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Is it possible to use a background image in a polygon without rasterizing the polygon?

I tried with textures, but they seem to be viable only for simple polygons.

I want to put a flag as the background of the polygon that represents a country shape. I can do this for one country by rasterizing the polygon:

ImageAdd[
    Graphics[CountryData["Monaco", "Polygon"]], 
    CountryData["Monaco", "Flag"]
]

monaco

But by rasterizing the polygon, I make it difficult to apply this procedure to several neigboring countries and assemble them together.

I would like to put each country flag in the background of, for example:

Graphics[
    {EdgeForm[White], 
     CountryData[#, "Polygon"] & /@ {"Venezuela", "Colombia"}}]

colombia and venezuela

Solution

After seeing cormullion answer, I was able to do what I wanted:

Graphics[
 {EdgeForm[Black],
  {{Texture[ImageReflect[CountryData[#, "Flag"], Top -> Right]], 
    CountryData[#, "Polygon"] /. 
      {Polygon[a_] :> Polygon[First[a], VertexTextureCoordinates -> 
       Transpose[Rescale /@ Transpose[First[CountryData[#, "Coordinates"]]]]]}} & /@ 
CountryData["SouthAmerica"]}}]

southamerica

The key part is the use of Rescale[]. Thank you!

share|improve this question
I wish Mathematica had more advanced vector-graphics and layering; this is so simple in a drawing program. A good solution would preserve everything as vector with no rasterized textures, but I don't think it can be done in a general way. -- edit I didn't notice that the Flag data is already raster. I guess Texture makes the most sense in that case. – Mr.Wizard♦ Feb 4 '12 at 23:45
You may find ImagePad useful if you want small flags inside country borders – Szabolcs Feb 5 '12 at 1:00
1  
One caveat: This texture-based approach leads to a graphic that cannot be exported to PDF (on Macs, at least). This seems worth mentioning since you specifically asked for a method preserving the vector character of the borders. Just in case anyone encounters this, a workaround for this problem is to export to svg first, and then use Inkscape to convert to PDF. – Jens Feb 5 '12 at 19:24

2 Answers

up vote 10 down vote accepted

This example is from the documentation for Texture in Mathematica version 8:

With[{vc = 
 Transpose[
  Rescale /@ Transpose[First[CountryData[#, "Coordinates"]]]]}, 
Show[CountryData[#, "Shape"], 
 ImageSize -> {{100}, {100}}] /. {RGBColor[__] :> 
  Texture[ImageReflect[Image[CountryData[#, "Flag"]], 
    Top -> Right]], 
 Polygon[a_] :> 
  Polygon[First[a], VertexTextureCoordinates -> vc]}] & /@ 
CountryData["SouthAmerica"]

but I don't know whether it does what you need. Still, it looks pretty.

flags

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up vote 3 down vote

Try:

Graphics[{EdgeForm[White], {{Texture[Image[CountryData[#, "Flag"]]], 
  Polygon[First@First[CountryData[#, "Polygon"]], 
   VertexTextureCoordinates ->Transpose[
     Rescale /@ Transpose[First@First[CountryData[#, 
         "Polygon"]]]]]}} & /@ {"Venezuela", "Colombia"}}]

which gives

maps and flags

share|improve this answer
Note that your country coordinates are somewhat rotated (transposed). – Artes Feb 5 '12 at 0:33
Thank you @Artes. I need to change Coordinates to Polygon in the first argument of Polygon. – kguler Feb 5 '12 at 0:36
Now, country polygons are correctly oriented while flags are rotated. – Artes Feb 5 '12 at 0:50
@Artes, thank you again. Just noticed, that OP alrady put together the solution more than an hour ago. – kguler Feb 5 '12 at 1:46

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