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Build Mercator Projection of Continents using InverseGudermannian
The Mercator map projection transforms the longitude (in radians) into gd-1().
In[1]:=

Click for copyable input
Table[Labeled[

    Graphics[{EdgeForm[Black], 

        FaceForm[RandomChoice[ColorData[10, "ColorList"]]], Polygon[

         CountryData[#, 

           "Coordinates"] /. {y_?NumberQ, x_} :> {x, 

            Sign[y] InverseGudermannian[Min[Abs[y], 85] Degree]/Degree}

         ]} & /@ CountryData[continent]], 

    Style[continent, 

     FontFamily -> "Helvetica"]], {continent, {"Europe", "Africa", 

     "NorthAmerica", "SouthAmerica", "Asia", "Oceania"}}] // 

  Partition[#, 3, 3] & // Grid
Out[1]=