[Tex/LaTex] How to add/translate points in axis cs

Question

I don't seem to have a problem placing a coordinate in the axis coordinate system, and translating in the x direction seems to work as expected also. But as soon as I try to translate in the y direction, I get puzzled by the result:

\documentclass{article}
    \usepackage{pgfplots}
    \usetikzlibrary{calc}
\begin{document}
    \begin{tikzpicture}
        \begin{axis}[grid=major,]
            \addplot plot coordinates{(1800,2.14) (1860,2.18)};
            \coordinate (bottomLeft) at (axis cs:1800,2.14);
            \coordinate (bottomRight) at ($(bottomLeft) + (30,0)$);
            \draw (bottomLeft) -- (bottomRight);
            \coordinate (topLeft) at ($(bottomLeft) + (0,0.02)$);
            \coordinate (topRight) at ($(topLeft) + (20,0)$);
            \draw[red,thick] (topLeft) -- (topRight);
        \end{axis}
    \end{tikzpicture}
\end{document}

generates

and shows that I translated in the x direction both times, but the y translation by (0,0.02) isn't calculated as I would have expected – I wanted a coordinate at (1800,2.16). You can skip to the bottom now unless you'd like to see my troubleshooting that didn't work.

I discovered that a calculation is happening with

\documentclass{article}
    \usepackage{pgfplots}
    \usetikzlibrary{calc}
\begin{document}
    \begin{tikzpicture}
        \begin{axis}[grid=major,]
            \addplot plot coordinates{(1800,2.14) (1860,2.18)};
            \coordinate (bottomLeft) at (axis cs:1800,2.14);
            \draw[purple] ($(bottomLeft) + (0,0.2)$) circle (0.3cm);
            \filldraw[purple] ($(bottomLeft) + (0,10)$) circle (0.3cm);
        \end{axis}
    \end{tikzpicture}
\end{document}

because I was able to translate in the y direction – it just doesn't seem to be translating in the axis cs the same way I could in the x direction:

The open circle didn't look translated at all, but upon closer examination, I got the filled circle to translate (a distance seemingly unrelated to the axis cs). I thought maybe the y axis would be handled differently from the x axis, so I tried to specify axis cs again:

\documentclass{article}
    \usepackage{pgfplots}
    \usetikzlibrary{calc}
\begin{document}
    \begin{tikzpicture}
        \begin{axis}[grid=major,]
            \addplot plot coordinates{(600,1) (1800,2.14) (1860,2.18)};
            \coordinate (bottomLeft) at (axis cs:1800,2.14);
            \coordinate (test) at ($(bottomLeft) + (axis cs:0,0.2)$);
            \draw[thick,purple] (test) circle (0.3cm);
            \draw[thick] (bottomLeft) -- (test);
        \end{axis}
    \end{tikzpicture}
\end{document}

but changing the scale (by changing the lower left point) shows that (test) doesn't stay in the same place relative to the axis cs:

I tried specifying axis cs for the whole calculation and with different bracket locations, but none would even compile.

\documentclass{article}
    \usepackage{pgfplots}
    \usetikzlibrary{calc}
\begin{document}
    \begin{tikzpicture}
        \begin{axis}[grid=major,]
            \addplot plot coordinates{(800,1) (1800,2.14) (1860,2.18)};
            \coordinate (bottomLeft) at (axis cs:1800,2.14);
            %\coordinate (test) at (axis cs:$(bottomLeft) + (0,0.2)$);%didn't compile
            %\coordinate (test) at (axis cs:{$(bottomLeft) + (0,0.2)$});%didn't compile
            %\coordinate (test) at (axis cs:$(bottomLeft) + {(0,0.2)}$);%didn't compile
            %\coordinate (test) at (axis cs:${(bottomLeft) + (0,0.2)}$);%didn't compile
            \coordinate (translation) at (axis cs:0,0.2);
            \coordinate (test) at ($(bottomLeft) + (translation)$);
            \draw[thick,purple] (test) circle (0.3cm);
            \draw[thick] (bottomLeft) -- (test);
        \end{axis}
    \end{tikzpicture}
\end{document}

When I tried creating both coordinates in advance of the calculation, (test) still doesn't appear to move with the axis cs:

Does anyone know how I can calculate a coordinate location using two other coordinates which have been defined in the axis coordinate system?

Answer 1

As noted in the pgfplots manual:

As noted in the documentation for axis cs, adding two coordinates by means of the TikZ ++ operator¹ may have unexpected effects. The correct way for ++ operations is axis direction cs.

¹ While you're not strictly using ++ here, + from the calc library is effectively the same as far as this is concerned.

To do relative coordinate transformation, use axis direction cs instead of axis cs:

\documentclass{standalone}
    \usepackage{pgfplots}
    \pgfplotsset{compat=1.12}
    \usetikzlibrary{calc}
\begin{document}
    \begin{tikzpicture}
        \begin{axis}[grid=major,]
            \addplot plot coordinates{(1800,2.14) (1860,2.18)};
            \coordinate (bottomLeft) at (axis cs:1800,2.14);
            \coordinate (bottomRight) at ($(bottomLeft) + (axis direction cs:30,0)$);
            \draw (bottomLeft) -- (bottomRight);
            \coordinate (topLeft) at ($(bottomLeft) + (axis direction cs:0,0.02)$);
            \coordinate (topRight) at ($(topLeft) + (axis direction cs:20,0)$);
            \draw[red,thick] (topLeft) -- (topRight);
        \end{axis}
    \end{tikzpicture}
\end{document}