This mesh quality criterion resembles to the Aspect ratio
criterion, however, it is also applied to 3D mesh elements: tetrahedrons,
pentahedrons, hexahedrons, etc.
There are 2 simple formulas to evaluate directly the value of quality Qk for simplex in 2D and 3D. The formulas are :
• For triangle :
where :
• For tetrahedron :
where :
To calculate Sk , it is needed to sum the area of each of the 3 faces with the formula given with the triangle.
For the other types of element like quadrangle, pentahedron and hexahedron the formula is the following :
Where Qi are the quality of all the possible simplex (of same dimension as the element) that compose the element.
See Also a sample TUI Script of an Aspect Ratio quality control operation.