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213 lines
8.0 KiB
HTML
Executable File
213 lines
8.0 KiB
HTML
Executable File
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<title>Aspect Ratio</title>
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<h1>Aspect Ratio</h1>
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<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>
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quality criterion for mesh elements reveals the degree of conformity of
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a mesh element to the regular element of its type (with all edges having
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the same length). The
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criterion can be defined as </p>
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<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>К</B></I></span>
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is the considered element of the mesh, <span style="font-weight: bold; font-style: italic;"><I><B>h</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>max</B></I></span> is the diameter of the element
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К (i.e. the length of the longest edge), <span style="font-weight: bold; font-style: italic;"><I><B>р</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>к</B></I></span> is the radius of the sphere
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inscribed in the element K, and <span style="font-weight: bold; font-style: italic;"><I><B>a</B></I></span>
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is a normalisation value chosen so that <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> = 1 when К is an equilateral
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simplex. </p>
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<p class="whs2"> </p>
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<p>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> varies between 1 and +oo and the
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closer it is to 1, the better the element К is. </p>
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<ul type="disc" class="whs4">
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<li class=kadov-p><p>The <span style="font-weight: bold;"><B>Aspect Ratio</B></span>
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of a <span style="font-weight: bold;"><B>triangle</B></span> 2D element consisting
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of 3 nodes is calculated by the formula:</p></li>
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</ul>
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<p> </p>
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<p class="whs2"><img src="../pics/image21.gif" x-maintain-ratio="TRUE" width="158px" height="110px" border="0" class="img_whs5"></p>
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<p class="whs2"><img src="../pics/image23.gif" x-maintain-ratio="TRUE" width="120px" height="48px" border="0" class="img_whs6"> ,</p>
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<p class="whs2"> </p>
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<p class="whs2">where <span style="font-weight: bold; font-style: italic;"><I><B>р</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>к</B></I></span> is the half perimeter of the
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element K and <span style="font-weight: bold; font-style: italic;"><I><B>S</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 its surface.</p>
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<p class="whs2"> </p>
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<p class="whs2"><img src="../pics/image27.gif" x-maintain-ratio="TRUE" width="234px" height="96px" border="0" class="img_whs7"></p>
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<p class="whs8"> </p>
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<ul type="disc" class="whs4">
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<li class=kadov-p><p class="whs8">The <span style="font-weight: bold;"><B>Aspect
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Ratio</B></span> of a <span style="font-weight: bold;"><B>quadrangle</B></span> 2D
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element consisting of 4 nodes is the worst (i.e. the greatest) value from
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all triangles which can be built taking three nodes of the quadrangle.
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There are four triangles to consider: </p></li>
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</ul>
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<p class="whs9"><img src="../pics/image138.gif" x-maintain-ratio="TRUE" width="622px" height="412px" border="0" class="img_whs10"></p>
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<p class="whs9">Note, that the Aspect Ratio criterion is
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applicable to 2D mesh elements only. For 3D elements we use the <a href="../aspect_ratio_3d.htm">Aspect
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Ratio 3D</a> criterion. </p>
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<p class="whs11"> </p>
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<p class=TODO>To apply the Aspect Ratio quality criterion to your mesh:</p>
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<p class=TODO> </p>
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<p class="whs2">1. Display your mesh in the viewer.</p>
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<p class="whs2"> </p>
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<p class="whs2">2. Choose <span style="font-weight: bold;"><B>Controls
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> Aspect Ratio </B></span>or click <img src="../image37.gif" width="25px" height="24px" border="0" class="img_whs12"> button in 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 class="whs2"> </p>
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<p class="whs2"><img src="../image94.jpg" width="439px" height="313px" border="0" class="img_whs13"></p>
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<p class="whs2"> </p>
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<p class="whs8"><span style="font-weight: bold;"><B>See Also</B></span>
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a sample TUI Script of an <a href="../quality_controls.htm#bookmark8">Aspect
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Ratio quality control</a> operation. </p>
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<p> </p>
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