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Polygon projection in CountryData incorrect?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg116270] Polygon projection in CountryData incorrect?
  • From: "Sjoerd C. de Vries" <sjoerd.c.devries at gmail.com>
  • Date: Wed, 9 Feb 2011 02:10:26 -0500 (EST)

CountryData contains a polygon for every country. It can be output in
various projections using a specification like  {"Polygon",
"Mercator"}.

However, the resulting polygon doesn't seem to be consistent with a
transformation using GeoGridPosition and GeoPosition.

If I plot Amsterdam using its CityData coordinates transformed with a
Mercator projection it falls outside the Netherland's borders (1st
example below). When I use the alternative approach (2nd example)
everything seems OK. Am I doing something wrong or is this a bug?


Graphics[
 {
  {FaceForm[], EdgeForm[Black],
   CountryData["Netherlands", {"Polygon", "Mercator"}]},
  Red, PointSize[0.02],
  Point@GeoGridPosition[
     GeoPosition[
      CityData[{"Amsterdam", "NoordHolland", "Netherlands"},
       "Coordinates"]], "Mercator"][[1]]
  }
 ]


Graphics[
 {
  {FaceForm[], EdgeForm[Black],
   Polygon[Map[GeoGridPosition[GeoPosition[#], "Mercator"][[1]] &,
     CountryData["Netherlands", "Coordinates"], {2}]]},
  Red, PointSize[0.02],
  Point@GeoGridPosition[
     GeoPosition[
      CityData[{"Amsterdam", "NoordHolland", "Netherlands"},
       "Coordinates"]], "Mercator"][[1]]
  }
 ]

Cheers -- Sjoerd


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