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};
}

Very useful, thank you !

To convert for other Lambert Projection, you can change constantes with value found here :

http://geodesie.ign.fr/contenu/fichiers/documentation/algorithmes/notice/NTG_71.pdf

LONG_0 == λ0 ; GRS80E == e

THX, u save my life today. I will be forever grateful.

work well! Thanks a lot

Hello blemoine, I am working on a project and I need to write this function in python. I never used javascript therefore I don't understand what you did before the function keyword. Merci d'avance.

if you talk about Math.tanh = ... and Math.atanh = ... , it's only to define the hyperbolic tangent and hyperbolic arctangent if they don't already exist.

Because JavaScript can be run in many different browsers, you never know if every function that you need will already be present or not.

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 };