Tikz: Rotate around center when using coordinates relative to image

Question

I'm currently trying to define my coordinates in terms of the image's east/west/south/east coordinates so that I can use the same coordinate system regardless of what image I use. However, when i try to use the \draw [rotate around={20:\O{}}, name path=a] \O{} -- \E{}; in the example below, it does not rotate the path. When instead I use coordinates in the traditional way (5,0) it rotates it just fine.

I really want to use these relative coordinates since it would mean I wouldn't have to look up the edges each time I do annotations for a new image. How can I make the rotate around functionality work with relative coordinates?

\documentclass[12pt]{article}

\usepackage{graphicx}                                   % Further formatting of figures
\usepackage{amsmath}                                    % Mathematics
\usepackage{tikz}                                       % Annotated Figures
\usetikzlibrary{intersections}                          % Detect intersections
\usetikzlibrary{calc}                                   % Calculate distances
\usetikzlibrary{positioning}                            % Better positioning tools
\usetikzlibrary{arrows.meta}                            % Better arrowheads

\begin{document}

\begin{figure}[!htb]
\centering
\begin{tikzpicture}
    \node[inner sep=0pt] (img) at (0,0)
    {\includegraphics[width=\textwidth]{Figures/Airfoil.png}};
    % 
    \def\alph{50};
    \def\anglechord{230};
    \def\angleradius{95};
    \def\O{(img.center)};
    \def\E{(img.east)};
    \def\W{(img.west)};
    \def\N{(img.north)};
    \def\S{(img.south)};
    \def\SW{(img.south west)};
    \def\SE{(img.south east)};
    \def\NW{(img.north west)};
    \def\NE{(img.north east)};
    \def\arrow{{Latex[length=2.8mm]}};
    \def\arrowshort{{Latex[length=2mm]}};
    % \draw[step=1,black, thick] \SW{} grid \NE{};
    \draw[fill] (img.center) circle (0.1);
    % 
    \draw [dashed, very thin, name path=horizontal] \W{} -- \W{};
    \draw [dashed, very thin, name path=vertical] \S{} -- \N{};
    \path [name path = right] \SE{} -- \NE{};

    \draw [rotate around={20:\O{}}, name path=a] \O{} -- \E{};
\end{tikzpicture}
% \caption{caption}
% \label{fig:topconfig}
\end{figure}

\end{document}

Answer 1

Yes, that's the behavior of TikZ. However, you are already loading the calc library, which allows you to convert symbolic coordinates to explicit ones.

\documentclass[12pt]{article}

\usepackage{amsmath}                                    % Mathematics
\usepackage{tikz}                                       % Annotated Figures
\usetikzlibrary{intersections}                          % Detect intersections
\usetikzlibrary{calc}                                   % Calculate distances
\usetikzlibrary{positioning}                            % Better positioning tools
\usetikzlibrary{arrows.meta}                            % Better arrowheads

\begin{document}

\begin{figure}[!htb]
\centering
\begin{tikzpicture}
    \node[inner sep=0pt] (img) at (0,0)
    {\includegraphics[width=\textwidth]{example-image-duck}};
    % 
    \def\alph{50};
    \def\anglechord{230};
    \def\angleradius{95};
    \def\O{(img.center)};
    \def\E{(img.east)};
    \def\W{(img.west)};
    \def\N{(img.north)};
    \def\S{(img.south)};
    \def\SW{(img.south west)};
    \def\SE{(img.south east)};
    \def\NW{(img.north west)};
    \def\NE{(img.north east)};
    \def\arrow{{Latex[length=2.8mm]}};
    \def\arrowshort{{Latex[length=2mm]}};
    % \draw[step=1,black, thick] \SW{} grid \NE{};
    \draw[fill] (img.center) circle (0.1);
    % 
    \draw [dashed, very thin, name path=horizontal] \W{} -- \W{};
    \draw [dashed, very thin, name path=vertical] \S{} -- \N{};
    \path [name path = right] \SE{} -- \NE{};
    \draw let \p1=($(img.center)$),\p2=($(img.east)$) 
    in [rotate around={20:\O}, name path=a,thick,red]
     (\x1,\y1)-- (\x2,\y2);
\end{tikzpicture}
% \caption{caption}
% \label{fig:topconfig}
\end{figure}

\end{document}

Another possibility is to use transform canvas:

\draw [transform canvas={rotate around={20:\O{}}}, name path=a] \O{} -- \E{};

However, I'd like to warn you that this option has to be used with great care.