 +06:00
2006-05-06 14:51:48 +06:00
< p class = "whs9" > < img src = "../pics/image138.gif" x-maintain-ratio = "TRUE" width = "622px" height = "412px" border = "0" class = "img_whs10" > < / p >
2005-12-12 20:29:54 +05:00
2006-05-06 14:51:48 +06:00
< 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 >
2004-06-18 14:55:35 +06:00
2006-05-06 14:51:48 +06:00
< p class = "whs11" > < / p >
2004-06-18 14:55:35 +06:00
< p class = TODO > To apply the Aspect Ratio quality criterion to your mesh:< / p >
< p class = TODO > < / p >
2006-05-06 14:51:48 +06:00
< p class = "whs2" > 1. Display your mesh in the viewer.< / p >
2004-06-18 14:55:35 +06:00
2006-05-06 14:51:48 +06:00
< p class = "whs2" > < / p >
2004-06-18 14:55:35 +06:00
2006-05-06 14:51:48 +06:00
< 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.
2005-11-28 14:57:47 +05:00
Your mesh will be displayed in the viewer with its elements colored according
to the applied mesh quality control criterion:< / p >
2004-06-18 14:55:35 +06:00
2006-05-06 14:51:48 +06:00
< p class = "whs2" > < / p >
2004-06-18 14:55:35 +06:00
2006-05-06 14:51:48 +06:00
< p class = "whs2" > < img src = "../image94.jpg" width = "439px" height = "313px" border = "0" class = "img_whs13" > < / p >
2005-11-28 14:57:47 +05:00
2006-05-06 14:51:48 +06:00
< p class = "whs2" > < / p >
2005-11-28 14:57:47 +05:00
2006-05-06 14:51:48 +06:00
< p class = "whs8" > < span style = "font-weight: bold;" > < B > See Also< / B > < / span >
2005-11-28 14:57:47 +05:00
a sample TUI Script of an < a href = "../quality_controls.htm#bookmark8" > Aspect
Ratio quality control< / a > operation. < / p >
< p > < / p >
2004-06-18 14:55:35 +06:00
< script type = "text/javascript" language = "javascript1.2" >
<!--
if (window.writeIntopicBar)
writeIntopicBar(0);
//-->
< / script >
< / body >
< / html >
