geographic maps with TikZ/pgfplots

Question

I have recently discovered pgfplots and I love it. I'm converting the figures from my thesis to pgfplots, or at least the ones I have made myself. One of my figures is a map that I created using the Matlab Mapping Toolbox. I'd love to convert it to LaTeX + pgfplots, but I feel like I don't really have the tools. For mapping, one would need:

• A projection, e.g. to convert from GIS coordinates to lat/lon (or UTM/UPS, or ...). This should be possible to build on top of the existing mathematical engine. Equirectangular projections are easiest. Preferably quite integrated, so one can use it as a coordinate system, such as (axis latlon:30.0,40.0).
• Something to keep track of scale, e.g. a scale-ruler would be quite nice to add directly.
• Anything else?

So far I used Matlab but I am not too happy about the result. Did anybody ever try to hack something like this together?

(This should be a community wiki question, but I don't see any button to mark it as such, maybe I don't have the reputation?)

Answer 1

I've used PGFplots to generate some maps of a local area in the past, doing watershed calculations in GRASS and exporting the vectors as ASCII files, which can be plotted by PGFplots relatively easily. That only required an xy coordinate system (spatial extent of about 100 km by 100 km), and distortions were negligible.

As you noted, on a (near) global scale, things become more complicated, and plate caree is by far the easiest thing to start with.

Here's a very basic attempt to get started (I've been meaning to look into this for a while):

World map in equidistant rectangular (Plate Caree) projection, with Tissot's Indicatrix in blue, and the Bermuda Triangle shown in orange

The world map is part of the Gnuplot data: world.dat

By setting disabledatascaling in PGFplots, you can use normal coordinates instead of axis cs coordinates, and the scaling factors to convert between canvas coordinates and data coordinates will be available in \pgfplotunitxlength and \pgfplotsunitylength.

axis equal makes sure that the x and y unit lengths are the same.

I've written a key called scale circle, which you can add to the options of a \draw circle. The key will scale the x radius according to the latitude.

What this approach doesn't do is curve lines that don't follow longitudes or latitudes. I'm not sure what the best approach for this is, I'm guessing some to path magic (Andrew Stacey?), or an \addplot expression. I'll have a think about this.

\documentclass{article}

\usepackage{pgfplots}

\begin{document}

\makeatletter
\pgfmathsetmacro\kmAtEquator{36/4200} % Degree/km at equator
\tikzset{
    scale circle/.code={
        \pgfgetlastxy{\x@coord}{\y@coord}
        \pgfmathsetmacro\xscale{\pgfkeysvalueof{/tikz/x radius}*1/cos(\y@coord/\pgfplotsunitylength)}
        \tikzset{/tikz/x radius=\xscale}
    },
    scale bar/.code={
        \pgfgetlastxy{\x@coord}{\y@coord}
        \pgfmathsetmacro\xscale{1/cos(\y@coord/\pgfplotsunitylength)}
        \tikzset{
            insert path={
                node [
                    below,
                    font=\scriptsize
                ] {0} 
                +(0,-2pt) -- +(0,0) -- ++(#1*\xscale*\kmAtEquator,0) 
                node [
                    below,
                    font=\scriptsize,
                    inner xsep=1pt,
                    label={[inner sep=0pt,font=\scriptsize]right:km}] {#1}
                -- +(0,-2pt)
            }
        }
    },
    scale bar/.default=2000
}
\makeatother


\begin{tikzpicture}
\begin{axis}[   
    grid=both, ytick={-60,-30,...,90}, xtick={-180,-150,...,180},
    grid style=black!10,
    enlargelimits=false,
    axis equal,
    scale only axis,
    width=10cm,
    height=5cm,
    disabledatascaling, clip=false
]

\addplot [] table {world.dat};



\pgfplotsextra{
    \foreach \x in {-160,-120,...,160}{
        \foreach \y in {-75,-50,...,75}{
            \fill [cyan, opacity=0.25] (\x,\y) circle [radius=5, scale circle];
        }
    }
    \fill [orange] (-64.9,32.3)   -- (-66.1,18.5) node [anchor=mid west, inner sep=1pt, orange!75!black, fill=white, text opacity=1,fill opacity=0.75, align=left] {Bermuda\\Triangle} -- (-80.4,25.2)   -- cycle;
    \draw (185,0) [scale bar];
    \draw (185,45) [scale bar];
    \draw (185,60) [scale bar];
}
\end{axis}
\end{tikzpicture}

\end{document}