Specify radius of an arc with pgfplots and axis direction cs?

Question

I'm trying to draw an arc (the top half of a circle of radius 8, centered at (-8,0)) but I can't figure out how to specify the radius in pgfplots's coordinate system. Here's a MWE:

\pgfplotsset{compat=1.5.1}
\begin{tikzpicture}
  \begin{axis}[
      xmin=-20,xmax=20,
    ]
    \addplot{x}; % not important, just to make things show up
    \draw (axis cs:-16,0) arc[start angle=180, end angle=0,
                              radius=8];
  \end{axis}
\end{tikzpicture}

I read about axis direction cs in the pgfplots manual, but it doesn't explain how to use it to calculate a distance like a radius -- it only says that for ellipses, it's done automatically. But I don't have an ellipse, I have an arc.

How can I specify a radius of 8 for my arc, using the coordinate system of my plot?

Answer 1

You can transform the distance for the radius using the function transformdirectionx (which is the math parser equivalent to \pgfplotstransformdirectionx):

\documentclass{article}

\usepackage{pgfplots}
\pgfplotsset{compat=1.5.1}
\begin{document}

\begin{tikzpicture}
  \begin{axis}[
      xmin=-10,xmax=10,
      axis equal,
      grid=both
    ]
    \addplot{x};
    \draw [ultra thick] (axis cs:0,-5) arc[start angle=-90, end angle=180,
                              radius={transformdirectionx(5)}];
  \end{axis}
\end{tikzpicture}
\end{document}