QuadShape.tex

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

The shape metric is 2 divided by the condition number of the Jacobian matrix:
\[
q =
  2 \min \left\{ \frac {\alpha_0} { \normvec{L_0}^2 + \normvec{L_3}^2 }, 
                 \frac {\alpha_1} { \normvec{L_1}^2 + \normvec{L_0}^2 }, 
                 \frac {\alpha_2} { \normvec{L_2}^2 + \normvec{L_1}^2 }, 
                 \frac {\alpha_3} { \normvec{L_3}^2 + \normvec{L_2}^2 }
  \right\}.
\]
Note that if $\alpha_i < DBL\_MIN$ or any edge has length $L < DBL\_MIN$, we set $q = 0$.

\quadmetrictable{shape}%
{$1$}%                                      Dimension
{$[0.3,1]$}%                                Acceptable range
{$[0,1]$}%                                  Normal range
{$[0,1]$}%                                  Full range
{$1$}%                                      Unit square
{\cite{knu:03}}%                            Citation
{v\_quad\_shape}%                           Verdict function name