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Anonymous 1123
[This question](https://tex.stackexchange.com/questions/600723/replicate-axis-region-reference-frame-and-drawing-to-it-saving-coordinates-2d) asked five days ago, and there is no answer. I cannot answer this question. How can to draw it? 
Top Answer
user 3.14159
This is not really an answer because I think what the OP wants is dangerous. One *can* make it work, but I do not recommend to put the axis in scope of a plane of the `3d` library. Such constructions are fragile, to see this try e.g. to introduce layers. What might be useful, though, is the `get xy window` key which I more or less copied from [here](https://topanswers.xyz/tex?q=1741#a1971). This allows you to avoid the `calc` methods the OP is using.
```
\documentclass{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.18}
\usetikzlibrary{3d}
\makeatletter
\pgfplotsset{get xy window/.code={\pgfkeys{/pgf/fpu}%
\pgfmathfloattofixed{\pgfplots@xmax}\let\myxmax\pgfmathresult
\pgfmathfloattofixed{\pgfplots@xmin}\let\myxmin\pgfmathresult
\pgfmathfloattofixed{\pgfplots@ymax}\let\myymax\pgfmathresult
\pgfmathfloattofixed{\pgfplots@ymin}\let\myymin\pgfmathresult
\pgfkeys{/pgf/fpu=false}},
window/ds/.initial=1}
\makeatother
\pgfplotsset{draw xy background/.style={%
	execute at begin axis={\pgfplotsset{get xy window}%
	\pgfmathsetmacro{\myxmineff}{\myxmin-\myymax+\myymin}%
	\pgfmathsetmacro{\myxminnext}{\myxmineff+\pgfkeysvalueof{/pgfplots/window/ds}}%
	\pgfmathsetmacro{\myxmaxeff}{\myxmax+\myymax-\myymin}%
	\draw[window background] foreach \X in {\myxmineff,\myxminnext,...,\myxmax}
	{(axis cs:\X,\myymin) -- ++ 
	(axis direction cs:\myymax-\myymin,\myymax-\myymin)};
	}}}
\tikzset{window background/.style={thin}}
\begin{document}

\begin{tikzpicture}[line join=round,line cap=round]
	\begin{axis}[axis equal, xmin=-.5, xmax=4.5, ymin=-.5, ymax=4.5,
		draw xy background]
		\addplot[black, opacity=0.5,smooth] {(x-3)^2};
	\end{axis}
\end{tikzpicture}

\begin{tikzpicture}[line join=round,line cap=round]
  \begin{scope}[
   x={(-0.7cm,0.4cm)},
   y={(.9cm,.2cm)},
   z={(0cm,1cm)},
   canvas is yx plane at z=0
  ]
	\begin{axis}[axis equal, xmin=-.5, xmax=4.5, ymin=-.5, ymax=4.5,
		draw xy background]
		\addplot[black, opacity=0.5,smooth] {(x-3)^2};
	\end{axis}
  \end{scope}
\end{tikzpicture}

\end{document}
```
![Screen Shot 2021-06-15 at 11.43.14 PM.png](/image?hash=e47f2433b2845ddd84f9e13ce6b2ba00a0df31f8f0d6fe4a10d2e806b9577bf0)

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