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

Let $J$ be the Jacobian as defined in \S\ref{s:tet-jacobian}

\[
\lambda_1 = \normvec{ L_0 }
            \normvec{ L_2 }
            \normvec{ L_3 }  
\]

\[
\lambda_2 = \normvec{ L_0 }
            \normvec{ L_1 }
            \normvec{ L_4 }  
\]

\[
\lambda_3 = \normvec{ L_1 }
            \normvec{ L_2 }
            \normvec{ L_5 }  
\]

\[
\lambda_4 = \normvec{ L_3 }
            \normvec{ L_4 }
            \normvec{ L_5 }  
\]


\[
\lambda_{\max} = \max\left\{\lambda_1, \lambda_2, \lambda_3, \lambda_4, J\right\} 
\]

\begin{equation*}
q = \frac{J\sqrt{2}}{\lambda_{\max}}
\end{equation*}

Note that if $\lambda_{\max} < DBL\_MIN$, we set $q = DBL\_MAX$.

\tetmetrictable{scaled Jacobian}%
{$1$}%                                        Dimension
{$[\frac{1}{2},\frac{\sqrt{2}}{2}]$}%         Acceptable range
{$[-\frac{\sqrt{2}}{2},\frac{\sqrt{2}}{2}]$}% Normal range
{$[-DBL\_MAX,DBL\_MAX]$}%                     Full range
{1}%                                          Equilateral tet
{\cite{knu:00}}%                              Citation
{v\_tet\_scaled\_jacobian}%                            Verdict function name