This mesh quality criterion resembles to the Aspect ratio
criterion, however, it is applied to 3D mesh elements: tetrahedrons,
pentahedrons, hexahedrons, etc.
There are simple formulas to evaluate directly the value of quality Qk for simplex in 3D. The formulas are :
• 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 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.
For example, hexahedron is analysed via 6 tetrahedrons this way:
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.
See Also a sample TUI Script of an Aspect Ratio quality control operation.