通过在 tikz 中揭示来显示不同的坐标系？

Question

我想beamer展示不同的线性变换如何作用于平面。我尝试通过发现不同的\pgftransformcm命令来实现这一点，但没有成功。最好的方法是什么？

这是我的代码：

    \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}

Answer 1

像这样

\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}

输出