1q) Suppose the map is to be 1000x800 pixels.  We want to do a map of just Japan. 
Where is the southernmost point of japan plotted?


Find the point
  select * from edges where Polygon in (select polygon from polygons where code = "ja") order by latitude limit 1;
   +---------+------+-----------+------------+
   | Polygon | Edge | Latitude  | Longitude  |
   +---------+------+-----------+------------+
   |     560 |  278 | 28.022601 | 116.984001 |
   +---------+------+-----------+------------+


Find the edges of the map
   select min(latitude), min(longitude), max(latitude), max(longitude) from edges where Polygon in (select polygon from polygons where code = "ja") ;
   +---------------+----------------+---------------+----------------+
   | min(latitude) | min(longitude) | max(latitude) | max(longitude) |
   +---------------+----------------+---------------+----------------+
   |     28.022601 |     116.172001 |     48.574901 |     125.048001 |
   +---------------+----------------+---------------+----------------+


Use the formula
   x = width * (lon - min_lon) / (max_lon - min_lon)
   x = 1000 * (116.984001 - 116.172001) / (125.048001 - 116.172001)
   x = 91.48

   y = height - height * (lat - min_lat) / (max_lat - min_lat)
   y = 800 - 800 * ( 28.022601 - 28.022601) / (28.022601 - 48.574901) 
   y = 0;