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plotting - How do I plot coordinates (latitude and longitude pairs) on a geographic map?


I'm attempting for the first time to create a map within Mathematica. In particular, I would like to take an output of points and plot them according to their lat/long values over a geographic map. I have a series of latitude/longitude values like so:


 {{32.6123, -117.041}, {40.6973, -111.9},   {34.0276, -118.046}, 
  {40.8231, -111.986}, {34.0446, -117.94},  {33.7389, -118.024}, 

  {34.122, -118.088},  {37.3881, -122.252}, {44.9325, -122.966}, 
  {32.6029, -117.154}, {44.7165, -123.062}, {37.8475, -122.47}, 
  {32.6833, -117.098}, {44.4881, -122.797}, {37.5687, -122.254}, 
  {45.1645, -122.788}, {47.6077, -122.692}, {44.5727, -122.65},
  {42.3155, -82.9408}, {42.6438, -73.6451}, {48.0426, -122.092}, 
  {48.5371, -122.09},  {45.4599, -122.618}, {48.4816, -122.659}, 
  {42.3398, -70.9843}}

I've tried finding documentation on how I would proceed but I cannot find anything that doesn't assume a certain level of introduction to geospatial data. Does anyone know of a good resource online or is there a simple explanation one can supply here?



Answer




data:


latlong = {{32.6123, -117.041}, {40.6973, -111.9}, {34.0276, -118.046}, 
{40.8231, -111.986}, {34.0446, -117.94}, {33.7389, -118.024}, 
{34.122, -118.088}, {37.3881, -122.252}, {44.9325, -122.966},
{32.6029, -117.154}, {44.7165, -123.062}, {37.8475, -122.47}, 
{32.6833, -117.098}, {44.4881, -122.797}, {37.5687, -122.254},
{45.1645, -122.788}, {47.6077, -122.692}, {44.5727, -122.65}, 
{42.3155, -82.9408}, {42.6438, -73.6451}, {48.0426, -122.092},
{48.5371, -122.09}, {45.4599, -122.618}, {48.4816, -122.659}, {42.3398, -70.9843}}


To put the data on latitude-longitude pairs on a map, yo will need to transform your data based on the projection method used by the map.


For example,


 coords = CountryData["UnitedStates", "Coordinates"];

gives the latitude-longitude data for US boundaries.


To use this data to put together a map with a specific projection method (say Mercator), you need to transform your data


 Map[ GeoGridPosition[ GeoPosition[#], "Mercator"][[1]] & , {latlong}, {2}]

which gives




  {{{1.09884, 0.602677}, {1.18857, 0.778879}, {1.0813, 
   0.632239}, {1.18707, 0.781777}, {1.08315, 0.632597}, {1.08169, 
   0.62617}, {1.08057, 0.634228}, {1.00789, 0.704491}, {0.995431, 
   0.879708}, {1.09687, 0.602482}, {0.993756, 0.874393}, {1.00409, 
   0.714614}, {1.09785, 0.604149}, {0.998381, 0.868794}, {1.00786, 
   0.708463}, {0.998538, 0.88544}, {1.00021, 0.947273}, {1.00095, 
   0.870866}, {1.694, 0.816595}, {1.85624, 0.824365}, {1.01069, 
   0.958578}, {1.01072, 0.97155}, {1.0015, 0.892771}, {1.00079, 
   0.970088}, {1.90268, 0.817169}}}


Doing this transformation for both your data and the latitude-longitude data for world countries inside Graphics:


 Graphics[{Red, Point /@ Map[ 
  GeoGridPosition[ GeoPosition[#], 
   "Mercator"][[1]] & , {latlong}, {2}], Gray, 
 Polygon[Map[ GeoGridPosition[ GeoPosition[#], "Mercator"][[1]] & , 
  CountryData[#, "Coordinates"], {2}]] & /@ 
 CountryData["Countries"]}]

you get:


world map and lat-long points



Now I know I can focus on US:


 Graphics[{ Gray, 
 Polygon[Map[ GeoGridPosition[ GeoPosition[#], "Mercator"][[1]] & , 
 CountryData["UnitedStates", "Coordinates"], {2}]], Red, 
 PointSize[.02], Point /@ Map[ 
 GeoGridPosition[ GeoPosition[#], 
   "Mercator"][[1]] & , {latlong}, {2}]}]

to get


us and points



A simpler method avoiding GeoPosition, GeoGridPosition ... etc


Get the coordinates of US:


 coords = CountryData["UnitedStates", "Coordinates"];

and use


 Graphics[{EdgeForm[Black], Polygon[Reverse /@ First[coords]], Red, 
 Point /@ Reverse /@ latlong}]

to get


simpler approach result



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