Calculation of coordinates for TikZ annotations in PGFplots axis environment

Question

I'm trying to do some annotation with TikZ in a PGFplots axis environment by means of nodes. However, the placement of the nodes is going wrong all the time, see the minimum working example below. How can I fix this? How do I calculate the coordinates for the TikZ annotation properly?

MWE:

\documentclass[margin=1cm]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=newest}
\usetikzlibrary{calc}
\begin{document}
    \begin{tikzpicture}
        \begin{axis}
        [
            xtick={-0.1,0,1,1.1},xmin=-0.1,xmax=1.1,xlabel=$x$,
            ytick={-0.2,0,2,2.2},ymin=-0.2,ymax=2.2,ylabel style={rotate=-90},ylabel=$y$,
            unit vector ratio=2 1 1,
        ]
            \addplot[blue,domain=0:1] {x};
            \addplot[red,domain=0:1] {2*x};

            % Annotation.
            \coordinate (SW) at (axis cs:-0.1,-0.2); % (S)outh (w)est.
            \coordinate (SE) at (axis cs:1.1,-0.2); % (S)outh (e)ast.
            \coordinate (NE) at (axis cs:1.1,2.2); % (N)orth (e)ast.
            \coordinate (NW) at (axis cs:-0.1,2.2); % (N)orth (w)est.

            \coordinate (A) at (axis cs:1,0);
            \fill[black] (A) circle (1pt) node[anchor=south]{A};

             % ??? WHY IS THIS NOT WORKING. SHOULD BE THE SAME AS NODE A. ???
            \coordinate (B) at ($(SE)+(axis cs:-0.1,0.2)$); % ??? WHY IS THIS NOT WORKING. SHOULD BE THE SAME AS NODE A. ???
            \fill[black] (B) circle (1pt) node[anchor=south east]{B}; % ??? WHY IS THIS NOT WORKING. SHOULD BE THE SAME AS NODE A. ???
             % ??? WHY IS THIS NOT WORKING. SHOULD BE THE SAME AS NODE A. ???

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

Answer 1

The origin of the canvas area is different from the origin of the plot area. A plot coordinate pair (-0.1, 0.2) inside the calc expression ($(SE) + (-0.1, 0.2)$) is transformed to canvas coordinates and added to the canvas coordinates of SE. But since the origins do not match, the result is moved by the displacement of the plot origin to the canvas origin. Actually you want to add "relative" coordinates:

($(SE) + (-0.1, 0.2) - (0, 0)$)

The following example tries to illustrate this:

\documentclass[margin=1cm]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=newest}
\usetikzlibrary{arrows.meta}
\usetikzlibrary{calc}
\begin{document}
    \begin{tikzpicture}
        \begin{axis}
        [
            xtick={-0.1,0,1,1.1},xmin=-0.1,xmax=1.1,xlabel=$x$,
            ytick={-0.2,0,.5,.7},
            ymin=-0.2,ymax=.7,
            ylabel style={rotate=-90},
            ylabel=$y$,
            unit vector ratio=2 1 1,
        ]
            % \addplot[blue,domain=0:1] {x};
            % \addplot[red,domain=0:1] {2*x};

            % Annotation.
            \coordinate (SW) at (axis cs:-0.1,-0.2); % (S)outh (w)est.
            \coordinate (SE) at (axis cs:1.1,-0.2); % (S)outh (e)ast.
            \coordinate (NE) at (axis cs:1.1,2.2); % (N)orth (e)ast.
            \coordinate (NW) at (axis cs:-0.1,2.2); % (N)orth (w)est.

            \coordinate (A) at ($(1,0)$);
            \fill[black] (A) circle (1pt) node[anchor=south]{A};

            \coordinate (CO) at (0pt, 0pt);% canvas origin
            \coordinate (PO) at (0, 0);% plot origin
            \coordinate (D) at (-0.1, 0.2);% displacement as plot point

            \begin{scope}[
              -{Triangle[]},
              node font=\footnotesize,
              inner sep=.15em,
            ]
              % Show canvas origin
              \draw
               (CO) ++(1em, .4em) node[above right] (tmp) {Canvas origin (CO)}
               (tmp.west) -- (CO);

              % Show plot origin
              \draw
                (PO) ++(1em, .4em) node[above right] (tmp) {Plot origin (PO)}
                (tmp.west) -- (PO);

              % Show displacement as absolute plot point
              \draw
                (D) ++(1em, .4em) node[above right] (tmp) {D}
                (tmp.west) -- (D);

              % Show SE
              \draw
                (SE) ++(-1.5em, .4em) node[above left] (tmp) {SE}
                (tmp.east) -- (SE);

               % Show SE + D
               \draw
                 ($(SE) + (D)$) coordinate (SE_D)
                 ++(-1em, .4em) node[above left] (tmp) {SE + D}
                 (tmp.east) -- (SE_D);

               % Show SE + D - plot origin
               \draw
                 ($(SE) + (D) - (PO)$) coordinate (SE_D_PO)
                 ++(-1em, 0em) node[left] (tmp) {SE + D - PO}
                 (tmp.east) -- (SE_D_PO);

               \draw[red, very thick, <->, >={latex[]}]
                 (CO) -- (D);
               \draw[red, very thick, <->, >={latex[]}]
                 (SE) -- (SE_D);

               \draw[blue, thick, <->, >={latex[]}]
                 (PO) -- (D);
               \draw[blue, thick, <->, >={latex[]}]
                 (SE) -- (SE_D_PO);
            \end{scope}
        \end{axis}
    \end{tikzpicture}
\end{document}

A more clear notation is using the coordinate system cs axis direction as shown in the answer of esdd.

Answer 2

You have to use the axis direction cs:

\coordinate (B) at ($(SE)+(axis direction cs:-0.1,0.2)$);

Code:

\documentclass[margin=1cm]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.12}
\usetikzlibrary{calc}
\begin{document}
    \begin{tikzpicture}
        \begin{axis}
        [
            xtick={-0.1,0,1,1.1},xmin=-0.1,xmax=1.1,xlabel=$x$,
            ytick={-0.2,0,2,2.2},ymin=-0.2,ymax=2.2,ylabel style={rotate=-90},ylabel=$y$,
            unit vector ratio=2 1 1,
        ]
            \addplot[blue,domain=0:1] {x};
            \addplot[red,domain=0:1] {2*x};

            % Annotation.
            \coordinate (SW) at (-0.1,-0.2); % (S)outh (w)est.
            \coordinate (SE) at (1.1,-0.2); % (S)outh (e)ast.
            \coordinate (NE) at (1.1,2.2); % (N)orth (e)ast.
            \coordinate (NW) at (-0.1,2.2); % (N)orth (w)est.

            \coordinate (A) at (1,0);
            \fill[black] (A) circle (1pt) node[anchor=south]{A};

             % ??? WHY IS THIS NOT WORKING. SHOULD BE THE SAME AS NODE A. ???
            \coordinate (B) at ($(SE)+(axis direction cs:-0.1,0.2)$);??? WHY IS THIS NOT WORKING. SHOULD BE THE SAME AS NODE A. ???
            \fill[red,fill opacity=.5] (B) circle (2pt) node[anchor=south east]{B}; % ??? WHY IS THIS NOT WORKING. SHOULD BE THE SAME AS NODE A. ???
             % ??? WHY IS THIS NOT WORKING. SHOULD BE THE SAME AS NODE A. ???

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