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204 lines
6.9 KiB
HTML
Executable File
204 lines
6.9 KiB
HTML
Executable File
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<h1>Aspect ratio 3D</h1>
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<p><img src="image86.jpg" width="416px" height="385px" border="0" class="img_whs1"></p>
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<p> </p>
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<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
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the same parameter as the <a href="files/aspect_ratio.htm">Aspect ratio</a>
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criterion, but it is applied to 3D mesh elements: tetrahedrons, pentahedrons,
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hexahedrons, etc. </p>
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<p> </p>
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<ul type="disc" class="whs3">
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<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
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Ratio</B></span> of a <span style="font-weight: bold;"><B>tetrahedron</B></span>
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3D element is calculated by the formula:</p></li>
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</ul>
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<p> </p>
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<p> </p>
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<p><img src="image19.gif" width="133px" height="56px" border="0" class="img_whs5">,</p>
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<p> </p>
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<p>where <span style="font-weight: bold; font-style: italic;"><I><B>S</B></I></span><span
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style="font-weight: bold;
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font-style: italic;
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vertical-align: Sub;"><I><B>K</B></I></span> is the sum of surfaces of the faces
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of К and <span style="font-weight: bold; font-style: italic;"><I><B>V</B></I></span><span
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style="vertical-align: Sub;
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font-weight: bold;
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font-style: italic;"><I><B>K</B></I></span> is the volume of К :</p>
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<p> </p>
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<p><img src="image18.gif" width="425px" height="192px" border="0" class="img_whs6">T</p>
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<p> </p>
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<ul type="disc" class="whs3">
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<li class=kadov-p><p>Other element types like quadrangle, pentahedron
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and hexahedron use the following formula:</p></li>
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</ul>
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<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
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style="vertical-align: Sub;
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font-weight: bold;
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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
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style="vertical-align: Sub;
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font-weight: bold;
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font-style: italic;"><I><B>k</B></I></span> for all possible simplexes (of the
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same dimension as the element) that compose the element.</p>
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<p>For example, a hexahedron is split in 6 tetrahedrons, the <span style="font-weight: bold;"><B>Aspect
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ratio 3D</B></span> is calculated for each of them, then the greatest <span
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style="font-weight: bold; font-style: italic;"><I><B>Q</B></I></span><span style="vertical-align: Sub;
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font-weight: bold;
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font-style: italic;"><I><B>k</B></I></span> is considered to be the <span
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style="font-weight: bold;"><B>Aspect ratio 3D</B></span>
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criterion for the whole hexahedron.</p>
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<p><img src="pics/image139.gif" x-maintain-ratio="TRUE" width="569px" height="386px" border="0" class="img_whs8"></p>
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<p> </p>
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<p class=TODO>To apply the Aspect Ratio 3D quality criterion to your mesh:</p>
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<p class=TODO> </p>
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<p class="whs9">1. Display your mesh in the viewer.</p>
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<p class="whs9"> </p>
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<p class="whs9">2. Choose <span style="font-weight: bold;"><B>Controls
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> Aspect Ratio 3D </B></span>or click <img src="image144.gif" width="24px" height="26px" border="0" class="img_whs10"> button of the toolbar.
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Your mesh will be displayed in the viewer with its elements colored according
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to the applied mesh quality control criterion:</p>
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<p> </p>
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<p class="whs11"><span style="font-weight: bold;"><B>See Also</B></span>
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a sample TUI Script of an <span style="font-weight: bold;"><B><a href="quality_controls.htm#bookmark11">Aspect
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Ratio 3D</B></span> quality control</a> operation. </p>
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<p> </p>
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<p> </p>
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<p> </p>
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<p> </p>
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