%---------------------------Shape---------------------------
\section{Shape\label{s:hex-shape}}

The shape metric is 3 divided by the minimum mean ratio
of the Jacobian matrix evaluated at the element corners:
\[
  q = 3\min_{i\in\{0,1,\ldots,8\}}
  \left\{
    \frac{{\alpha_i}^{\frac {2}{3}}} {|A_i|^2}, 
  \right\}.
\]

Note that if $\alpha_i \leq DBL\_MIN$ or $|A_i|^2 \leq DBL\_MIN$ for any $i$, we set $q = 0$.

\hexmetrictable{shape}%
{$1$}%                                        Dimension
{$[0.3,1]$}%                                  Acceptable range
{$[0,1]$}%                                    Normal range
{$[0,1]$}%                                    Full range
{$1$}%                                        Cube
{\cite{knu:03}}%                              Citation
{v\_hex\_shape}%                              Verdict function name