%---------------------------Taper---------------------------
\section{Taper\label{s:hex-taper}}

Taper measures the maximum ratio of a cross-derivative to its shortest associated principal axis.
Given a pair of principal axes $f$ and $g$, the taper is
\[
  T_{fg} = \frac{\normvec{ X_{fg}}}{\min\left\{\normvec{ X_f},\normvec{X_g}\right\}}
\]
The metric is then the maximum taper of any cross-derivative
\[
  q = \max\left\{ T_{12}, T_{13}, T_{23} \right\}
\]

Note that if $\normvec{X_1}$ or $\normvec{X_2}$ or $\normvec{X_3} < DBL\_MIN$, we set $q = DBL\_MAX$.

\hexmetrictable{taper}%
{$1$}%                                        Dimension
{$[0,0.5]$}%                                  Acceptable range
{$[0,DBL\_MAX]$}%                             Normal range
{$[0,DBL\_MAX]$}%                             Full range
{$0$}%                                        Cube
{Adapted from \cite{tf:89}}%                  Citation
{v\_hex\_taper}%                              Verdict function name