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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
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criterion, however, it is applied to 3D mesh elements: tetrahedrons,
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pentahedrons, hexahedrons, etc. < / p >
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< p > There are simple formulas to evaluate directly the value of quality
Qk for simplex in 3D. The formulas are :< / p >
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< br >
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< p > <EFBFBD> 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 >
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< p > For the other types of element like pentahedron and hexahedron
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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 >
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< p > For example, hexahedron is analysed via 6 tetrahedrons this way:< / p >
< p > < img src = "image139.gif" border = "0" class = "img_whs10" > < / p >
< p > < / p >
< p > For 3D elements with quadrangular faces, aspect ratio of such faces
is also analysed and the maximal one over 3D and 2D qualities is taken.< / p >
< p > < / p >
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< p > < / p >
< p class = "whs10" > < span style = "font-weight: bold;" > < B > See Also< / B > < / span >
a sample TUI Script of an < a href = "quality_controls.htm#bookmark11" > Aspect
Ratio quality control< / a > operation. < / p >
< p > < / p >
< p > < / p >
< p > < / p >
< p > < / p >
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