Quality Evaluation

The quality is evaluated separately for triangular and tetrahedral elements. By default only elements on the output are subjected to the quality evaluation. There are recognized three distinct quality quantities

• element shape based quality,
• dihedral angle based quality, and
• connectivity based quality.

The elements shape based quality is evaluated according to the following formulas (quality is normalized )

• triangular element
  
  where is the area of the triangle and , , and are the lengths of its sides,
• tetrahedral element
  
  where denotes the volume of the tetrahedron and , , , and are the areas of its faces.

The dihedral angle based quality is evaluated according to the following formula

where is the minimal and the maximal dihedral angle in a particular element.
The connectivity based quality compares the valence of individual nodes with the optimal valence which is exactly 6 for triangular mesh and approximately 12 for tetrahedral mesh.