TriCondition.tex

%---------------------------Condition Number-----------------------------
\section{Condition\label{s:tri-condition}}

The condition number of the weighted Jacobian matrix is
\[
  q = \frac{
    \left(\vec L_2\cdot\vec L_2 + \vec L_1\cdot\vec L_1 + \vec L_1\cdot\vec L_2 \right)}%
    {2A\sqrt{3}}.
\]

Note that when $A = 0$, we set $q = DBL\_MAX$.
In theory the condition number is invariant to which node it is computed at,
but floating point truncation error can contribute to differences between
values computed for each node.
\verd\ always uses the first vertex.

\trimetrictable{condition}%
{$1$}%                                                Dimension
{$[1,1.3]$}%                                          Acceptable range
{$[1,DBL\_MAX]$}%                                     Normal range
{$[1,DBL\_MAX]$}%                                     Full range
{$1$}%                                                Unit equilateral triangle value
{\cite{knu:00,knu:03}}%                               Reference(s)                   
{v\_tri\_condition}%                            Verdict function name