title: Latitude/longtitude conversion to image x/y coordinates (Miller Cylindrical projection)
body: <p>As already said in the title, I need some help with converting lat/long to x/y coords in Miller Cylindrical projection. I`m currently writing an app (in Java) which gets city list as an input and then gets lat/long for each city from Yahoo Placefinder. I used <a href="http://mathworld.wolfram.com/MillerCylindricalProjection.html" rel="nofollow">these</a> formulas in my code. <a href="http://img29.imageshack.us/img29/6572/99432143.png" rel="nofollow">Here is an example</a> of what I get. (image is for the reference only, not the one I use). As you can see the X positions are only a few pixels (2-3) off, this can be a problem with my calculations of prime meridian shift (CENTRAL_MERIDIAN_OFFSET) in this map. But the main problem is incorrect Y coordinates.</p>
  
  <p>Here is my code (updated - 34px compensation for equator offset):</p>
  
  <pre><code>public final double W = 6343;
  public final double H = 4767 - 34;
  
  protected Point toMillerXY(double lon, double lat)
  {
      double x, y;
  
      lon = Utils.degToRad(lon);
      lat = Utils.degToRad(lat);
  
      x = lon - CENTRAL_MERIDIAN_OFFSET;
      y = 1.25 * Math.log( Math.tan( 0.25 * Math.PI + 0.4 * lat ) );
  
      x = ( W / 2 ) + ( W / (2 * Math.PI) ) * x;
      y = ( H / 2 ) - ( H / ( 2 * 2.303412543 ) ) * y;
  
      y += 34;
  
      return new Point(x, y);
  }
  
  Output:  
  Fetching data with: http://where.yahooapis.com/geocode?location=Buenos+Aires,Argentina
  Latitude: -34.608521, longitude: -58.373539
  ---
  Fetching data with: http://where.yahooapis.com/geocode?location=Tokyo,Japan
  Latitude: 35.670479, longitude: 139.740921
  ---
  Fetching data with: http://where.yahooapis.com/geocode?location=Cape+Town,CAR
  Latitude: -33.919060, longitude: 18.421961
  ---
  Fetching data with: http://where.yahooapis.com/geocode?location=Rome,Italy
  Latitude: 41.903110, longitude: 12.495760
  ---
  Total cities: 4
  Result for Buenos Aires: 1964.598428, 3046.740995
  Result for Tokyo: 5455.265150, 1732.669551
  Result for Cape Town: 3317.692474, 3032.814395
  Result for Rome: 3213.276105, 1602.176163
  </code></pre>
  
  <p>Obviously, something is wrong with Y coord calculation. I`m not sure whether 5.6 should really be the right value but the vertical range of Millers projection was said to be -2.3..+2.3 in one of the references I read so I used it.</p>