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I'm sure I'm overlooking something obvious, but I can't draw groups of countries. Here are two countries and two country groups:

france = CountryData["France", "Coordinates"] ;
usa = CountryData["United States", "Coordinates"];  
eu = CountryData["EU", "Coordinates"];
africa = CountryData["Africa", "Coordinates"];

Swapping the coordinates so that longitude comes before latitude:

franceA = Cases[france , {lat_, long_} :> {long, lat}, Infinity];
usaA = Cases[usa, {lat_, long_} :> {long, lat}, Infinity];
euA = Cases[eu, {lat_, long_} :> {long, lat}, Infinity];
africaA = Cases[africa, {lat_, long_} :> {long, lat}, Infinity];

They should all plot:

Table[Graphics[Line[coords]], 
 {coords, {franceA, usaA, euA, africaA}}]

but the groups don't:

error

And I tried this:

Table[
 Graphics[
  Polygon /@ Map[
    GeoGridPosition[GeoPosition[#], 
       "Mercator"][[1]] &, {coords}, {2}]], 
 {coords, {france, usa, eu, africa}}]

with a similar problem:

error 2

I'm thinking that two of the lists are the wrong shape or size, but they look OK:

Dimensions[#] & /@ 
  {france, usa, eu, africa, franceA, usaA, euA, africaA}

{{2}, {1, 4672, 2}, {27}, {58}, {1110, 2}, {4672, 2}, {18404, 2}, {16082, 2}}

I may need some Flattening magic somewhere...?

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3 Answers 3

up vote 6 down vote accepted

One of the problems, as halirutan has already mentioned, is that the patterns are not restrictive enough. {x_, y_} will also match {{dog}, {cat}}, whereas we want it to only match pairs of numerical coordinates. However, that is not the reason for the error that you're getting (although it makes it harder to fix). As it turns out, you get the same error with your original eu and africa (before flipping). Why does this happen only with these two and not france or usa?

Observe that both these are continents, which gives us a hint at where the problem lies. The coordinate list structure for countries looks like (pseudocode)

{
    {{lat11, lon11}, ..., {lat1N, lon1N}}, (* largest land polygon *)
    {{lat21, lon22}, ..., {lat2M, lon2M}}, (* next largest polygon *)
    ...
}

so when you use Line to plot them, you're using this definition of Line:

Line[{{pt11, pt12, ...}, {pt21, ...}, ...}] represents a collection of points

However, the list structure for continents looks like

{
    {   (* Country A *)
        {{latA11, lonA11}, ..., {latA1NA, lonA1NA}}, (* largest land polygon of A *)
        {{latA21, lonA22}, ..., {latA2MA, lonA2MA}}, (* next largest polygon of A *)
        ...
    },

    {   (* Country B *)
        {{latB11, lonB11}, ..., {latB1NB, lonB1NB}}, (* largest land polygon of B *)
        {{latB21, lonB22}, ..., {latB2MB, lonB2MB}}, (* next largest polygon of B *)
        ...
    },
    ...
}

which does not match any valid syntax for Line.


Let's look at where exactly the problem lies in your euA:

Table[Graphics[Line@Take[euA, n]] ~Labeled~ n, {n, 5161, 5170, 1}]

euA[[5167]] // Short

Element 5167 is a list of lists and not a pair of coordinates as the first 5166 were. And indeed, Dimensions@euA[[5167]] returns {2}, and as I explained above, the pattern just matched the sublists and flipped them, leaving the coordinates intact.


Now coming to plotting eu, I don't think Cases is the right tool, since it removes all information about how the polygons are grouped. Instead, you can just Flatten it appropriately and reverse the coordinates as

Graphics[Line@Flatten[eu, 1] /. {lat_?NumericQ, lon_?NumericQ} :> {lon, lat}]

Line correctly interprets this as a collection of lines and plots disconnected islands, and thus you don't get the crisscrossing of lines across the plot as in halirutan's answer.

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1  
Ah, that's excellent - you've explained exactly what's going on. Many thanks! –  cormullion Aug 10 '13 at 20:50

You need to ensure that your rule only matches when you have a pair of numeric coordinates:

france = CountryData["France", "Coordinates"];
usa = CountryData["United States", "Coordinates"];
eu = CountryData["EU", "Coordinates"];
africa = CountryData["Africa", "Coordinates"];

rule = {lat_?NumericQ, long_?NumericQ} :> {long, lat};
franceA = Cases[france, rule, Infinity];
usaA = Cases[usa, rule, Infinity];
euA = Cases[eu, rule, Infinity];
africaA = Cases[africa, rule, Infinity];

Table[Graphics[Line[coords]], {coords, {franceA, usaA, euA, africaA}}]

Mathematica graphics

Is there any particular reason why you don't use this here:

Graphics@CountryData["EU", "Polygon"] /. Polygon :> Line

Mathematica graphics

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Cool, thanks. What's in there that doesn't work like France and USA? I couldn't see anything - I had a look for MissingValue... (And there's usually no reason for my odd coding... :) –  cormullion Aug 10 '13 at 18:14
    
I assume the different countries are stored in different point sublists. Therefore, with your code something like this is likely to happen: Cases[{{{a,b},{c,d}},{{e,f},{g,h}}},{lat_,long_}:>{long,lat},Infinity] –  halirutan Aug 10 '13 at 18:39
    
@rm-rf I suppose I was fooled by the fact that France worked even though it had two pieces... –  cormullion Aug 10 '13 at 18:49

Since you're getting only coordinates, you can map Reverse instead of using ReplaceAll.

Graphics[{EdgeForm[Black], Opacity[0], Polygon@Flatten[Map[Reverse, eu, {-2}], 1]}]

Mathematica graphics

Unless I missed something, I don't think anyone has pointed out yet that if you use Line instead of Polygon, you get small gaps in each segment. For instance there is one where France meets Italy:

enter image description here

For the rest, I think rm-rf and halirutan have explained it admirably.

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Monte Carlo not being in the EU. - I'd forgotten. –  cormullion Aug 11 '13 at 7:24

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