Use macro as coordinate in pgfplots plot

Question

I'm trying to come up with a solution to the question How to maintain consistency with TikZ and Pgfplots?. Essentially, what is needed is a way to save a coordinate as a macro (or a global key, maybe?) that can then be used instead of the usual <x>,<y> pair, both in normal nodes/paths and in pgfplots plots.

For clarification: I would like to be able to define a macro \PointA that I can call whenever the syntax (<x>,<y>) is expected. This might be in the definition of a node using \node at (<x>,<y>) {};, or in a pgfplots plot using \addplot coordinates { (0,0) (<x>,<y>) (1,1) };

Just using \def\<name>{<x>,<y>} works fine for normal nodes and paths, but when I try to use it as a coordinate in a pgfplots plot, it fails with the error message:

File ended while scanning use of \pgfplots@foreach@plot@coord@NEXT.

An expansion issue, yet again? Or should I use a totally different approach?

\documentclass{article}
\usepackage{pgfplots}

\def\PointA{1,2}

\begin{document}
\begin{tikzpicture}

  \draw [gray] (0,0) grid (3,3);
  \fill (\PointA) circle (2pt); % Works

  \begin{axis}[xshift=3.5cm,width=6cm,xmin=0,xmax=3,ymin=0,ymax=3,grid=both]

    \fill [orange] (axis cs:\PointA) circle (4pt); % Works
    \addplot coordinates { (0,0) (1,2) (2,2) }; % Works
%    \addplot coordinates { (0,0) (\PointA) (2,2) }; % Fails

  \end{axis}
\end{tikzpicture}
\end{document}

Answer 1

One way to achieve this is to patch the internal macro responsible of reading the coordinates. The \pgfplots@foreach@plot@coord@NEXT in pgfplotscoordprocessing.code.tex is called after the opening ( is detected and will read (#1,#2) from the input stream. In your example you have (\PointA) (2,2), so \PointA) (2 is taken as X and 2 as Y part. The idea is to patch this macro to expand the next token following ( to reveal the , in it. This can be done using the following code:

\documentclass{article}
\usepackage{pgfplots}

\def\PointA{1,2}

\makeatletter
\let\orig@pgfplots@foreach@plot@coord@NEXT\pgfplots@foreach@plot@coord@NEXT
\def\pgfplots@foreach@plot@coord@NEXT{%
    \expandafter\orig@pgfplots@foreach@plot@coord@NEXT\expandafter
}
\makeatother

\begin{document}
\begin{tikzpicture}

  \draw [gray] (0,0) grid (3,3);
  \fill (\PointA) circle (2pt); % Works

  \begin{axis}[xshift=3.5cm,width=6cm,xmin=0,xmax=3,ymin=0,ymax=3,grid=both]

    \fill [orange] (axis cs:\PointA) circle (4pt); % Works
%    \addplot coordinates { (0,0) (1,2) (2,2) }; % Works
    \addplot coordinates { (0,0) (\PointA) (2,2) }; % Works now!!

  \end{axis}
\end{tikzpicture}
\end{document}

Another method would be do patch the macro responsable to read the { } after coordinate to expanding that argument completely before processing it further. This has the benefit that you can include macros which hold several coordinates or other macros which wouldn't be expanded as well with the above code. The macro in question is called \pgfplots@addplotimpl@coordinates@ and reads the coordinates as #3. The following code expands that argument using \edef:

\documentclass{article}
\usepackage{pgfplots}

\def\PointA{1,2}

\def\mycoordinates{ (1,0) (2,1) (3,0) }

\makeatletter
\long\def\pgfplots@addplotimpl@coordinates@#1#2#3#4{%
    \pgfplots@start@plot@with@behavioroptions{#1,/pgfplots/.cd,#2}%
    \pgfplots@PREPARE@COORD@STREAM{#4}%
    \begingroup
    \edef\@tempa{{#3}}%
    \ifpgfplots@curplot@threedim
        \expandafter\endgroup\expandafter
        \pgfplots@coord@stream@foreach@threedim\@tempa
    \else
        \expandafter\endgroup\expandafter
        \pgfplots@coord@stream@foreach\@tempa
    \fi
}%
\makeatother

\begin{document}
\begin{tikzpicture}

  \draw [gray] (0,0) grid (3,3);
  \fill (\PointA) circle (2pt); % Works

  \begin{axis}[xshift=3.5cm,width=6cm,xmin=0,xmax=3,ymin=0,ymax=3,grid=both]

    \fill [orange] (axis cs:\PointA) circle (4pt); % Works
%    \addplot coordinates { (0,0) (1,2) (2,2) }; % Works
    \addplot coordinates { (0,0) (\PointA) (2,2) }; % Works now!!
    \addplot coordinates \mycoordinates; % Works as well!!
    \addplot coordinates { (0,1) \mycoordinates (6,7) }; % Works as well!!

  \end{axis}
\end{tikzpicture}
\end{document}

Alternatively you could define \PointAX and \PointAY and then write (\PointAX,\PointAY) which should also work without any patches.

Answer 2

You could store each coordinate separately or define a table:

\documentclass{article}
\usepackage{pgfplots}


\def\PointAx{1}
\def\PointAy{2}
\def\PointA{\PointAx,\PointAy}
\pgfplotstableread{%
  2 2
}{\PointB}

\begin{document}
\begin{tikzpicture}

  \draw [gray] (0,0) grid (3,3);
  \fill (\PointA) circle (2pt); % Works

  \begin{axis}[xshift=3.5cm,width=6cm,xmin=0,xmax=3,ymin=0,ymax=3,grid=both]

    \fill [orange] (axis cs:\PointA) circle (4pt); % Works
    \addplot coordinates { (1,2) }; % Works
    \addplot coordinates { (\PointAx,\PointAy) }; % Works
    \addplot table {\PointB}; % Works

  \end{axis}
\end{tikzpicture}
\end{document}

Answer 3

A different angle at looking at the issue:

\documentclass{article}
\usepackage{tikz}
\usepackage{pgfplots}

\def\PointA{1,2}
\def\PointB{coordinates {(3,3)}}
\begin{document}


\begin{tikzpicture}
  \draw [gray] (0,0) grid (3,3);
  \fill (\PointA) circle (2pt); % Works

  \begin{axis}[xshift=3.5cm,width=6cm,xmin=0,xmax=3,ymin=0,ymax=3,grid=both]
    \fill [orange] (axis cs:\PointA) circle (4pt); % Works
    \expandafter\addplot\PointB; % Works
  \end{axis}
\end{tikzpicture}
\end{document}

This is a simple and clean solution. Variations to it are possible. For example you can define a macro:

\def\Coordinates#1#2{%
  \def\A{#1}
  \def\B{#2}
  \def\PointB{coordinates {(\A,\B)}}
  \expandafter\addplot\PointB;
}

This will also work, just call it from within \begin{axis}...\end{axis}.