Calculate lat lon bounds for individual tile generated from gdal2tiles

Question

I have multiple tile sources generated using gdal2tiles I'd like to present on the same map. So when presenting a tile I need to determine which source to serve it up from, checking against the bounds.

Anyone know how to calculate the lat lon bounds for a single tile based purely on zoom, x, and y (from the file structure generated by gdal2tiles)? BTW: I'm using Google Maps API v3 in case there's a need to call some functionality from the API to help with calculations.

The reason I'm restricted to purely zoom, x, and y is because the tiles aren't just getting called by an overlay on the map but also some custom print functionality that allows printing outside of the map.

Answer 1

The math is described at:

http://www.maptiler.org/google-maps-coordinates-tile-bounds-projection/

…including the source code for command line utility and an online demonstration.

It is also pretty simple math:

function tile2long(x,z) { return (x/Math.pow(2,z)*360-180); }

function tile2lat(y,z) {
    var n=Math.PI-2*Math.PI*y/Math.pow(2,z);
    return (180/Math.PI*Math.atan(0.5*(Math.exp(n)-Math.exp(-n))));
}

Note the difference between XYZ/Google vs TMS in y axis.

Google Maps API V3 gives you the required functions too via .fromPointToLatLng() of map.getProjection().

Answer 2

This OpenStreetMap wiki page might be helpful for other languages as well:

https://wiki.openstreetmap.org/wiki/Slippy_map_tilenames#Implementations

Answer 3

This is my working code:

jsfiddle sample of google image map type overlay

jsfiddle another sample of google overlay image

function tile2long(x,z) {

  return (x/Math.pow(2,z)*360-180);

}





function tile2lat(y,z) {

  var n=Math.PI-2*Math.PI*y/Math.pow(2,z);

  return (180/Math.PI*Math.atan(0.5*(Math.exp(n)-Math.exp(-n))));

}





 var x = coord.x;

 var y = coord.y;

 var z = zoom;



 var NW_long = tile2long(x,z);



 var SW_long = tile2long(x,z);

 var SW_lat =  tile2lat(y+1,z);



 var NE_long = tile2long(x+1,z);

  var NE_lat =  tile2lat(y,z);







  var export_bbox = SW_long + ',' + SW_lat + ',' + NE_long + ',' + NE_lat;



     var url_param = '&format=png&size=256,256&transparent=true&f=image&bboxSR=4326&imageSR=4326';





   var url_layers =''





       var root_url = 'https://sampleserver1.arcgisonline.com/ArcGIS/rest/services/Specialty/ESRI_StateCityHighway_USA/MapServer/export?bbox=';



     var tile_url = root_url + export_bbox + url_param + url_layers;

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