Some Results about the Quality of Planar Mesh Elements
Résumé
In this report are presented some new results about both triangle and planar quadrangle quality measures. First, in the context of triangular mesh optimization based on control over edge lenghts, the relations between the edge ratio and the usual shape quality measure are fully examined. Second, a modification of the norm is proposed, in order to comply with the case where the reference element is no longer equilateral, but a right isosceles triangle. Third, generalizations of and to planar quadrangle quality measure are proposed and justified, and their limitations, depending on the user expectations, are exhibited, justifying the use of a more complex quality measure. Finally, a natural use of the norm for quadrangular elements is proposed.