# Showing different coordinate systems by uncovering in tikz?

Using beamer I want to show how different linear transformations act on the plane. I tried to do this by uncovering different \pgftransformcm commands, but it doesn't work. What would be the best way to do this?

Here's my code:

    \documentclass{beamer}
\usepackage{tikz}
\begin{document}
\begin{frame}
$\begin{tikzpicture} \begin{scope} \clip (0,0) rectangle (10cm,6cm); \uncover<1>{\pgftransformcm{1}{0}{0}{1}{\pgfpoint{5cm}{2cm}};} %\uncover<2>{\pgftransformcm{1}{-0.5}{1}{1}{\pgfpoint{5cm}{2cm}};} %\uncover<3>{\pgftransformcm{1}{1}{1}{-1}{\pgfpoint{5cm}{2cm}};} \draw[style=help lines,dashed] (-14,-14) grid[step=1cm] (14,14); \draw[thick,red,->] (0,0)--(1,0) node[anchor=south]{e_1}; \draw[thick,blue,->] (0,0)--(0,1) node[anchor=south]{e_2}; \draw[thick,green,->] (0,0)--(1,3) node[anchor=south]{v}; \end{scope} \end{tikzpicture}$
\end{frame}
\end{document}


Like this

\documentclass{beamer}
\usepackage{tikz}
\begin{document}
\begin{frame}
\def\mypicture{
\draw[style=help lines,dashed] (-14,-14) grid[step=1cm] (14,14);
\draw[thick,red,->]  (0,0)--(1,0) node[anchor=south]{$e_1$};
\draw[thick,blue,->] (0,0)--(0,1) node[anchor=south]{$e_2$};
\draw[thick,green,->](0,0)--(1,3) node[anchor=south]{$v$};
}
\begin{tikzpicture}
\begin{scope}
\clip (0,-0.02) rectangle (10cm,6cm);

\only<1>{
\pgftransformcm{1}{0}{0}{1}{\pgfpoint{5cm}{2cm}};
\mypicture
}
\only<2>{
\pgftransformcm{1}{-0.5}{1}{1}{\pgfpoint{5cm}{2cm}};
\mypicture
}
\only<3>{
\pgftransformcm{1}{1}{1}{-1}{\pgfpoint{5cm}{2cm}};
\mypicture
}

\end{scope}
\end{tikzpicture}
\end{frame}
\end{document}


Output

• I also meant for the grid to transform, but it was an easy fix. Thanks! – Jompa Aug 13 '16 at 19:44
• Answer updated, \clip (0,-0.02) rectangle (10cm,6cm); here -0.02 to show arrow head in the third slide. – Salim Bou Aug 13 '16 at 19:59