Converting coordinates from EPSG 3857 to 4326

Question

I have in my DB a list of coordinates in EPSG 3857 format. I need to convert them in EPSG 4326 I'm trying to use DotSpatial but my code always retun a double array of Infinity.

public double[] ConvertCoodinates()
    {
        double[] xy = new double[2];
        xy[0] = 5085240.8300000000;
        xy[1] = 1530088.9600000000;
    //An array for the z coordinate
        double[] z = new double[1];
        z[0] = 0;
        ProjectionInfo pStart = KnownCoordinateSystems.Geographic.World.WGS1984;
        pStart.AuthorityCode = 3857;
        ProjectionInfo pEnd = KnownCoordinateSystems.Geographic.World.WGS1984;
        pEnd.AuthorityCode = 4326;
        Reproject.ReprojectPoints(xy, z, pStart, pEnd, 0, 1);
        return xy;
    }

The xy array always cointain infinity; Can someone help me?

Answer 1

In the end I found a math formula to convert the coordinates.

I implemented it in a stored procedure because I have a list of point and this stored procedure calculates the distance.

DECLARE @e FLOAT=2.7182818284
DECLARE @X DECIMAL(18,2) =20037508.34

SET @StartLat3857 =(SELECT TOP 1 Latitude FROM Coordinates WHERE IdCoord=@IdCoord ORDER By IdTDFPath ASC)
SET @StartLng3857=(SELECT TOP 1 Longitude FROM Coordinates WHERE IdCoord=@IdCoord ORDER By IdTDFPath ASC)

--converting the logitute from epsg 3857 to 4326
            SET @StartLng=(@StartLng3857*180)/@X

--converting the latitude from epsg 3857 to 4326
            SET @StartLat = @StartLat3857/(@X/180)
            SET @StartLat = ((ATAN(POWER(@e,((PI()/180)*@StartLat))))/(PI()/360))-90

In the end is just a math formula that can be used in every language. for example is Javascript it will be

const e = 2.7182818284
const X = 20037508.34

const lat3857 = 1743704.947843 
const long3857 = 16978473.105100

//converting the logitute from epsg 3857 to 4326
const long4326 = (lat3857*180)/X

//converting the latitude from epsg 3857 to 4326 split in multiple lines for readability

let lat4326 = lat3857/(X / 180)
const exponent = (Math.PI / 180) * lat4326

lat4326 = Math.atan(e ** exponent)
lat4326 = lat4326 / (Math.PI / 360)
lat4326 = lat4326 - 90

Answer 2

It seems there is a mistake in the Javascript version of the selected answer... It always gives me a 2 times bigger answer than it really should, so I ended up diving by 360 instead of 180 (but I admit the Math here are beyond my field of expertise).

Here is the working code :

  coord3857To4326(coord) {
    
    const e_value = 2.7182818284;
    const X = 20037508.34;
    
    const lat3857 = coord.lat
    const long3857 = coord.lng;
    
    //converting the longitute from epsg 3857 to 4326
    const long4326 = (long3857*180)/X;
    
    //converting the latitude from epsg 3857 to 4326 split in multiple lines for readability        
    let lat4326 = lat3857/(X / 180);
    const exponent = (Math.PI / 180) * lat4326;
    
    lat4326 = Math.atan(Math.pow(e_value, exponent));
    lat4326 = lat4326 / (Math.PI / 360); // Here is the fixed line
    lat4326 = lat4326 - 90;

    return {lat:lat4326, lng:long4326};
    
}

I also successfully reversed it :

  coord4326To3857(coord) {

    const X = 20037508.34;

    let long3857 = (coord.lng * X) / 180;

    let lat3857 = parseFloat(coord.lat) + 90;
    lat3857 = lat3857 * (Math.PI/360);
    lat3857 = Math.tan(lat3857);
    lat3857 = Math.log(lat3857);
    lat3857 = lat3857 / (Math.PI / 180);
    
    lat3857 = (lat3857 * X) / 180;

    return {lat:lat3857, lng:long3857};
}

Hope this will help others !

Answer 3

It is a bit tricky to project EPSG 3857 coordinates to EPSG 4326 coordinate system. Microsoft recommends using ProjNet4GeoAPI so I decided to use that.

https://learn.microsoft.com/en-us/ef/core/modeling/spatial#srid-ignored-during-client-operations

I have verified that it works here:

http://epsg.io/transform#s_srs=3857&t_srs=4326&x=1530088.9600000&y=5085240.8300000

Example conversion:

var x = 1530088.96d;
var y = 5085240.83d;

var epsg3857ProjectedCoordinateSystem = ProjNet.CoordinateSystems.ProjectedCoordinateSystem.WebMercator;
var epsg4326GeographicCoordinateSystem = ProjNet.CoordinateSystems.GeographicCoordinateSystem.WGS84;

var coordinateTransformationFactory = new ProjNet.CoordinateSystems.Transformations.CoordinateTransformationFactory();
var coordinateTransformation = coordinateTransformationFactory.CreateFromCoordinateSystems(epsg3857ProjectedCoordinateSystem, epsg4326GeographicCoordinateSystem);

var epsg3857Coordinate = new GeoAPI.Geometries.Coordinate(x, y);

var epsg4326Coordinate = coordinateTransformation.MathTransform.Transform(epsg3857Coordinate);

Answer 4

I got this to work in Rust using the following code:

use std::f64::consts::{E, PI};

fn convert_coordinates(pos: &Vec<f64>) -> Vec<f64> {
    
    // Longitude <-> X
    // Latitude <-> Y
    // Output Decimal degree (WGS84)
    // X:-7920923.8631988168, Y: 5197114.9130207254
    //            0                     1
    // Longitude: -71.1548697°, Latitude: 42.2407752°
    //
    
    let long3857: f64 = pos[0];
    let lat3857: f64 = pos[1];

    let long4326: f64 = (long3857 * 180.0) / 20037508.34;
    let lat4326: f64 = (lat3857 * 180.0) / 20037508.34;

    let lat_rad: f64 = (lat4326 / 180.0) * PI;
    let lat4326_final: f64 = (2.0 * lat_rad.exp().atan() - PI / 2.0).to_degrees();

    vec![long4326, lat4326_final]
}

assert_eq!(-71.1548697_f64.round(), convert_coordinates(&vec![-7920923.8631988168, 5197114.9130207254])[0].round());
println!("Longitude Passed");
assert_eq!(42.2407752_f64.round(), convert_coordinates(&vec![-7920923.8631988168, 5197114.9130207254])[1].round());
println!("Latitude Passed");