doc/salome/gui/SMESH/aspect_ratio_3d.htm

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  81 <h1>Aspect ratio 3D</h1>\r
  82 \r
  83 <p><img src="image86.jpg" width="416px" height="385px" border="0" class="img_whs1"></p>\r
  84 \r
  85 <p>&nbsp;</p>\r
  86 \r
  87 <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 \r
  88  criterion, however, it is also applied to 3D mesh elements: tetrahedrons, \r
  89  pentahedrons, hexahedrons, etc. &nbsp;</p>\r
  90 \r
  91 <p>There are 2 simple formulas to evaluate directly the value of quality \r
  92  Qk for simplex in 2D and 3D. The formulas are :</p>\r
  93 \r
  94 <p>\95 For triangle :</p>\r
  95 \r
  96 <p>&nbsp;</p>\r
  97 \r
  98 <p><img src="image21.gif" width="158px" height="110px" border="0" class="img_whs3"></p>\r
  99 \r
 100 <p><img src="image23.gif" width="120px" height="48px" border="0" class="img_whs4"></p>\r
 101 \r
 102 <p>where :</p>\r
 103 \r
 104 <p>&nbsp;</p>\r
 105 \r
 106 <p><img src="image27.gif" width="234px" height="96px" border="0" class="img_whs5"></p>\r
 107 \r
 108 <p>&nbsp;</p>\r
 109 \r
 110 <p>&nbsp;</p>\r
 111 \r
 112 <p>\95 For tetrahedron :</p>\r
 113 \r
 114 <p>&nbsp;<img src="image20.gif" width="258px" height="246px" border="0" class="img_whs6"></p>\r
 115 \r
 116 <p>&nbsp;<img src="image19.gif" width="133px" height="56px" border="0" class="img_whs7"></p>\r
 117 \r
 118 <p>where :</p>\r
 119 \r
 120 <p><img src="image18.gif" width="425px" height="192px" border="0" class="img_whs8"> </p>\r
 121 \r
 122 <p>To calculate Sk , it is needed to sum the area of each of the 3 faces \r
 123  with the formula given with the triangle.</p>\r
 124 \r
 125 <p>&nbsp;</p>\r
 126 \r
 127 <p>For the other types of element like quadrangle, pentahedron and hexahedron \r
 128  the formula is the following :</p>\r
 129 \r
 130 <p><img src="image30.gif" width="89px" height="32px" border="0" class="img_whs9"> </p>\r
 131 \r
 132 <p>Where Qi are the quality of all the possible simplex (of same dimension \r
 133  as the element) that compose the element.</p>\r
 134 \r
 135 <p>&nbsp;</p>\r
 136 \r
 137 <p>&nbsp;</p>\r
 138 \r
 139 <p>&nbsp;</p>\r
 140 \r
 141 <p>&nbsp;</p>\r
 142 \r
 143 <p>&nbsp;</p>\r
 144 \r
 145 <p>&nbsp;</p>\r
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