## "Fossies" - the Fresh Open Source Software archive

### Member "VTK5.10.1/Utilities/verdict/docs/VerdictUserManual2007/QuadMaximumAngle.tex" of archive vtk-5.10.1.zip:

%---------------------------Maximum Angle-----------------------------
\section{Maximum Angle}

In order to properly compute the included angle, we'll need to
correct for incorrectly oriented elements.
Let
$s_i = \left\{ \begin{array}{ll} 1\rule{2em}{0pt} & \alpha_i < 0\\ 0 & \alpha_i \geq 0 \end{array}\right.$
The included angle between two neighboring edges is
$\theta_i = (-1)^{s_i} \arccos{ \left( - \frac {\vec L_{i} \cdot \vec L_{i+1} } {\normvec{L_{i}} \normvec{L_{i+1}}} \right) } \left( \frac {180} {\pi} \right) + 360\dgr s_i$
where $i\in\{0,1,2,3\}$ and $\vec L_4 = \vec L_0$.
We take the maximum of this quantity as the value of the metric:
$q = \max_{i\in\{0,1,2,3\}}\left\{ \theta_i \right\}$

Note that if $\normvec{L_i} \leq DBL\_MIN$ or $\normvec{L_{i+1}} \leq DBL\_MIN$,
\verd\ returns $q = 0\dgr$.

\quadmetrictable{maximum included angle}%
{$A^1$}%                                    Dimension
{$[90\dgr,135\dgr]$}%                       Acceptable range
{$[90\dgr,360\dgr]$}%                       Normal range
{$[0\dgr,360\dgr]$}%                        Full range
{$90\dgr$}%                                 Unit square
{--}%                                       Citation
{v\_quad\_maximum\_angle}%                  Verdict function name