QuadScaledJacobian.tex

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

The scaled Jacobian is the minimum of
the Jacobian at each corner divided by the lengths of the 2 edge vectors
(which is the minimum sine of the included angles):
\[
q =
  \min \left\{ \frac {\alpha_0} {\normvec{L_0} \normvec{L_3}}, 
               \frac {\alpha_1} {\normvec{L_1} \normvec{L_0}},
               \frac {\alpha_2} {\normvec{L_2} \normvec{L_1}},
               \frac {\alpha_3} {\normvec{L_3} \normvec{L_2}}
  \right\}.
\]
Note that if any edge has $L< DBL\_MIN$, we take $q = 0$.

\quadmetrictable{scaled Jacobian}%
{$1$}%                                      Dimension
{$[0.3,1]$}%                                Acceptable range
{$[-1,1]$}%                                 Normal range
{$[-1,1]$}%                                 Full range
{$1$}%                                      Unit square
{\cite{knu:00}}%                            Citation
{v\_quad\_scaled\_jacobian}%                Verdict function name