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diff --git a/Master/texmf-dist/doc/latex/tikz-ext/tikz-ext-manual-en-pgf-trans.tex b/Master/texmf-dist/doc/latex/tikz-ext/tikz-ext-manual-en-pgf-trans.tex new file mode 100644 index 00000000000..b0f0f2906d8 --- /dev/null +++ b/Master/texmf-dist/doc/latex/tikz-ext/tikz-ext-manual-en-pgf-trans.tex @@ -0,0 +1,175 @@ +% !TeX spellcheck = en_US +% !TeX root = tikz-ext-manual.tex +% Copyright 2022 by Qrrbrbirlbel +% +% This file may be distributed and/or modified +% +% 1. under the LaTeX Project Public License and/or +% 2. under the GNU Free Documentation License. +% + +\section{Transformations: Mirroring} +\label{pgflibrary:transformations} + +\begin{purepgflibrary}{ext.transformations.mirror} + This library adds mirror transformations to PGF. +\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 PGFmath. + +\item Using built-in transformations (see right column). + + This depends on |\pgfmathanglebetween|\indexCommandO\pgfmathanglebetween which involves the arctangent (|atan2|\indexMathFunctionO{atan2}) function of PGFmath. +\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*} + +\switchcolumn% > + +\stepcounter{subsection} +\subsection{Using built-in transformations} + +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}{\pgftransformxmirror\marg{value}} + Sets up a transformation that mirrors along a vertical line that goes through point $(\text{\meta{value}}, 0)$. + +\begin{codeexample}[preamble=\usepgflibrary{transformations.mirror}] +\begin{tikzpicture} +\draw[help lines] (-0.25, -.25) grid (3.25, 1.25); +\draw[-latex] (0,0) .. controls (.5,1) .. (1,1); + +\draw[dashed] (1.5, -.25) -- (1.5, 1.25); +\pgftransformxmirror{1.5} + +\draw[-latex] (0,0) .. controls (.5,1) .. (1,1); +\end{tikzpicture} +\end{codeexample} +\end{command} + +\switchcolumn% > + +\begin{command}{\pgftransformxMirror\marg{value}} + Sets up a transformation that mirrors along a vertical line that goes through point $(\text{\meta{value}}, 0)$. + +\begin{codeexample}[preamble=\usepgflibrary{transformations.mirror}] +\begin{tikzpicture} +\draw[help lines] (-0.25, -.25) grid (3.25, 1.25); +\draw[-latex] (0,0) .. controls (.5,1) .. (1,1); + +\draw[dashed] (1.5, -.25) -- (1.5, 1.25); +\pgftransformxMirror{1.5} + +\draw[-latex] (0,0) .. controls (.5,1) .. (1,1); +\end{tikzpicture} +\end{codeexample} +\end{command} + +\switchcolumn*% < + +\begin{command}{\pgftransformymirror\marg{value}} + Sets up a transformation that mirrors along a horizontal line that goes through point $(0, \text{\meta{value})}$. +\end{command} + +\begin{command}{\pgftransformmirror\marg{point A}\marg{point B}} + Sets up a transformation that mirrors along the line that goes through \meta{point A} and \meta{point B}. + +\begin{codeexample}[preamble=\usepgflibrary{transformations.mirror}] +\begin{tikzpicture} +\draw[help lines] (-.25, -2.25) grid (2.5, 1.25); +\draw[-latex] (0,0) .. controls (.5,1) .. (1,1); + +\draw[dashed] (0, -1) -- (2, 0); +\pgftransformmirror{\pgfpointxy{0}{-1}} + {\pgfpointxy{2}{ 0}} + +\draw[-latex] (0,0) .. controls (.5,1) .. (1,1); +\end{tikzpicture} +\end{codeexample} +\end{command} + +\switchcolumn% > + +\begin{command}{\pgftransformyMirror\marg{value}} + Sets up a transformation that mirrors along a horizontal line that goes through point $(0, \text{\meta{value})}$. +\end{command} + +\begin{command}{\pgftransformMirror\marg{point A}\marg{point B}} + Sets up a transformation that mirrors along the line that goes through \meta{point A} and \meta{point B}. + +\begin{codeexample}[preamble=\usepgflibrary{transformations.mirror}] +\begin{tikzpicture} +\draw[help lines] (-.25, -2.25) grid (2.5, 1.25); +\draw[-latex] (0,0) .. controls (.5,1) .. (1,1); + +\draw[dashed] (0, -1) -- (2, 0); +\pgftransformMirror{\pgfpointxy{0}{-1}} + {\pgfpointxy{2}{ 0}} + +\draw[-latex] (0,0) .. controls (.5,1) .. (1,1); +\end{tikzpicture} +\end{codeexample} +\end{command} + +\switchcolumn*% < + +\begin{command}{\pgfqtransformmirror\marg{point A}} + Sets up a transformation that mirrors along the line that goes through the origin and \meta{point A}. + +\begin{codeexample}[preamble=\usepgflibrary{transformations.mirror}] +\begin{tikzpicture} +\draw[help lines] (-.25, -.25) grid (2.25, 1.25); +\draw[-latex] (0,0) .. controls (.5,1) .. (1,1); + +\draw[dashed] (0, 0) -- (2, 1); +\pgfqtransformmirror{\pgfpointxy{2}{1}} + +\draw[-latex] (0,0) .. controls (.5,1) .. (1,1); +\end{tikzpicture} +\end{codeexample} +\end{command} + +\switchcolumn + +\begin{command}{\pgfqtransformMirror\marg{point A}} + Sets up a transformation that mirrors along the line that goes through the origin and \meta{point A}. + +\begin{codeexample}[preamble=\usepgflibrary{transformations.mirror}] +\begin{tikzpicture} +\draw[help lines] (-.25, -.25) grid (2.25, 1.25); +\draw[-latex] (0,0) .. controls (.5,1) .. (1,1); + +\draw[dashed] (0, 0) -- (2, 1); +\pgfqtransformMirror{\pgfpointxy{2}{1}} + +\draw[-latex] (0,0) .. controls (.5,1) .. (1,1); +\end{tikzpicture} +\end{codeexample} +\end{command} + +\end{paracol} +\endinput |