doc/salome/gui/SMESH/files/aspect_ratio.htm

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 101 <h1>Aspect Ratio</h1>
 102
 103 <p><img src="../i_blue.jpg" x-maintain-ratio="TRUE" width="30px" height="30px" border="0" class="img_whs1"> The <span style="font-weight: bold;"><B>Aspect Ratio</B></span>
 104  quality criterion for mesh elements reveals the degree of conformity of
 105  a mesh element to the regular element of its type (with all edges having
 106  the same length). &nbsp;The
 107  criterion can be defined as </p>
 108
 109 <p class="whs2"><img src="../image142.gif" width="120px" height="56px" border="0" class="img_whs3">where <span style="font-weight: bold; font-style: italic;"><I><B>&#1050;</B></I></span>
 110  is the considered element of the mesh, <span style="font-weight: bold; font-style: italic;"><I><B>h</B></I></span><span
 111  style="vertical-align: Sub;
 112                 font-weight: bold;
 113                 font-style: italic;"><I><B>max</B></I></span> is the diameter of the element
 114  &#1050; (i.e. the length of the longest edge), <span style="font-weight: bold; font-style: italic;"><I><B>&#1088;</B></I></span><span
 115  style="vertical-align: Sub;
 116                 font-weight: bold;
 117                 font-style: italic;"><I><B>&#1082;</B></I></span> is the radius of the sphere
 118  inscribed in the element K, and <span style="font-weight: bold; font-style: italic;"><I><B>a</B></I></span>
 119  is a normalisation value chosen so that <span style="font-weight: bold; font-style: italic;"><I><B>Q</B></I></span><span
 120  style="vertical-align: Sub;
 121                 font-weight: bold;
 122                 font-style: italic;"><I><B>K</B></I></span> = 1 when &#1050; is an equilateral
 123  simplex. </p>
 124
 125 <p class="whs2">&nbsp;</p>
 126
 127 <p>The value of <span style="font-weight: bold; font-style: italic;"><I><B>Q</B></I></span><span
 128  style="vertical-align: Sub;
 129                 font-weight: bold;
 130                 font-style: italic;"><I><B>K</B></I></span> varies between 1 and +oo and the
 131  closer it is to 1, the better the element &#1050; is. </p>
 132
 133 <ul type="disc" class="whs4">
 134
 135         <li class=kadov-p><p>The <span style="font-weight: bold;"><B>Aspect Ratio</B></span>
 136  of a <span style="font-weight: bold;"><B>triangle</B></span> 2D element consisting
 137  of 3 nodes is calculated by the formula:</p></li>
 138 </ul>
 139
 140 <p>&nbsp;</p>
 141
 142 <p class="whs2"><img src="../pics/image21.gif" x-maintain-ratio="TRUE" width="158px" height="110px" border="0" class="img_whs5"></p>
 143
 144 <p class="whs2"><img src="../pics/image23.gif" x-maintain-ratio="TRUE" width="120px" height="48px" border="0" class="img_whs6"> ,</p>
 145
 146 <p class="whs2">&nbsp;</p>
 147
 148 <p class="whs2">where <span style="font-weight: bold; font-style: italic;"><I><B>&#1088;</B></I></span><span
 149  style="vertical-align: Sub;
 150                 font-weight: bold;
 151                 font-style: italic;"><I><B>&#1082;</B></I></span> is the half perimeter of the
 152  element K and <span style="font-weight: bold; font-style: italic;"><I><B>S</B></I></span><span
 153  style="vertical-align: Sub;
 154                 font-weight: bold;
 155                 font-style: italic;"><I><B>K</B></I></span> is its surface.</p>
 156
 157 <p class="whs2">&nbsp;</p>
 158
 159 <p class="whs2"><img src="../pics/image27.gif" x-maintain-ratio="TRUE" width="234px" height="96px" border="0" class="img_whs7"></p>
 160
 161 <p class="whs8">&nbsp;</p>
 162
 163 <ul type="disc" class="whs4">
 164
 165         <li class=kadov-p><p class="whs8">The <span style="font-weight: bold;"><B>Aspect
 166  Ratio</B></span> of a <span style="font-weight: bold;"><B>quadrangle</B></span> 2D
 167  element consisting of 4 nodes is the worst (i.e. the greatest) value from
 168  all triangles which can be built taking three nodes of the quadrangle.
 169  There are four triangles to consider: </p></li>
 170 </ul>
 171
 172 <p class="whs9"><img src="../pics/image138.gif" x-maintain-ratio="TRUE" width="622px" height="412px" border="0" class="img_whs10"></p>
 173
 174 <p class="whs9">Note, that the Aspect Ratio criterion is
 175  applicable to 2D mesh elements only. For 3D elements we use the <a href="../aspect_ratio_3d.htm">Aspect
 176  Ratio 3D</a> criterion. &nbsp;&nbsp;</p>
 177
 178 <p class="whs11">&nbsp;</p>
 179
 180 <p class=TODO>To apply the Aspect Ratio quality criterion to your mesh:</p>
 181
 182 <p class=TODO>&nbsp;</p>
 183
 184 <p class="whs2">1. Display your mesh in the viewer.</p>
 185
 186 <p class="whs2">&nbsp;</p>
 187
 188 <p class="whs2">2. Choose <span style="font-weight: bold;"><B>Controls
 189  &gt; Aspect Ratio </B></span>or click <img src="../image37.gif" width="25px" height="24px" border="0" class="img_whs12"> button in the toolbar.
 190  Your mesh will be displayed in the viewer with its elements colored according
 191  to the applied mesh quality control criterion:</p>
 192
 193 <p class="whs2">&nbsp;</p>
 194
 195 <p class="whs2"><img src="../image94.jpg" width="439px" height="313px" border="0" class="img_whs13"></p>
 196
 197 <p class="whs2">&nbsp;</p>
 198
 199 <p class="whs8"><span style="font-weight: bold;"><B>See Also</B></span>
 200  a sample TUI Script of an <a href="../quality_controls.htm#bookmark8">Aspect
 201  Ratio quality control</a> operation. &nbsp;</p>
 202
 203 <p>&nbsp;</p>
 204
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