Assigning coordinates in TikZ

Question

I use TikZ to draw arrows and labels on maps, generated from other applications.

A minimal example with a global mercator projection might look like this:

\documentclass[]{standalone}
\usepackage{tikz}

\begin{document}
    \begin{tikzpicture}
        \node[anchor=south west,inner sep=0] (image) at (0,0) 
            {\includegraphics[width=18cm]{my_mercator_world_map.jpg}};
            \begin{scope}[x={(image.south east)},y={(image.north west)}]
                \draw [->] (0.5,1) -- (0.5421,0.6353);
                \node[draw] at (0.2,0.05) {a}; 
        \end{scope}
    \end{tikzpicture}   
\end{document}

It's easy to normalise map coordinates to TikZ coordinates, but sometimes I have many labels or even TikZ generated polygons. It would be very convenient to give the coordinates as geographical coordinates instead of a number between 0 and 1.

Is there a simple way to normalise TikZ coordinates so that they can be given in e.g. decimal lat-lon if I know the exact extent of the map?

In the case above, I'd like to be able to give coordinates as:

\draw [->] (0,90) -- (7.578,12.177);
\node[draw] at (-108,-81) {a}; 

I also work with local maps, but we can assume that all have a rectangular grid. Map coordinates to any projection would be fantastic, but I guess that is beyond the scope of TikZ.

---

EDIT

A partly working answer can be found here: tex.stackexchange.com/a/9562/121799

Answer 1

Based on the linked answer, and using coordinate transformations, you can do this:

\documentclass[tikz]{standalone}
\usetikzlibrary{fpu, calc}
\begin{document}
\begin{tikzpicture}
    \node[anchor=south west,inner sep=0] (image) at (0,0) {\includegraphics[width=0.9\textwidth]{example-image}};
    \begin{scope}[x={($1/360*(image.south east)$)},
        y={($1/180*(image.north west)$)},
        shift={(180,90)},
        ]
        \draw[help lines, red, xstep=45,ystep=30] (-180,-90) grid (180,90);
        \foreach \x in {-180, -135,...,180} { \node [anchor=north] at (\x,-90) {\x}; }
        \foreach \y in {-90,-60,...,90} { \node [anchor=east] at (-180,\y) {\y}; }
    \end{scope}
\end{tikzpicture}
\end{document}

For more complex transformation, you can define your own coordinate system; look at the tikz manual, section 13.2.5 "Defining New Coordinate System" (at pag. 137 in my copy) and at this example.

Then you can use it, like for example:

\documentclass[tikz]{standalone}
\usetikzlibrary{fpu, calc}
\newcommand{\showpoint}[3][5,-15]{
    \path (#2) node[circle, fill=blue, inner sep=1pt]{} coordinate(tmp);
    \draw [thick, blue, <-] (tmp) -- ++(#1) 
        node[fill=white,]{#3};
    }
\begin{document}
\begin{tikzpicture}
    \node[anchor=south west,inner sep=0] (image) at (0,0) {\includegraphics[width=0.9\textwidth]{example-image}};
    \begin{scope}[x={($1/360*(image.south east)$)},
        y={($1/180*(image.north west)$)},
        shift={(180,90)},
        ]
        \draw[help lines, red, xstep=45,ystep=30] (-180,-90) grid (180,90);
        \foreach \x in {-180, -135,...,180} { \node [anchor=north] at (\x,-90) {\x}; }
        \foreach \y in {-90,-60,...,90} { \node [anchor=east] at (-180,\y) {\y}; }
        % use them
            \showpoint{0,90}{North Pole}
            \showpoint{100,90}{still North Pole}
            \showpoint{-100,90}{North Pole, again}
            \showpoint{-3,40}{Madrid}
            \showpoint{-105,40}{Denver}
            \showpoint[5,15]{10,44}{Sarzana}
            %
            \showpoint{0,0}{geolocation list bug}
    \end{scope}
\end{tikzpicture}
\end{document}