1 <!doctype HTML public "-//W3C//DTD HTML 4.0 Frameset//EN">
6 <title>Aspect ratio 3D</title>
7 <meta http-equiv="content-type" content="text/html; charset=windows-1252">
8 <meta name="generator" content="RoboHelp by eHelp Corporation www.ehelp.com">
9 <link rel="stylesheet" href="default_ns.css"><script type="text/javascript" language="JavaScript" title="WebHelpSplitCss">
11 if (navigator.appName !="Netscape")
12 { document.write("<link rel='stylesheet' href='default.css'>");}
15 <style type="text/css">
17 img_whs1 { border:none; width:416px; height:385px; border-style:none; }
18 img_whs2 { border:none; width:30px; height:30px; float:none; border-style:none; }
19 ul.whs3 { list-style:disc; }
20 img_whs4 { border:none; width:258px; height:246px; border-style:none; float:left; }
21 img_whs5 { border:none; width:133px; height:56px; border-style:none; }
22 img_whs6 { border:none; width:425px; height:192px; border-style:none; }
23 img_whs7 { border:none; width:89px; height:32px; border-style:none; }
24 img_whs8 { border:none; width:569px; height:386px; float:none; border-style:none; }
25 p.whs9 { margin-left:40px; }
26 img_whs10 { border:none; width:24px; height:26px; border-style:none; }
27 p.whs11 { margin-left:0px; }
29 </style><script type="text/javascript" language="JavaScript">
31 if ((navigator.appName == "Netscape") && (parseInt(navigator.appVersion) == 4))
33 var strNSS = "<style type='text/css'>";
34 strNSS += "p.whs11 {margin-left:1pt; }";
36 document.write(strNSS);
40 <script type="text/javascript" language="JavaScript" title="WebHelpInlineScript">
43 if (innerWidth != origWidth || innerHeight != origHeight)
46 if ((parseInt(navigator.appVersion) == 4) && (navigator.appName == "Netscape")) {
47 origWidth = innerWidth;
48 origHeight = innerHeight;
54 <style type="text/css">
56 div.WebHelpPopupMenu { position:absolute; left:0px; top:0px; z-index:4; visibility:hidden; }
57 p.WebHelpNavBar { text-align:right; }
59 </style><script type="text/javascript" language="javascript1.2" src="whmsg.js"></script>
60 <script type="text/javascript" language="javascript" src="whver.js"></script>
61 <script type="text/javascript" language="javascript1.2" src="whproxy.js"></script>
62 <script type="text/javascript" language="javascript1.2" src="whutils.js"></script>
63 <script type="text/javascript" language="javascript1.2" src="whtopic.js"></script>
64 <script type="text/javascript" language="javascript1.2">
68 if (window.setRelStartPage)
70 addTocInfo("MESH module\nQuality controls\nAspect ratio 3D");
71 addButton("show",BTN_IMG,"Show","","","","",0,0,"whd_show0.gif","whd_show2.gif","whd_show1.gif");
72 addButton("hide",BTN_IMG,"Hide","","","","",0,0,"whd_hide0.gif","whd_hide2.gif","whd_hide1.gif");
77 if (window.setRelStartPage)
79 setRelStartPage("index.htm");
89 document.location.reload();
93 <body><script type="text/javascript" language="javascript1.2">
95 if (window.writeIntopicBar)
99 <h1>Aspect ratio 3D</h1>
101 <p><img src="image86.jpg" width="416px" height="385px" border="0" class="img_whs1"></p>
105 <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
106 the same parameter as the <a href="files/aspect_ratio.htm">Aspect ratio</a>
107 criterion, but it is applied to 3D mesh elements: tetrahedrons, pentahedrons,
108 hexahedrons, etc. </p>
112 <ul type="disc" class="whs3">
114 <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
115 Ratio</B></span> of a <span style="font-weight: bold;"><B>tetrahedron</B></span>
116 3D element is calculated by the formula:</p></li>
123 <p><img src="image19.gif" width="133px" height="56px" border="0" class="img_whs5">,</p>
127 <p>where <span style="font-weight: bold; font-style: italic;"><I><B>S</B></I></span><span
128 style="font-weight: bold;
130 vertical-align: Sub;"><I><B>K</B></I></span> is the sum of surfaces of the faces
131 of К and <span style="font-weight: bold; font-style: italic;"><I><B>V</B></I></span><span
132 style="vertical-align: Sub;
134 font-style: italic;"><I><B>K</B></I></span> is the volume of К :</p>
138 <p><img src="image18.gif" width="425px" height="192px" border="0" class="img_whs6">T</p>
142 <ul type="disc" class="whs3">
144 <li class=kadov-p><p>Other element types like quadrangle, pentahedron
145 and hexahedron use the following formula:</p></li>
148 <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
149 style="vertical-align: Sub;
151 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
152 style="vertical-align: Sub;
154 font-style: italic;"><I><B>k</B></I></span> for all possible simplexes (of the
155 same dimension as the element) that compose the element.</p>
157 <p>For example, a hexahedron is split in 6 tetrahedrons, the <span style="font-weight: bold;"><B>Aspect
158 ratio 3D</B></span> is calculated for each of them, then the greatest <span
159 style="font-weight: bold; font-style: italic;"><I><B>Q</B></I></span><span style="vertical-align: Sub;
161 font-style: italic;"><I><B>k</B></I></span> is considered to be the <span
162 style="font-weight: bold;"><B>Aspect ratio 3D</B></span>
163 criterion for the whole hexahedron.</p>
165 <p><img src="pics/image139.gif" x-maintain-ratio="TRUE" width="569px" height="386px" border="0" class="img_whs8"></p>
169 <p class=TODO>To apply the Aspect Ratio 3D quality criterion to your mesh:</p>
171 <p class=TODO> </p>
173 <p class="whs9">1. Display your mesh in the viewer.</p>
175 <p class="whs9"> </p>
177 <p class="whs9">2. Choose <span style="font-weight: bold;"><B>Controls
178 > Aspect Ratio 3D </B></span>or click <img src="image144.gif" width="24px" height="26px" border="0" class="img_whs10"> button of the toolbar.
179 Your mesh will be displayed in the viewer with its elements colored according
180 to the applied mesh quality control criterion:</p>
184 <p class="whs11"><span style="font-weight: bold;"><B>See Also</B></span>
185 a sample TUI Script of an <span style="font-weight: bold;"><B><a href="quality_controls.htm#bookmark11">Aspect
186 Ratio 3D</B></span> quality control</a> operation. </p>
196 <script type="text/javascript" language="javascript1.2">
198 if (window.writeIntopicBar)