Generalised: Accessing the logic values of a TikZ coordinate

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Accessing the logic values of a TikZ coordinate

I used these functions, until I came to a scaled tikzpicture and then it was off. I now have added a factor for the scaling, but I am looking for a method to make it universal. That would mean the xcoord/ycoord would take the picture's scaling into account through a tikz/pgf variable.

\makeatletter
\newcommand\xcoord[2][center]{{%
  \pgfpointanchor{#2}{#1}%
  \pgfmathparse{\pgf@x/\pgf@xx}%
  \pgfmathprintnumber{\pgfmathresult}%
}}
\newcommand\ycoord[2][center]{{%
  \pgfpointanchor{#2}{#1}%
  \pgfmathparse{\pgf@y/\pgf@yy}%
  \pgfmathprintnumber{\pgfmathresult}%
 }}
 \makeatother

Any suggestion to that effect?

An MWE is:

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

\makeatletter
\newcommand\xcoorda[2][center]{{%
  \pgfpointanchor{#2}{#1}%
  \pgfmathparse{\pgf@x/\pgf@xx}%
  \pgfmathprintnumber{\pgfmathresult}%
}}

\makeatletter
\newcommand\xcoord[2][center]{{%
 \pgfpointanchor{#2}{#1}%
 \pgfmathparse{\pgf@x/\pgf@xx/.17}%
 \pgfmathprintnumber{\pgfmathresult}%
}}

\newcommand\ycoorda[2][center]{{%
  \pgfpointanchor{#2}{#1}%
  \pgfmathparse{\pgf@y/\pgf@yy}%
  \pgfmathprintnumber{\pgfmathresult}%
}}
\makeatother

\usetikzlibrary{intersections}


\begin{document}

\begin{tikzpicture}[domain=-0.01:0.55,xscale=17,yscale=0.01] 
% the scaling is also in xcoord
\draw[-stealth,name path=xline] (0,0) -- (0.55,0);
\draw[stealth-stealth,name path=yline] (0,-220) -- (0,220);
\draw[color=blue,name path=func] (0,200) parabola bend (.25,-50) (.50,200);
\path[name intersections={of=func and xline,by={i1,i2}}];
\node[above=15pt] (i1label) at(i1) {\xcoord{i1}\%};
\draw[-stealth,green] (i1label.south) -- (i1);
\node[below=20pt,text width=2cm,align=center,draw,fill=red!25] (i1label_a) 
 at(i1) {\xcoorda{i1}\%\\ sans scaling \\ wrong!};
\draw[-stealth,red] (i1label_a.north) -- (i1);
\node[above=15pt] (i2label) at(i2) {\xcoord{i2}\%};
\draw[-stealth,green] (i2label.south) -- (i2);
\node[below=20pt,text width=2cm,draw,align=center,fill=red!25] (i2label_a) 
 at(i2) {\xcoorda{i2}\%\\ sans scaling \\ wrong!};
\draw[-stealth,red] (i2label_a.north) -- (i2);
\foreach \t in {10,20,...,50} {
\pgfmathparse{\t/100}\edef\v{\pgfmathresult}
  \draw[thin] (\v,10) -- (\v,-10) node[below] {\t\%};
}
\foreach \t in {-200,-100,...,200} {
 \draw[thin] (.010,\t) -- (-0.01,\t) node[left] {\small\t};
}
\end{tikzpicture}

\end{document}

I used a parabola in the MWE and marked the scaled and unscaled xcoord's in both cases.

Answer 1

The problem arises because \xcoorda is called inside a node, which resets the transformation matrix, so \pgf@xx is not scaled correctly. What you can do to avoid this is to save the transformation matrix into a macro at the start of the tikzpicture using \pgfgettransform{<macro>}, and set it inside the \xcoorda macro using \pgfsettransform{<macro>}. In order to use the resulting coordinate in a \pgfmathparse expression, I'd recommend turning the macro into a pgfmath function. I've included this approach in the code below.

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{intersections}

\makeatletter
\newcommand\xcoorda[2][center]{{%
%
% Set the transformation matrix that was saved at the beginning of the tikzpicture
%
  \pgfsettransform{\transform}%
  \pgfpointanchor{#2}{#1}%
  \pgfmathparse{\pgf@x/\pgf@xx}%
  \pgfmathresult%
}}

\pgfmathdeclarefunction{xcoord}{1}{
  \pgfsettransform{\transform}%
  \pgfpointanchor{#1}{center}%
  \pgfmathparse{\pgf@x/\pgf@xx}%
}

\makeatother

\begin{document}

\begin{tikzpicture}[domain=-0.01:0.55,xscale=17,yscale=0.01] 

% Save the transformation matrix
\pgfgettransform{\transform}

\draw[-stealth,name path=xline] (0,0) -- (0.55,0);
\draw[stealth-stealth,name path=yline] (0,-220) -- (0,220);
\draw[color=blue,name path=func] (0,200) parabola bend (.25,-50) (.50,200);
\path[name intersections={of=func and xline,by={i1,i2}}];
\node[below=20pt,text width=2cm,align=center,draw,fill=green!25] (i1label_a) 
 at(i1) {\xcoorda{i1}\\correct};
\draw[-stealth,red] (i1label_a.north) -- (i1);
\node[below=20pt,text width=2cm,draw,align=center,fill=green!25] (i2label_a) 
 at(i2) {\pgfmathparse{xcoord("i2")*100}\pgfmathprintnumber{\pgfmathresult}\,\%\\ correct};
\draw[-stealth,red] (i2label_a.north) -- (i2);
\foreach \t in {10,20,...,50} {
\pgfmathsetmacro\v{\t/100}
  \draw[thin] (\v,10) -- (\v,-10) node[below] {\t\%};
}
\foreach \t in {-200,-100,...,200} {
 \draw[thin] (.010,\t) -- (-0.01,\t) node[left] {\small\t};
}
\end{tikzpicture}

\end{document}

---

If you're using PGFplots, you can avoid having to manually save and restore the coordinate transformation, since in this case you can use \pgfplotsunitxlength, which holds the length of the x unit vector multiplied by 1000, and \pgfplotspointaxisorigin, which holds the point (0,0) of the current axis:

\documentclass{article}
\usepackage{pgfplots}
\usetikzlibrary{intersections}

\newcommand\xcoord[2][center]{{%
    \pgfpointanchor{#2}{#1}%
    \pgfgetlastxy{\ix}{\iy}%
    \pgfplotspointaxisorigin%
    \pgfgetlastxy{\ox}{\oy}
    \pgfmathparse{(\ix-\ox)/\pgfplotsunitxlength/1000}
    \pgfmathprintnumber{\pgfmathresult}}
}

\begin{document}

\vspace{1cm}
\begin{tikzpicture}
\begin{axis}[
    domain=0:0.5,
    samples=100,
    no markers,
    axis lines=middle,
    enlarge x limits=upper,
    enlarge y limits=true,
    xticklabel=\pgfmathparse{\tick*100}\pgfmathprintnumber{\pgfmathresult}\,\%,
    x axis line style={{name path global=xaxis}}
    ]
\addplot +[name path global=plot] {4000*(x-0.25)^2-50};

\pgfplotsextra{
\fill [name intersections={of=xaxis and plot, name=i, total=\t}] 
    [red, every node/.style={black}] 
    (i-1) circle (2pt) node [pin={\xcoord{i-1}}] {}
    (i-2) circle (2pt) node [pin={\xcoord{i-2}}] {};
}
\end{axis}
\end{tikzpicture}
\end{document}