# Drawing a transformation with tikz picture

I want to illustrate a transformation from $xy$ to $uv$ plane. but I don't know how to link these planes. This is supposed to be the $xy$ plane

 \begin{document}
\begin{figure}
\centering
\begin{tikzpicture}[vect/.style={->,shorten >=2pt,>=latex'}]  \tkzInit[xmin=-.5, xmax=3, ymin=-.5, ymax=3.5]
\tkzDrawXY[noticks,label={}]
\tkzDefPoints{1/1/A, 0/2/B, 1/3/C, 2/2/D}  \tkzDrawPoints(A,B,C,D)
\tkzLabelPoint[left](B){$B$}
\tkzLabelPoint[below](A){$A$}
\tkzLabelPoint[above](C){$C$}
\tkzLabelPoint[right](D){$D$}
\tkzDrawSegments(A,B B,C C,D A,D)
\end{tikzpicture}
\end{figure}
\end{document}


and the now the $uv$ plane

 \begin{document}
\begin{figure}[h]
\centering
\begin{tikzpicture}[vect/.style={->,shorten >=2pt,>=latex'}]
\tkzInit[xmin=-3.5, xmax=3, ymin=-1, ymax=2.5]
\tkzDrawXY[noticks,label={}]
\tkzDefPoints{1/1/A, 0/2/B, 1/3/C, 2/2/D, -1/-1/E, 0/0/F, -1/1/G, -2/0/H}
\tkzDrawPoints(A,B,C,D,E,F,G,H)
\tkzLabelPoint[left](B){$B$}
\tkzLabelPoint[below](A){$A$}
\tkzLabelPoint[above](C){$C$}
\tkzLabelPoint[right](D){$D$}
\tkzDrawSegments[dashed](A,B B,C C,D A,D)
\tkzLabelPoint[below right](F){$B'$}
\tkzLabelPoint[below](E){$A'$}
\tkzLabelPoint[above](G){$C'$}
\tkzLabelPoint[below left](H){$D'$}
\tkzDrawSegments(E,F F,G G,H H,E)
\end{tikzpicture}
\end{figure}
\end{document}


How to put an arrow between them with the label $T(z)$?

I am not sure I read the question correctly but you could put the sub pictures in local bounding boxes and connect those.

\documentclass{article}
\usepackage{tkz-euclide}
\begin{document}
\begin{figure}
\centering
\begin{tikzpicture}[vect/.style={->,shorten >=2pt,>=latex'}]
\begin{scope}[local bounding box=L]
\tkzInit[xmin=-.5, xmax=3, ymin=-.5, ymax=3.5]
\tkzDrawXY[noticks,label={}]
\tkzDefPoints{1/1/A, 0/2/B, 1/3/C, 2/2/D}  \tkzDrawPoints(A,B,C,D)
\tkzLabelPoint[left](B){$B$}
\tkzLabelPoint[below](A){$A$}
\tkzLabelPoint[above](C){$C$}
\tkzLabelPoint[right](D){$D$}
\tkzDrawSegments(A,B B,C C,D A,D)
\end{scope}
\begin{scope}[xshift=8.5cm,local bounding box=R]
\tkzInit[xmin=-3.5, xmax=3, ymin=-1, ymax=2.5]
\tkzDrawXY[noticks,label={}]
\tkzDefPoints{1/1/A, 0/2/B, 1/3/C, 2/2/D, -1/-1/E, 0/0/F, -1/1/G, -2/0/H}
\tkzDrawPoints(A,B,C,D,E,F,G,H)
\tkzLabelPoint[left](B){$B$}
\tkzLabelPoint[below](A){$A$}
\tkzLabelPoint[above](C){$C$}
\tkzLabelPoint[right](D){$D$}
\tkzDrawSegments[dashed](A,B B,C C,D A,D)
\tkzLabelPoint[below right](F){$B'$}
\tkzLabelPoint[below](E){$A'$}
\tkzLabelPoint[above](G){$C'$}
\tkzLabelPoint[below left](H){$D'$}
\tkzDrawSegments(E,F F,G G,H H,E)
\end{scope}
\draw[thick,-latex] (L) -- node[above]{$T(z)$} (R.west|-L);
\end{tikzpicture}
\end{figure}
\end{document}


• Interesting... thanks again for helping me. I have never heard abount \scope and local bounding box. where can I find more information about it? – Marcos Paulo May 21 at 6:29
• @MarcosPaulo You're welcome! The local bounding box key can be found on p. 1141 of pgfmanual v3.1.5, and the scopes are explained in section 12.3 Using Scopes to Structure a Picture of the same manual. – user194703 May 21 at 6:31
• Looking at these pages quickly I did not see any examples related to my question. I think if I read it, I'd never imagine that the solution could be on theses pages. Would you suggest any video tutorials based in all my previous questions that you answered? – Marcos Paulo May 21 at 6:42
• @MarcosPaulo Did you look at the pgfmanual? I do not know any video material. There is the Visual TikZ manual but it does not seem to discuss local bounding boxes nor scopes in detail. – user194703 May 21 at 6:46
• Not the whole manual of course. I will search this other that you pointed out – Marcos Paulo May 21 at 8:11