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% Copyright 2022 by Qrrbrbirlbel
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% 1. under the LaTeX Project Public License and/or
% 2. under the GNU Free Documentation License.
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\begin{purepgflibrary}{ext.transformations.mirror}
This library adds mirror transformations to \pgfname.
\end{purepgflibrary}
Two approaches to mirror transformation exist:
\begin{enumerate}
\item Using the reflection matrix (see left column).
This depends on |\pgfpointnormalised|\indexCommandO\pgfpointnormalised which involves
the sine\indexMathFunctionO{sin} and the cosine\indexMathFunctionO{cos} functions of \pgfname math.
\item Using built-in transformations (see right column).
This depends on |\pgfmathanglebetweenpoints|\indexCommandO\pgfmathanglebetweenpoints which
involves the arctangent (|atan2|\indexMathFunctionO{atan2}) function of \pgfname math.
\end{enumerate}
Which one is better? I don't know.
Choose one you're comfortable with.
\begin{paracol}{2}
\subsection{Using the reflection matrix}
The following commands use the reflection matrix that sets the transformation matrix following
\begin{equation*}
A = \frac{1}{\Vert\vec l\Vert^2} \begin{bmatrix}
l_x^2-l_y^2 & 2l_xl_y \\
2l_xl_y & l_y^2-l_x^2\\
\end{bmatrix}.
\end{equation*}
The following commands use a combination of shifting, rotating, $-1$ scaling,
rotating back and shifting back to reach the mirror transformation.
The commands are named the same as on the left side,
only the |m| in |mirror| is capitalized.
\switchcolumn*% <
\begin{command}{\pgfexttransformxmirror\marg{value}}\cmdcompat\pgftransformxmirror
Sets up a transformation that mirrors along a vertical line that goes through point $(\text{\meta{value}}, 0)$.
\begin{command}{\pgfexttransformxMirror\marg{value}}\cmdcompat\pgftransformxMirror
Sets up a transformation that mirrors along a vertical line that goes through point $(\text{\meta{value}}, 0)$.
\begin{command}{\pgfexttransformymirror\marg{value}}\cmdcompat\pgftransformymirror
Sets up a transformation that mirrors along a horizontal line that goes through point $(0, \text{\meta{value})}$.
\end{command}
\begin{command}{\pgfexttransformmirror\marg{point A}\marg{point B}}\cmdcompat\pgftransformmirror
Sets up a transformation that mirrors along the line that goes through \meta{point A} and \meta{point B}.
\begin{command}{\pgfexttransformyMirror\marg{value}}\cmdcompat\pgftransformyMirror
Sets up a transformation that mirrors along a horizontal line that goes through point $(0, \text{\meta{value})}$.
\end{command}
\begin{command}{\pgfexttransformMirror\marg{point A}\marg{point B}}\cmdcompat\pgftransformMirror
Sets up a transformation that mirrors along the line that goes through \meta{point A} and \meta{point B}.
\begin{command}{\pgfextqtransformmirror\marg{point A}}\cmdcompat\pgfqtransformmirror
Sets up a transformation that mirrors along the line that goes through the origin and \meta{point A}.
\begin{command}{\pgfextqtransformMirror\marg{point A}}\cmdcompat\pgfqtransformMirror
Sets up a transformation that mirrors along the line that goes through the origin and \meta{point A}.
