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< h1 > Aspect Ratio< / h1 >
< 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
a mesh element to the regular element of its type (with all edges having
the same length). The
criterion can be defined as < / p >
< 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 >
is the considered element of the mesh, < span style = "font-weight: bold; font-style: italic;" > < I > < B > h< / B > < / I > < / span > < span
style="vertical-align: Sub;
font-weight: bold;
font-style: italic;">< I > < B > max< / B > < / I > < / span > is the diameter of the element
К (i.e. the length of the longest edge), < span style = "font-weight: bold; font-style: italic;" > < I > < B > р < / B > < / I > < / span > < span
style="vertical-align: Sub;
font-weight: bold;
font-style: italic;">< I > < B > к < / B > < / I > < / span > is the radius of the sphere
inscribed in the element K, and < span style = "font-weight: bold; font-style: italic;" > < I > < B > a< / B > < / I > < / span >
is a normalisation value chosen so that < 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 > = 1 when К is an equilateral
simplex. < / p >
< p class = "whs2" > < / p >
< p > 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 > varies between 1 and +oo and the
closer it is to 1, the better the element К is. < / p >
< ul type = "disc" class = "whs4" >
< li class = kadov-p > < p > The < span style = "font-weight: bold;" > < B > Aspect Ratio< / B > < / span >
of a < span style = "font-weight: bold;" > < B > triangle< / B > < / span > 2D element consisting
of 3 nodes is calculated by the formula:< / p > < / li >
< / 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
style="vertical-align: Sub;
font-weight: bold;
font-style: italic;">< I > < B > к < / B > < / I > < / span > is the half perimeter of the
element K and < span style = "font-weight: bold; font-style: italic;" > < I > < B > S< / B > < / I > < / span > < span
style="vertical-align: Sub;
font-weight: bold;
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" >
< li class = kadov-p > < p class = "whs8" > The < span style = "font-weight: bold;" > < B > Aspect
Ratio< / B > < / span > of a < span style = "font-weight: bold;" > < B > quadrangle< / B > < / span > 2D
element consisting of 4 nodes is the worst (i.e. the greatest) value from
all triangles which can be built taking three nodes of the quadrangle.
There are four triangles to consider: < / p > < / li >
< / 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
applicable to 2D mesh elements only. For 3D elements we use the < a href = "../aspect_ratio_3d.htm" > Aspect
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 >
< 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
> 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
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
Ratio quality control< / a > operation. < / p >
< p > < / p >
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