My question here is fairly basic, and I'm sure I'm overlooking something basic. I know about CountryData for creating shapes of entire countries, and it works, to an extent; I can plot geographical data on it with the coordinates, but I'd like to have a magnified view of a state alone. The goal is to be able to measure borderlines. Is there built-in functionality for this, or do I have to import a shape file of a state?


There is no built in option, however for the US it's very easy because the coordinates of the state borderlines are all over the Internet. This led me to one such data set. I'll include how I cleaned it up, like this:

data = Import["http://econym.org.uk/gmap/states.xml"];
name[{"name" -> n_, ___}] := n
coordinates[XMLElement["point", {"lat" -> lat_, "lng" -> lng_}, {}]] := {lat, lng}
states = 
  {name@Part[#, 1], coordinates /@ Part[#, 2]} & /@ 
    Partition[Cases[data, XMLElement["state", state__] :> state, Infinity], 2];

However there is no point in redoing those things over and over. You might as well define states like this (the link leads to Pastebin where the list of coordinates is available. The list is too large to post here.)

To draw a specific state you can do something like this:

state[name_] := states /. {___, {name, pts_}, ___} :> (ToExpression /@ pts)

    RGBColor[0.896, 0.8878, 0.8548], EdgeForm[GrayLevel[0]], 
    PointSize[Medium], Red,
    Point[CityData[{"Clinton", "Indiana", "United States"}, "Coordinates"]],
    Point[CityData[{"Indianapolis", "Indiana", "United States"}, "Coordinates"]]
    }], Pi/2], Right]


Of course you will be able to design better utility functions than I have to stuff away operations such as ImageReflect and ImageRotate.

Just another example to show how this can be used to draw the US map in it's entirety. You could very easily style each state individually.

    RGBColor[0.896, 0.8878, 0.8548], EdgeForm[GrayLevel[0]], 
    Polygon[state[First@#] & /@ (
       states /. {
         {"Hawaii", __} -> Sequence[],
         {"Alaska", __} -> Sequence[]
    PointSize[Medium], Red,
    Point[CityData[{"Clinton", "Indiana", "United States"}, "Coordinates"]],
    Point[CityData[{"Indianapolis", "Indiana", "United States"}, "Coordinates"]]
    }], Pi/2], Right]

enter image description here

(I know your purpose is not visualization, but someone will surely come along sooner or later looking for how to do visualization.)


As of Mathematica 10 we don't have to find data sources ourselves.

indiana = GeoGraphics[{
    Entity["AdministrativeDivision", {"Indiana", "UnitedStates"}]]},
  GeoBackground -> None,
  Frame -> True,
  FrameTicks -> None


To extract the polygon coordinates we may do this:

pts = Cases[indiana, Polygon[data_] :> data, Infinity];
(* To plot the polygon: Graphics[Polygon[First@pts]] *)

Or we can get the polygon like this:

EntityValue[Entity["AdministrativeDivision", {"Indiana", "UnitedStates"}], "Polygon"]
| improve this answer | |
  • $\begingroup$ Thank you so much! I had already worked out a similar approach before your answer, in part from the comments above, but this has helped streamline it a bit. Just as a side question, is there any way to make your two points above different sizes in the same Graphics function? $\endgroup$ – Smith W. Mar 23 '14 at 2:18
  • $\begingroup$ @SmithW. Yes, you can easily change the settings in between graphics primitives, for example {Red, PointSize[Small], Point[{0,0,0}], Green, PointSize[Large], Point[{1,0,0}]} creates two different points with different colors and sizes. Look up PointsSize to see how you can specify different sizes. $\endgroup$ – C. E. Mar 23 '14 at 2:31
  • 1
    $\begingroup$ Technically, both GeoGraphics and Entity use wolfram-alpha, so they're dependent on external data sources. $\endgroup$ – rcollyer Aug 22 '14 at 12:35
  • $\begingroup$ @rcollyer Thanks, I changed my wording. $\endgroup$ – C. E. Aug 22 '14 at 12:55

As mentioned this is dead easy now with Entity:

 With[{h = RandomReal[.9], s = RandomReal@{.4, .8}, 
      b = RandomReal@{.4, .6}},
      EdgeForm@Hue[h, s, b + .2], Hue[h, s + .2, b - .2], Polygon@#}
     ] & /@ (EntityList[
      EntityClass["AdministrativeDivision", "AllUSStatesPlusDC"]] // 
       Entity["AdministrativeDivision", {"DistrictOfColumbia" | 
          "Alaska" | "Hawaii", "UnitedStates"}]] &) // 
  RandomSample[#, 15] &

enter image description here

And with all the Geo* functionality we can get things like perimeters trivially:

In[90]:= Map[(#[[2, 1]] -> 
       Apply[Join]@First@First@EntityValue[#, "Polygon"]) &, 

Out[90]= {"NorthCarolina" -> 3500.57, "Connecticut" -> 682.115, 
 "Tennessee" -> 1278.5, "SouthDakota" -> 1265.04, "Hawaii" -> 1440.61,
  "Delaware" -> 502.202, "Florida" -> 6264.55, "Iowa" -> 1089.67, 
 "Alaska" -> 58774.3, "Oklahoma" -> 1565.76, "Missouri" -> 1428.25, 
 "Arkansas" -> 1286.78, "Texas" -> 4460.52, "WestVirginia" -> 1136.57,
  "NewHampshire" -> 529.748}
| improve this answer | |
  • $\begingroup$ +1, but I would not call it "dead easy"... $\endgroup$ – Anton Antonov May 20 '17 at 22:52

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