Convert Lambert 93 to GPS Coordinates Latitude / Longitude (wgs84)

gistfile1.js

Math.tanh = Math.tanh || function(x) {
    if(x === Infinity) {
        return 1;
    } else if(x === -Infinity) {
        return -1;
    } else {
        return (Math.exp(x) - Math.exp(-x)) / (Math.exp(x) + Math.exp(-x));
    }
};

Math.atanh = Math.atanh || function(x) {
    return Math.log((1+x)/(1-x)) / 2;
};

function lambert93toWGPS(lambertE, lambertN) {

    var constantes = {
        GRS80E: 0.081819191042816,
        LONG_0: 3,
        XS: 700000,
        YS: 12655612.0499,
        n: 0.7256077650532670,
        C: 11754255.4261
    }

    var delX = lambertE - constantes.XS;
    var delY = lambertN - constantes.YS;
    var gamma = Math.atan(-delX / delY);
    var R = Math.sqrt(delX * delX + delY * delY);
    var latiso = Math.log(constantes.C / R) / constantes.n;
    var sinPhiit0 = Math.tanh(latiso + constantes.GRS80E * Math.atanh(constantes.GRS80E * Math.sin(1)));
    var sinPhiit1 = Math.tanh(latiso + constantes.GRS80E * Math.atanh(constantes.GRS80E * sinPhiit0));
    var sinPhiit2 = Math.tanh(latiso + constantes.GRS80E * Math.atanh(constantes.GRS80E * sinPhiit1));
    var sinPhiit3 = Math.tanh(latiso + constantes.GRS80E * Math.atanh(constantes.GRS80E * sinPhiit2));
    var sinPhiit4 = Math.tanh(latiso + constantes.GRS80E * Math.atanh(constantes.GRS80E * sinPhiit3));
    var sinPhiit5 = Math.tanh(latiso + constantes.GRS80E * Math.atanh(constantes.GRS80E * sinPhiit4));
    var sinPhiit6 = Math.tanh(latiso + constantes.GRS80E * Math.atanh(constantes.GRS80E * sinPhiit5));

    var longRad = Math.asin(sinPhiit6);
    var latRad = gamma / constantes.n + constantes.LONG_0 / 180 * Math.PI;

    var longitude = latRad / Math.PI * 180;
    var latitude = longRad / Math.PI * 180;

    return {longitude: longitude, latitude: latitude};
}

Thx a lot !
Would you consider make it an NPM package ?

Hi,

If you need an npm package, you can user proj4js , a project that has the goal to convert from "any" coordinate system to any other coordinate system. To help you further, you can find here https://spatialreference.org/ref/epsg/rgf93-lambert-93/
the definition of lambert 93 for proj4s (https://spatialreference.org/ref/epsg/rgf93-lambert-93/proj4js/ to be precise ),

so you can after that probably do something like (pseudo-code, I haven't tested):

proj4.defs["EPSG:2154"] = "+proj=lcc +lat_1=49 +lat_2=44 +lat_0=46.5 +lon_0=3 +x_0=700000 +y_0=6600000 +ellps=GRS80 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs";

function lambert93toWGPS(lambertE, lambertN) {
    return proj4('EPSG:2154', 'WGS84', [lambertE, lambertN]);
}

Otherwise, a good old copy/pasta will do the job (and you will even be able to rename constantes to constants) :)

Thanks, this will save me time to convert it to C#.

Hello I've had to make a Lambert CC Zone 49 version today in ES6 so here it is.

Thanks a lot. I grabbed the constants from your link and updated it accordingly.

// Référentiel IAG GRS 80 / Constantes Lambert-CC zone 49
const geodesicReferential = {
  GRS80E: 0.08181919112,
  LONG_0: 3, // OK
  XS: 1700000.00, // OK
  YS: 13754395.745, // OK
  n: 0.75473138518, // OK
  C: 11626445.901, // OK
};

const findGPSFromLambertCC = (lambertE, lambertN) => {
  const delX = lambertE - geodesicReferential.XS;
  const delY = lambertN - geodesicReferential.YS;
  const gamma = Math.atan(-delX / delY);
  const R = Math.sqrt(delX * delX + delY * delY);
  const latiso = Math.log(geodesicReferential.C / R) / geodesicReferential.n;
  const sinPhiit0 = Math.tanh(
    latiso +
      geodesicReferential.GRS80E *
        Math.atanh(geodesicReferential.GRS80E * Math.sin(1))
  );
  const sinPhiit1 = Math.tanh(
    latiso +
      geodesicReferential.GRS80E *
        Math.atanh(geodesicReferential.GRS80E * sinPhiit0)
  );
  const sinPhiit2 = Math.tanh(
    latiso +
      geodesicReferential.GRS80E *
        Math.atanh(geodesicReferential.GRS80E * sinPhiit1)
  );
  const sinPhiit3 = Math.tanh(
    latiso +
      geodesicReferential.GRS80E *
        Math.atanh(geodesicReferential.GRS80E * sinPhiit2)
  );
  const sinPhiit4 = Math.tanh(
    latiso +
      geodesicReferential.GRS80E *
        Math.atanh(geodesicReferential.GRS80E * sinPhiit3)
  );
  const sinPhiit5 = Math.tanh(
    latiso +
      geodesicReferential.GRS80E *
        Math.atanh(geodesicReferential.GRS80E * sinPhiit4)
  );
  const sinPhiit6 = Math.tanh(
    latiso +
      geodesicReferential.GRS80E *
        Math.atanh(geodesicReferential.GRS80E * sinPhiit5)
  );

  const longRad = Math.asin(sinPhiit6);
  const latRad =
    gamma / geodesicReferential.n +
    (geodesicReferential.LONG_0 / 180) * Math.PI;

  const longitude = (latRad / Math.PI) * 180;
  const latitude = (longRad / Math.PI) * 180;

  return { lon: longitude, lat: latitude };
  
};
export { findGPSFromLambertCC, geodesicReferential };