2005-11-28 14:57:47 +05:00
<!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; }
2006-05-06 14:51:48 +06:00
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; }
2005-11-28 14:57:47 +05:00
-->
< / style > < script type = "text/javascript" language = "JavaScript" >
<!--
if ((navigator.appName == "Netscape") & & (parseInt(navigator.appVersion) == 4))
{
var strNSS = "< style type = 'text/css' > " ;
2006-05-06 14:51:48 +06:00
strNSS += "p.whs11 {margin-left:1pt; }";
2005-11-28 14:57:47 +05:00
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" >
<!--
div.WebHelpPopupMenu { position:absolute; left:0px; top:0px; z-index:4; visibility:hidden; }
-->
< / 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 >
< / head >
< body > < script type = "text/javascript" language = "javascript1.2" >
<!--
if (window.gbWhTopic)
{
if (window.addTocInfo)
{
addTocInfo("MESH module\nQuality controls\nAspect ratio 3D");
addButton("show",BTN_TEXT,"Show","","","","",0,0,"","","");
}
if (window.writeBtnStyle)
writeBtnStyle();
if (window.writeIntopicBar)
writeIntopicBar(1);
if (window.setRelStartPage)
{
setRelStartPage("smesh.htm");
autoSync(1);
sendSyncInfo();
sendAveInfoOut();
}
}
else
if (window.gbIE4)
document.location.reload();
//-->
< / script >
< h1 > Aspect ratio 3D< / h1 >
< p > < img src = "image86.jpg" width = "416px" height = "385px" border = "0" class = "img_whs1" > < / p >
< p > < / p >
2006-05-06 14:51:48 +06:00
< 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 >
2005-11-28 14:57:47 +05:00
2006-05-06 14:51:48 +06:00
< p > < / p >
2005-11-28 14:57:47 +05:00
2006-05-06 14:51:48 +06:00
< 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 >
2005-11-28 14:57:47 +05:00
2006-05-06 14:51:48 +06:00
< p > < / p >
2005-11-28 14:57:47 +05:00
2006-05-06 14:51:48 +06:00
< p > < / p >
2005-11-28 14:57:47 +05:00
2006-05-06 14:51:48 +06:00
< p > < img src = "image19.gif" width = "133px" height = "56px" border = "0" class = "img_whs5" > ,< / p >
2005-11-28 14:57:47 +05:00
2006-05-06 14:51:48 +06:00
< p > < / p >
2005-11-28 14:57:47 +05:00
2006-05-06 14:51:48 +06:00
< 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 >
2005-11-28 14:57:47 +05:00
< p > < / p >
2006-05-06 14:51:48 +06:00
< p > < img src = "image18.gif" width = "425px" height = "192px" border = "0" class = "img_whs6" > T< / p >
2005-11-28 14:57:47 +05:00
2006-05-06 14:51:48 +06:00
< p > < / p >
2005-11-28 14:57:47 +05:00
2006-05-06 14:51:48 +06:00
< 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 >
2005-11-28 14:57:47 +05:00
2006-05-06 14:51:48 +06:00
< p > < / p >
2005-12-21 13:30:31 +05:00
2006-05-06 14:51:48 +06:00
< p class = TODO > To apply the Aspect Ratio 3D quality criterion to your mesh:< / p >
2005-12-21 13:30:31 +05:00
2006-05-06 14:51:48 +06:00
< p class = TODO > < / p >
2005-12-21 13:30:31 +05:00
2006-05-06 14:51:48 +06:00
< p class = "whs9" > 1. Display your mesh in the viewer.< / p >
2005-12-21 13:30:31 +05:00
2006-05-06 14:51:48 +06:00
< 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 >
2005-12-21 13:30:31 +05:00
2005-11-28 14:57:47 +05:00
< p > < / p >
2006-05-06 14:51:48 +06:00
< 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 >
2005-11-28 14:57:47 +05:00
< p > < / p >
< p > < / p >
< p > < / p >
< p > < / p >
< script type = "text/javascript" language = "javascript1.2" >
<!--
if (window.writeIntopicBar)
writeIntopicBar(0);
//-->
< / script >
< / body >
< / html >
