%---------------------------Scaled Jacobian---------------------------
\section{Scaled Jacobian}

This metric is the minimum determinant of the Jacobian matrix
evaluated at each corner and the center of the element,
divided by the corresponding edge lengths.
\[
q = \min_{i\in\{0,1,\ldots,8\}}\left\{\hat\alpha_i\right\}.
\]

Note that if ${L_{\min}}^2 \leq DBL\_MIN$, we set $q = DBL\_MAX$.

\hexmetrictable{scaled Jacobian}%
{$1$}%                                        Dimension
{$[0.5,1]$}%                                  Acceptable range
{$[-1,1]$}%                                   Normal range
{$[-1,DBL\_MAX]$}%                            Full range
{$1$}%                                        Cube
{\cite{knu:00}}%                              Citation
{v\_hex\_scaled\_jacobian}%                   Verdict function name
