# Aspect ratio 3D

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.