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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 >
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< p > < img src = "i_blue.jpg" x-maintain-ratio = "TRUE" width = "30px" height = "30px" border = "0" class = "img_whs2" > The Aspect Ratio 3D mesh quality criterion calculates
the same parameter as the < a href = "files/aspect_ratio.htm" > Aspect ratio< / a >
criterion, but it is applied to 3D mesh elements: tetrahedrons, pentahedrons,
hexahedrons, etc. < / p >
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< p > < / p >
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< ul type = "disc" class = "whs3" >
< li class = kadov-p > < p > < img src = "image20.gif" width = "258px" height = "246px" align = "left" border = "0" class = "img_whs4" > The < span style = "font-weight: bold;" > < B > Aspect
Ratio< / B > < / span > of a < span style = "font-weight: bold;" > < B > tetrahedron< / B > < / span >
3D element is calculated by the formula:< / p > < / li >
< / ul >
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< p > < / p >
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< p > < / p >
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< p > < img src = "image19.gif" width = "133px" height = "56px" border = "0" class = "img_whs5" > ,< / p >
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< p > < / p >
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< p > where < span style = "font-weight: bold; font-style: italic;" > < I > < B > S< / B > < / I > < / span > < span
style="font-weight: bold;
font-style: italic;
vertical-align: Sub;">< I > < B > K< / B > < / I > < / span > is the sum of surfaces of the faces
of К and < span style = "font-weight: bold; font-style: italic;" > < I > < B > V< / B > < / I > < / span > < span
style="vertical-align: Sub;
font-weight: bold;
font-style: italic;">< I > < B > K< / B > < / I > < / span > is the volume of К :< / p >
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< p > < / p >
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< p > < img src = "image18.gif" width = "425px" height = "192px" border = "0" class = "img_whs6" > T< / p >
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< p > < / p >
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< ul type = "disc" class = "whs3" >
< li class = kadov-p > < p > Other element types like quadrangle, pentahedron
and hexahedron use the following formula:< / p > < / li >
< / ul >
< p > < img src = "image30.gif" width = "89px" height = "32px" border = "0" class = "img_whs7" > , where < span style = "font-weight: bold; font-style: italic;" > < I > < B > Q< / B > < / I > < / span > < span
style="vertical-align: Sub;
font-weight: bold;
font-style: italic;">< I > < B > i< / B > < / I > < / span > represents the value of < span style = "font-weight: bold; font-style: italic;" > < I > < B > Q< / B > < / I > < / span > < span
style="vertical-align: Sub;
font-weight: bold;
font-style: italic;">< I > < B > k< / B > < / I > < / span > for all possible simplexes (of the
same dimension as the element) that compose the element.< / p >
< p > For example, a hexahedron is split in 6 tetrahedrons, the < span style = "font-weight: bold;" > < B > Aspect
ratio 3D< / B > < / span > is calculated for each of them, then the greatest < span
style="font-weight: bold; font-style: italic;">< I > < B > Q< / B > < / I > < / span > < span style = "vertical-align: Sub ;
font-weight: bold;
font-style: italic;">< I > < B > k< / B > < / I > < / span > is considered to be the < span
style="font-weight: bold;">< B > Aspect ratio 3D< / B > < / span >
criterion for the whole hexahedron.< / p >
< p > < img src = "pics/image139.gif" x-maintain-ratio = "TRUE" width = "569px" height = "386px" border = "0" class = "img_whs8" > < / p >
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< p > < / p >
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< p class = TODO > To apply the Aspect Ratio 3D quality criterion to your mesh:< / p >
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< p class = TODO > < / p >
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< p class = "whs9" > 1. Display your mesh in the viewer.< / p >
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< p class = "whs9" > < / p >
< p class = "whs9" > 2. Choose < span style = "font-weight: bold;" > < B > Controls
> Aspect Ratio 3D < / B > < / span > or click < img src = "image144.gif" width = "24px" height = "26px" border = "0" class = "img_whs10" > button of the toolbar.
Your mesh will be displayed in the viewer with its elements colored according
to the applied mesh quality control criterion:< / p >
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< p > < / p >
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< p class = "whs11" > < span style = "font-weight: bold;" > < B > See Also< / B > < / span >
a sample TUI Script of an < span style = "font-weight: bold;" > < B > < a href = "quality_controls.htm#bookmark11" > Aspect
Ratio 3D< / B > < / span > quality control< / a > operation. < / p >
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< p > < / p >
< p > < / p >
< p > < / p >
< p > < / p >
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