Ok, I will try to add some formula and explanation on the webpage.

So, the quality in Mmg is a measure of the shape ratio in the metric space reconstructed from the size map.

A “perfect” element has quality 1. Quality 0 correspond to element with volume null.

For an isotropic metric an element of quality 1 is equilateral, for an anisotropic metric it is inscribed in the metric tensor.

More precisely, if I note e_i the i^{th} edges of an element, l_i their lengths, \bar{M} the mean metric over this element, V_{\bar{M}_i} the volume of this element in the mean metric:

- quality formula for a triangle is:

Q_T = \alpha \frac{V_{\bar{M}}}{\sum_{e_i} l_i^2}

- quality formula for a tetra is:

Q_T = \alpha \frac{V_{\bar{M}}}{(\sqrt{\sum_{e_i} l_i^2})^{\frac{3}{2}}}

with \alpha a normalization coefficient such as quality is 1 for an isotropic metric and and equilateral element.

Hope that it helps,

Best Regards,

Algiane