QuadShear.tex

%---------------------------Shear-----------------------------
\section{Shear\label{s:quad-shear}}

The shear metric
\[
q = \min \left\{ \frac {\alpha_0} {\normvec{L_0} \normvec{L_3}}, 
                 \frac {\alpha_1} {\normvec{L_1} \normvec{L_0}},
                 \frac {\alpha_2} {\normvec{L_2} \normvec{L_1}},
                 \frac {\alpha_3} {\normvec{L_3} \normvec{L_2}} \right\}
\]
is the same as the scaled Jacobian, except that it has a truncated range.

Note that if $\alpha_i < DBL\_MIN$ or any edge has length $L < DBL\_MIN$, we set $q = 0$.

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