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<title>Aspect ratio 3D</title>
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<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">This mesh quality criterion resembles to the Aspect ratio
criterion, however, it is also applied to 3D mesh elements: tetrahedrons,
pentahedrons, hexahedrons, etc. </p>
<p>There are 2 simple formulas to evaluate directly the value of quality
Qk for simplex in 2D and 3D. The formulas are :</p>
<p>� For triangle :</p>
<p> </p>
<p><img src="image21.gif" width="158px" height="110px" border="0" class="img_whs3"></p>
<p><img src="image23.gif" width="120px" height="48px" border="0" class="img_whs4"></p>
<p>where :</p>
<p> </p>
<p><img src="image27.gif" width="234px" height="96px" border="0" class="img_whs5"></p>
<p> </p>
<p> </p>
<p>� For tetrahedron :</p>
<p> <img src="image20.gif" width="258px" height="246px" border="0" class="img_whs6"></p>
<p> <img src="image19.gif" width="133px" height="56px" border="0" class="img_whs7"></p>
<p>where :</p>
<p><img src="image18.gif" width="425px" height="192px" border="0" class="img_whs8"> </p>
<p>To calculate Sk , it is needed to sum the area of each of the 3 faces
with the formula given with the triangle.</p>
<p> </p>
<p>For the other types of element like quadrangle, pentahedron and hexahedron
the formula is the following :</p>
<p><img src="image30.gif" width="89px" height="32px" border="0" class="img_whs9"> </p>
<p>Where Qi are the quality of all the possible simplex (of same dimension
as the element) that compose the element.</p>
<p> </p>
<p> </p>
<p> </p>
<p> </p>
<p> </p>
<p> </p>
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