Cannot combine GeoPosition polygons in version 10.4

Question

I was using with Mathematica 10 for plotting different kinds of maps the function PolygonCombine. It seems that this fucntion has disappeared with the version 10.4? Here is a classical example for the use of this function:

Graphics`Mesh`MeshInit[];

world = CountryData[#, "FullPolygon"] & /@ 
    CountryData["Continents"] // Flatten;

worldplot = 
 Graphics[{FaceForm[White], EdgeForm[Black], PolygonCombine@world} /. 
   Polygon -> Line, Frame -> True, 
  FrameLabel -> {"Longitude", "Latitude"}, ImageSize -> Full]

How I could do the same thing now by replacing the function PolygonCombine without changing all my programs? Thank you.

---

Thank you for your help. But now I have detected another problem: I cannot remove Antartica continents like I was doing previously?

See the following example:

Graphics`Mesh`MeshInit[];

world = CountryData[#,"FullPolygon"] & /@ 
    Cases[CountryData["Continents"], Except["Antarctica"]] // Flatten;

worldplot = 
 Graphics[{FaceForm[White], EdgeForm[Black], 
    Polygon[GeoPosition[#]] & @@ (PolygonCombine[
       Polygon @@@ world[[All, 1]]])} /. Polygon -> Line, 
  Frame -> True, FrameLabel -> {"Longitude", "Latitude"}, 
  ImageSize -> Full]

Thanks a lot.

Answer 1

So when I tried the code from the OP in version 10.3, I get the error message

Graphics`PolygonUtils`PolygonCombine is not a Graphics primitive or directive.

while in version 9 it returns this image

So it is natural to assume that the undocumented function is the culprit, and WRI just removed it without saying anything, which is their prerogative. But I think the issue is with the GeoPosition polygons instead.

Let's look at the representation of the polygons in version 10.3,

CountryData["Germany", "FullPolygon"]

and compare it to the same thing in version 9,

CountryData["Germany", "FullPolygon"]
(* Polygon[{{{7.24916, 53.3298}, {6.99916, 53.359}, ...
            .... {8.59249, 54.5073}}}] *)

So now there is some sort of internal gray box between us and the polygon coordinates, and it seems to be confusing the PolygonCombine function. (Thanks to SquareOne for making this easier) You can convert it to a normal Polygon via

Polygon @@ First@CountryData["Germany", "FullPolygon"]
(* Polygon[{{{53.3298, 7.24916}, {53.359, 6.99916},
            ......{54.5073, 8.59249}}}] *)

But the x and y coordinates have been reversed. For some reason, GeoPosition seems to tell Polygon to swap the coordinates. For this I'll Map Reverse to the second-deepest level of the polygon.

Polygon @@ First@CountryData["Germany", "FullPolygon"] // 
  Map[Reverse, #, {-2}] & // Graphics

Of course you get the exact same output if you use CountryData["Germany", "FullPolygon"], but it is not a normal polygon. Just try Cases[CountryData["Germany", "FullPolygon"] // Graphics, Polygon[_]] to see this.

It's pretty easy to apply this to the world list, just adding one line to the code in the OP

Graphics`Mesh`MeshInit[];

world = CountryData[#, "FullPolygon"] & /@ CountryData["Continents"] //
    Flatten;
world = Map[Reverse, #, {-2}] &@*Polygon @@@ world[[All, 1]];

worldplot = 
 Graphics[{FaceForm[White], EdgeForm[Black], PolygonCombine@world} /. 
   Polygon -> Line, Frame -> True, 
  FrameLabel -> {"Longitude", "Latitude"}, ImageSize -> 600]

SquareOne pointed out that you could skip the Map step and use the fact that GeoPosition inverts the coordinates to your advantage by replacing PolygonCombine@world with Polygon[GeoPosition[#]] & @@ (PolygonCombine[ Polygon @@@ world[[All, 1]]]) This does result in a slightly shorter code (by 6 bytes :-P), but I prefer the Map method for clarity and because it seems to run faster without the extra step of reusing GeoPosition.

To get the map without Antarctica (who needs it!!), we use this

world = CountryData[#, "FullPolygon"] & /@ 
    Cases[CountryData["Continents"], 
     Except[EntityClass["Country", "Antarctica"]]] // Flatten;

world = Map[Reverse, #, {-2}] &@*Polygon @@@ world[[All, 1]];

worldplot = 
 Graphics[{FaceForm[White], EdgeForm[Black], PolygonCombine@world} /. 
   Polygon -> Line, Frame -> True, 
  FrameLabel -> {"Longitude", "Latitude"}, ImageSize -> 600]