How determine slope of straight line (with auto scale of axis) in PGF plots

Question

I want to allow automatic scaling of the axis (so don't want to set axis equal=true), and be able to place a label on a line at a manually chosen point along the line. Of course if axis equal=true, then I could simply rotate the node 45 degrees and things work fine. Since I am manually specifying the lengths of the x-axis and y-axis, I attempted to use arctan(\YAxisMax/\XAxisMax), but this isn't quite right. What I need is that ratio of the scale factors applied to each axis.

    \documentclass{standalone}
    \usepackage{pgfplots}

    \begin{document}
    \begin{tikzpicture}

    \newcommand*{\XAxisMin}{-7.0}
    \newcommand*{\XAxisMax}{7.0}
    \newcommand*{\YAxisMin}{-2.0}
    \newcommand*{\YAxisMax}{2.0}

    % Determine angle of rotation
    \pgfmathsetmacro{\Angle}{atan(\YAxisMax/\XAxisMax)}%

     \begin{axis}[
            axis y line=center, %axis equal=true,
            axis x line=middle, 
            axis on top=true,
            xmin=\XAxisMin,
            xmax=\XAxisMax, 
            ymin=\YAxisMin,
            ymax=\YAxisMax, 
] 

addplot[mark=none, domain=\XAxisMin:\XAxisMax, red, thick] ({x},{x});%

% This works fine if axis equal=true above is uncommented.
addplot [mark=none] coordinates{(-1,-1)} node [green, above, rotate=45] {$k=0$};%

\addplot [mark=none] coordinates{(1,1)} node [blue, above, rotate=\Angle] {$k=0$};%

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

Here is the output that this produces:

I thought I found the solution here so tried this which also did not work:

\makeatletter
\pgfpointxy{1}{1}%
\pgfmathsetmacro{\Angle}{atan(\pgf@y/\pgf@x)}%
\makeatother

Answer 1

Starting from version 1.5.1, you can place nodes on a plot by adding node [pos=<value>] {...} to the \addplot command. If you add the sloped option to the node options, the node will be rotated to match the plot:

\documentclass{article}
\usepackage{pgfplots}

\begin{document}
\begin{tikzpicture}

 \begin{axis}[
        axis y line=center,
        axis x line=middle, 
        axis on top=true,
        xmin=-7,
        xmax=7,
        ymin=-4,
        ymax=4
] 

\addplot[
    mark=none,
    domain=-4:6,
    samples=80,
    red,
    thick
] {(x<-2)*-2 + (!(x<-2) && (x<3))*x + (!(x<3)) * 3}
    node [pos=0.0, above, sloped] {$f(x)=-2$}
    node [pos=0.6, above, sloped, blue] {$f(x)=x$}
    node [pos=0.9, above, sloped, green!70!black] {$f(x)=3$}
;%
\end{axis}
\end{tikzpicture}
\end{document}

---

With older versions, one possibility was to use a decoration to place the node. The decorations.markings library allows you to place a (correctly rotated) node somewhere along a path. To use the library in \addplot, you have to apply it through an every path/.style, which leads to a problem with the decoration being applied to itself. Thankfully, this has been solved already: Applying a postaction to every path in TikZ.

Also, PGFplots seems to have a problem with using TikZ nodes in the decorations. This can be avoided by using \pgfnode instead, which does exactly the same as \node, but looks a bit unusual.

Here's an example where a plotlabel style is defined (based on Altermundus' idea in How to label a path drawn using tikz with \draw plot?, and adapted to work around the described problems). You specify the label with plotlabel={<rel pos along path>}{<label text>}. To change the color of the label, you can use \color{<color name>}<label text>. The plotlabel option can be used multiple times to add different labels to the same plot.

\documentclass{article}
\usepackage{pgfplots}
\usetikzlibrary{decorations.markings}
\makeatletter
\tikzset{
    nomorepostaction/.code={\let\tikz@postactions\pgfutil@empty},
    plotlabel/.style 2 args={
        every path/.append style={
            postaction={
                nomorepostaction,
                decorate,
                decoration={
                    markings,
                    mark=at position #1 with {
                        \pgfnode{rectangle}{south}{#2}{}{}
                    }
                }
            }
        }
    }
}
\makeatother

\begin{document}
\begin{tikzpicture}

 \begin{axis}[
        axis y line=center,
        axis x line=middle, 
        axis on top=true,
        xmin=-7,
        xmax=7,
        ymin=-4,
        ymax=4
] 

\addplot[
    mark=none,
    domain=-4:6,
    samples=80,
    red,
    thick,
    plotlabel={0.0}{\color{purple}$f(x)=-2$},
    plotlabel={0.6}{\color{blue}$f(x)=x$},
    plotlabel={0.9}{\color{green!70!black}$f(x)=3$}
] {(x<-2)*-2 + (!(x<-2) && (x<3))*x + (!(x<3)) * 3};%
\end{axis}
\end{tikzpicture}
\end{document}

Answer to the original question: You can use Martin Scharrer's method for determining the slope of a line in PGFplots, but only after the axis is finished (otherwise the unit vector is not defined yet) -- you can't calculate the slope before starting the axis. So you have to include your \Angle calculation in a \pgfplotsextra command, which will get executed at the end of the plot. The labels then have to be placed using \nodes positioned using (axis cs:x,y), not with \addplot commands:

\documentclass{standalone}
\usepackage{pgfplots}

\begin{document}
\begin{tikzpicture}

\newcommand*{\XAxisMin}{-7.0}
\newcommand*{\XAxisMax}{7.0}
\newcommand*{\YAxisMin}{-2.0}
\newcommand*{\YAxisMax}{2.0}

\begin{axis}[
      axis y line=center, %axis equal=true,
      axis x line=middle, 
      axis on top=true,
      xmin=\XAxisMin,
      xmax=\XAxisMax, 
      ymin=\YAxisMin,
      ymax=\YAxisMax, 
] 

addplot[mark=none, domain=\XAxisMin:\XAxisMax, red, thick] ({x},{x});%

\makeatletter
\pgfplotsextra{
\pgfpointxy{1}{1}%
\pgfmathsetmacro{\Angle}{atan(\pgf@y/\pgf@x)}%
\node at (axis cs:-1,-1) [green, above, rotate=\Angle] {$k=0$};
}
\makeatother

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