\hypertarget{classHurricane_1_1Transformation_1_1Orientation}{}\section{Hurricane\+:\+:Transformation\+:\+:Orientation Class Reference}
\label{classHurricane_1_1Transformation_1_1Orientation}\index{Hurricane\+::\+Transformation\+::\+Orientation@{Hurricane\+::\+Transformation\+::\+Orientation}}


\subsection{Detailed Description}
This enumeration defines the orientation associated to a transformation object.

\begin{center} 
\tabulinesep=1mm
\begin{longtabu} spread 0pt [c]{*{8}{|X[-1]}|}
\caption{\mbox{\hyperlink{classHurricane_1_1Transformation_1_1Orientation}{Orientation}} codes and associated transformation matrix}\label{_}\\
\hline
\rowcolor{\tableheadbgcolor}\textbf{ \begin{center}\mbox{\hyperlink{classHurricane_1_1Name}{Name}}\end{center}  }&\textbf{ \begin{center}Aspect\end{center}  }&\textbf{ \begin{center}Code\end{center}  }&\textbf{ \begin{center}Signification\end{center}  }&\textbf{ \begin{center}a\end{center}  }&\textbf{ \begin{center}b\end{center}  }&\textbf{ \begin{center}c\end{center}  }&\textbf{ \begin{center}d\end{center}  }\\\cline{1-8}
\endfirsthead
\hline
\endfoot
\hline
\rowcolor{\tableheadbgcolor}\textbf{ \begin{center}\mbox{\hyperlink{classHurricane_1_1Name}{Name}}\end{center}  }&\textbf{ \begin{center}Aspect\end{center}  }&\textbf{ \begin{center}Code\end{center}  }&\textbf{ \begin{center}Signification\end{center}  }&\textbf{ \begin{center}a\end{center}  }&\textbf{ \begin{center}b\end{center}  }&\textbf{ \begin{center}c\end{center}  }&\textbf{ \begin{center}d\end{center}  }\\\cline{1-8}
\endhead
\begin{center}{\bfseries ID}\end{center}  & &\begin{center}{\bfseries 0}\end{center}  &Identity &\begin{center}1\end{center}  &\begin{center}0\end{center}  &\begin{center}0\end{center}  &\begin{center}1\end{center}  \\\cline{1-8}
\begin{center}{\bfseries R1}\end{center}  & &\begin{center}{\bfseries 1}\end{center}  &Simple rotation (90°) &\begin{center}0\end{center}  &\begin{center}-\/1\end{center}  &\begin{center}1\end{center}  &\begin{center}0\end{center}  \\\cline{1-8}
\begin{center}{\bfseries R2}\end{center}  & &\begin{center}{\bfseries 2}\end{center}  &Double rotation (180°) &\begin{center}-\/1\end{center}  &\begin{center}0\end{center}  &\begin{center}0\end{center}  &\begin{center}-\/1\end{center}  \\\cline{1-8}
\begin{center}{\bfseries R3}\end{center}  & &\begin{center}{\bfseries 3}\end{center} &Triple rotation (270°) &\begin{center}0\end{center} &\begin{center}1\end{center} &\begin{center}-\/1\end{center} &\begin{center}0\end{center}  \\\cline{1-8}
\begin{center}{\bfseries MX}\end{center}  & &\begin{center}{\bfseries 4}\end{center}  &\mbox{\hyperlink{classHurricane_1_1Horizontal}{Horizontal}} symetry (Mirror X) &\begin{center}-\/1 \end{center} &\begin{center}0 \end{center} &\begin{center}0 \end{center} &\begin{center}1\end{center}  \\\cline{1-8}
\begin{center}{\bfseries XR}\end{center}  & &\begin{center}{\bfseries 5}\end{center} &\mbox{\hyperlink{classHurricane_1_1Horizontal}{Horizontal}} symetry followed by a 90° rotation &\begin{center}0\end{center}  &\begin{center}-\/1\end{center}  &\begin{center}-\/1\end{center}  &\begin{center}0\end{center}  \\\cline{1-8}
\begin{center}{\bfseries MY}\end{center} & &\begin{center}{\bfseries 6}\end{center} &\mbox{\hyperlink{classHurricane_1_1Vertical}{Vertical}} symetry (Mirror Y) &\begin{center}1\end{center}  &\begin{center}0\end{center}  &\begin{center}0\end{center}  &\begin{center}-\/1\end{center}  \\\cline{1-8}
\begin{center}{\bfseries YR}\end{center}  & &\begin{center}{\bfseries 7}\end{center} &\mbox{\hyperlink{classHurricane_1_1Vertical}{Vertical}} symetry followed by a 90° rotation &\begin{center}0\end{center}  &\begin{center}1\end{center}  &\begin{center}1\end{center}  &\begin{center}0\end{center}  \\\cline{1-8}
\end{longtabu}
\end{center} 

The transformation formula is given by\+: \[ \Large \left \{ \begin{array}{r c l l l l l} x' & = & (a \times x) & + & (b \times y) & + & tx \\ y' & = & (c \times x) & + & (d \times y) & + & ty \end{array} \right . \] where x and y are the coordinates of any point, x\textquotesingle{} and y\textquotesingle{} the coordinates of the transformed point, tx and ty the horizontal and vertical components of the translation and where a, b, c and d are the coefficients of the matrix associated to the orientation. 

The documentation for this class was generated from the following file\+:\begin{DoxyCompactItemize}
\item 
Transformation.\+h\end{DoxyCompactItemize}
