%---------------------------Oddy-----------------------------
\section{Oddy}

Let $\vec L_4 = \vec L_0$. The Oddy metric is then defined as
\[
q = \max_{i\in\{0,1,2,3\}}\left\{
    \frac{(\normvec{L_i}^2 - \normvec{L_{i+1}}^2)^2 
    + 4 (\vec L_i \cdot \vec L_{i+1})^2}
    {2 \normvec{N_{i+1}}^2 }
  \right\}.
\]
This metric measures the maximum deviation of the metric tensor at the corners of the quadrilateral.

Note that if $\normvec{N_{i+1}}^2 < DBL\_MIN$, we set $q = DBL\_MAX$.

\quadmetrictable{Oddy}%
{$1$}%                                      Dimension
{$[0,0.5]$}%                                Acceptable range
{$[0,DBL\_MAX]$}%                           Normal range
{$[0,DBL\_MAX]$}%                           Full range
{$0$}%                                      Unit square
{\cite{odd:88}}%                            Citation
{v\_quad\_oddy}%                            Verdict function name