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Say I'm looking at a portion of a map that's displayed using Mercator projection with the view bounded at 40°N and 20°N. How do I compute the latitude of the point that's in the centre of that view?
I figured it's not 30° and can compute it by firstly projecting the bounding latitudes onto a square using Mercator, computing the middle point, and then projecting back onto a sphere. But is there a simpler way of achieving the same without having to project to and from Mercator?
Assuming you know the map coordinates of the center -- from those of the top and bottom of the map window -- the problem is called inverse (or reverse) map projection.
From wikipedia: Mercator projection, The spherical model:
latitude = 2 arctan ( exp [y / R]) - pi/2
where y = map coordinates of the center
and R = earth radius
If you are using ArcGIS, you can use a cursor object and pass in the desired spatial reference on the geometry object.
with arcpy.da.SearchCursor(somedatapath, "SHAPE@", spatial_reference=arcpy.SpatialReference(4326)) as rows:
for row in rows:
print row[0].JSON # wow the data is in Lat/Long
Just change the 4326 to what every coordinate system you want to project into.
