# [OSM-dev] Code to convert lat/lon to metres in Mercator projection?

Christopher Schmidt crschmidt at metacarta.com
Tue Jan 9 22:21:14 GMT 2007

On Tue, Jan 09, 2007 at 09:47:29PM +0000, Nick Whitelegg wrote:
> Hello everyone,
>
> Has anyone written any code to convert lat/lon to Mercator projection in metre
> units (metres east and north of the intersection of the Greenwich meridian
> and equator)? There's plenty of lat/lon to Mercator converters around (e.g.
> that in JOSM) but they give the answer in obscure units, e.g:

There's code in the wiki somewhere to do this,but I don't know if it's
up to date. The tried and tested code that I'm using (tried and tested
in over a half-dozen applications) is in
http://labs.metacarta.com/osm/osm.js . Javascript code follows.

(This code is a direct port of the proj4 code for projection.)

return ang * (180.0/Math.PI)
}
return ang * (Math.PI/180.0)
}
function merc_x(lon) {
var r_major = 6378137.000;
}
function unmerc_x(lon) {
var r_major = 6378137.000;
}

function unmerc_y(y) {
var r_major = 6378137.000;
var r_minor = 6356752.3142;
var temp = r_minor / r_major;
var es = 1.0 - (temp * temp);
var eccent = Math.sqrt(es);
var eccnth = .5 * eccent;
var ts = Math.exp(- y / r_major);
var phi = Math.PI/2 - 2 * Math.atan(ts);
var i = 0;
dphi = 1;
var M_PI_2 = Math.PI/2;
while(Math.abs(dphi) > 0.000000001 && i < 15) {
var con = eccent * Math.sin (phi);
dphi = M_PI_2 - 2. * Math.atan (ts * Math.pow((1. - con) /
(1. + con), eccnth)) - phi;
phi += dphi;
i++;
}
}
function merc_y(lat) {
if (lat > 89.5)
lat = 89.5;
if (lat < -89.5)
lat = -89.5;
var r_major = 6378137.000;
var r_minor = 6356752.3142;
var temp = r_minor / r_major;
var es = 1.0 - (temp * temp);
var eccent = Math.sqrt(es);
var sinphi = Math.sin(phi);
var con = eccent * sinphi;
var com = .5 * eccent;
con = Math.pow(((1.0-con)/(1.0+con)), com);
var ts = Math.tan(.5 * ((Math.PI*0.5) - phi))/con;
var y = 0 - r_major * Math.log(ts);
return y;
}
function merc(x,y) {
return [merc_x(x),merc_y(y)];
}

Regards,
--
Christopher Schmidt
MetaCarta