Transformations

Transform coordinates between various coordinate systems used in Bulgaria.

Contents

• Info
• How to use
• API
  • Transformations methods
  • GeoPoint
  • GeoExtent
  • Ellipsoids
  • Projections
• Examples
  • Transform between geographic coordinates and projected in Lambert projection
  • Transform between geographic coordinates and projected in UTM
  • Transform between geographic coordinates and projected in Gauss–Krüger
  • Transform between geographic coordinates and projected in Web Mercator
  • Transform between geographic and geocentric coordinates
  • Transform between BGS coordinates
  • Format decimal degrees from/to degrees, minutes and seconds
• TODO
• Dependencies
• Tests
• License

Info

The project can be used for transforming coordinates between various coordinate systems:

• BGS 1930
• BGS 1950
• BGS Sofia
• BGS 1970 (there can be no control points near by if the point is close to the zone's border)
• BGS 2005

Following projections are available:

• Lambert Conformal Conic with 2SP
• Universal Transverse Mercator
• Gauss–Krüger
• Spherical Web Mercator

You can transform between:

• Geographic coordinates
• Projected coordinates
• Geocentric coordinates

Transformations between BGS coordinate systems are done by calculating transformation parameters for Affine or Thin Plate SPlite (TPS) transformation based on predefined control points (ControlPoints namespace). You can control what type of transformation is used by passing useTPS boolean parameter to TransformBGSCoordinates(). All other transformations are done directly as the transformation parameters are known.

The library is available in JavaScript too: transformations.

How to use

You can install it with Nuget:

Install-Package Transformations.NET

using BojkoSoft.Transformations;

Transformations tr = new Transformations();

GeoPoint input = new GeoPoint(42.450682, 24.749747);
GeoPoint result = tr.TransformGeographicToUTM(input);

API

Transformations methods

• Transform geographic coordinates to projected in Lambert projection

public GeoPoint TransformGeographicToLambert(GeoPoint inputPoint, enumProjection outputProjection = enumProjection.BGS_2005_KK, enumEllipsoid outputEllipsoid = enumEllipsoid.WGS84)

• Transform projected coordinates in Lambert projection to geographic

public GeoPoint TransformLambertToGeographic(GeoPoint inputPoint, enumProjection inputProjection = enumProjection.BGS_2005_KK, enumEllipsoid inputEllipsoid = enumEllipsoid.WGS84)

• Transform geographic coordinates to projected in UTM

public GeoPoint TransformGeographicToUTM(GeoPoint inputPoint, enumProjection outputUtmProjection = enumProjection.UTM35N, enumEllipsoid inputEllipsoid = enumEllipsoid.WGS84)

• Transform projected coordinates in UTM to geographic

public GeoPoint TransformUTMToGeographic(GeoPoint inputPoint, enumProjection inputUtmProjection = enumProjection.UTM35N, enumEllipsoid outputEllipsoid = enumEllipsoid.WGS84)

• Transform geographic coordinates to projected in Gauss–Krüger

public GeoPoint TransformGeographicToGauss(GeoPoint inputPoint, enumProjection outputProjection = enumProjection.BGS_1930_24, enumEllipsoid inputEllipsoid = enumEllipsoid.HAYFORD)

• Transform projected coordinates in Gauss–Krüger to geographic

public GeoPoint TransformGaussToGeographic(GeoPoint inputPoint, enumProjection inputProjection = enumProjection.BGS_1930_24, enumEllipsoid outputEllipsoid = enumEllipsoid.HAYFORD)

• Transform geographic coordinates to projected in Web Mercator

public GeoPoint TransformGeographicToWebMercator(GeoPoint inputPoint)

• Transform projected coordinates in Web Mercator to geographic

public GeoPoint TransformWebMercatorToGeographic(GeoPoint inputPoint)

• Transform geographic coordinates to geocentric

public GeoPoint TransformGeographicToGeocentric(GeoPoint inputPoint, enumEllipsoid outputEllipsoid = enumEllipsoid.WGS84)

• Transform geocentric coordinates to geographic

public GeoPoint TransformGeocentricToGeographic(GeoPoint inputPoint, enumEllipsoid inputEllipsoid = enumEllipsoid.WGS84)

• Transform projected coordinates between BGS coordinate systems

public GeoPoint TransformBGSCoordinates(GeoPoint inputPoint, enumProjection inputProjection = enumProjection.BGS_1970_K9, enumProjection outputProjection = enumProjection.BGS_2005_KK, bool useTPS = true)

• Format geographic coordinates from decimal degrees to degrees, minutes and seconds

public string ConvertDecimalDegreesToDMS(double DEG)

• Format geographic coordinates from degrees, minutes and seconds to decimal degrees

public double ConvertDMStoDecimalDegrees(string DMS)

GeoPoint

Represents a point that will be or is transformed. Coordinates hold different values for different coordinate systems:

• X coordinate:
  • Geographic: represents Latitude
  • Lambert: represents Northing
  • UTM: represents Northing
  • Old BGS: represents X
  • Cartesian: y
• Y coordinate:
  • Geographic: represents Longitude
  • Lambert: represents Easting
  • UTM: represents Easting
  • Old BGS: represents Y
  • Cartesian: x
• Z coordinate
  • in geocentric: Z
  • in others: Elevation

Ellipsoids

using BojkoSoft.Transformations.Constants;

• GRS80 - GRS 1980
• BESSEL_1841 - Bessel 1841
• CLARKE_1866 - Clarke 1866
• EVEREST - Everest (Sabah and Sarawak)
• HELMERT - Helmert 1906
• HAYFORD - Hayford
• KRASSOVSKY - Krassovsky, 1942
• WALBECK - Walbeck
• WGS72 - WGS 1972
• WGS84 - WGS 1984
• SPHERE - Normal Sphere (R=6378137)

Projections

using BojkoSoft.Transformations.Constants;

• WGS84_GEOGRAPHIC (EPSG:4326) - geographic coordinates with WGS84 ellipsoid
• BGS_SOFIA - BGS Sofia. Local projection based on BGS 1950
• BGS_1930_24 - Gauss–Krüger projection based on Hayford ellipsoid
• BGS_1930_27 - Gauss–Krüger projection based on Hayford ellipsoid
• BGS_1950_3_24 - Gauss–Krüger projection based on Krassovsky ellipsoid
• BGS_1950_3_27 - Gauss–Krüger projection based on Krassovsky ellipsoid
• BGS_1950_6_21 - Gauss–Krüger projection based on Krassovsky ellipsoid
• BGS_1950_6_27 - Gauss–Krüger projection based on Krassovsky ellipsoid
• BGS_1970_K3 - ~ Northewest Bulgaria
• BGS_1970_K5 - ~ Southeast Bulgaria
• BGS_1970_K7 - ~ Northeast Bulgaria
• BGS_1970_K9 - ~ Southwest Bulgaria
• BGS_2005_KK (EPSG:7801) - Lambert Conformal Conic with 2SP used by Cadastral Agency
• UTM34N (EPSG:32634) - Universal Transverse Mercator zone 34 North
• UTM35N (EPSG:32635) - Universal Transverse Mercator zone 35 North

Examples

Transform between geographic coordinates and projected in Lambert projection

Transformations tr = new Transformations();

GeoPoint input = new GeoPoint(42.7589996, 25.3799991);
GeoPoint result = tr.TransformGeographicToLambert(input);
// result is: 4735953.342, 490177.508

GeoPoint input = new GeoPoint(4735953.349, 490177.508);
GeoPoint result = tr.TransformLambertToGeographic(input);
// result is: 42.7589997, 25.3799991

Transform between geographic coordinates and projected in UTM

Transformations tr = new Transformations();

GeoPoint input = new GeoPoint(42.450682, 24.749747);
GeoPoint result = tr.TransformGeographicToUTM(input);
// result is: 4702270.178, 314955.869

GeoPoint input = new GeoPoint(4702270.179, 314955.869);
GeoPoint result = tr.TransformUTMToGeographic(input);
// result is: 42.450682, 24.749747

Transform between geographic coordinates and projected in Gauss–Krüger

Transformations tr = new Transformations();

GeoPoint input = new GeoPoint(42.7602978166667, 25.3824052611111);
GeoPoint result = tr.TransformGeographicToGauss(input);
// result is: 4736629.503, 8613154.606

GeoPoint input = new GeoPoint(4736629.503, 8613154.607);
GeoPoint result = tr.TransformGaussToGeographic(input);
// result is: 42.7602978, 25.38240528

Transform between geographic coordinates and projected in Web Mercator

Transformations tr = new Transformations();

GeoPoint input = new GeoPoint(42.450682, 24.749747);
GeoPoint result = tr.TransformGeographicToWebMercator(input);
// result is: 2755129.233, 5228730.328

GeoPoint input = new GeoPoint(2755129.23, 5228730.33);
GeoPoint result = tr.TransformWebMercatorToGeographic(input);
// result is: 42.4506820, 24.7497470

Transform between geographic and geocentric coordinates

Transformations tr = new Transformations();

GeoPoint input = new GeoPoint(42.450682, 24.749747);
GeoPoint result = tr.TransformGeographicToGeocentric(input);
// result is: X: 4280410.654, 1973273.422, 4282674.061

GeoPoint input = new GeoPoint(4280410.654, 1973273.422, 4282674.061);
GeoPoint result = tr.TransformGeocentricToGeographic(input);
// result is: 42.450682, 24.749747

Transform between BGS coordinates

• BGS 1930

Transformations tr = new Transformations();

GeoPoint input = new GeoPoint(4728966.163, 8607005.227);
GeoPoint result = tr.TransformBGSCoordinates(input, enumProjection.BGS_1930_24, enumProjection.BGS_2005_KK);
// result is: 4728401.432, 483893.508

GeoPoint input = new GeoPoint(4728401.432, 483893.508);
GeoPoint result = tr.TransformBGSCoordinates(input,  enumProjection.BGS_2005_KK, enumProjection.BGS_1930_24);
// result is: 4728966.153, 8607005.214

• BGS 1950

Transformations tr = new Transformations();

GeoPoint input = new GeoPoint(4729331.175, 8606933.614);
GeoPoint result = tr.TransformBGSCoordinates(input, enumProjection.BGS_1950_3_24, enumProjection.BGS_2005_KK);
// result is: 4728401.442, 483893.521

GeoPoint input = new GeoPoint(4728401.432, 483893.508);
GeoPoint result = tr.TransformBGSCoordinates(input, enumProjection.BGS_2005_KK, enumProjection.BGS_1950_3_24);
// result is: 4729331.165, 8606933.601

• BGS Sofia

Transformations tr = new Transformations();

GeoPoint input = new GeoPoint(48276.705, 45420.988);
GeoPoint result = tr.TransformBGSCoordinates(input, enumProjection.BGS_SOFIA, enumProjection.BGS_2005_KK);
// result is: 4730215.221, 322402.929

GeoPoint input = new GeoPoint(4730215.229, 322402.935);
GeoPoint result = tr.TransformBGSCoordinates(input, enumProjection.BGS_2005_KK, enumProjection.BGS_SOFIA);
// result is: 48276.713, 45420.993

• BGS 1970

Transformations tr = new Transformations();

GeoPoint input = new GeoPoint(4725270.684, 8515734.475);
GeoPoint result = tr.TransformBGSCoordinates(input, enumProjection.BGS_1970_K3, enumProjection.BGS_2005_KK);
// result is: 4816275.688, 332535.346

GeoPoint input = new GeoPoint(4816275.680, 332535.401);
GeoPoint result = tr.TransformBGSCoordinates(input, enumProjection.BGS_2005_KK, enumProjection.BGS_1970_K3);
// result is: 4725270.677, 8515734.530

GeoPoint input = new GeoPoint(4613479.192, 9493233.633);
GeoPoint result = tr.TransformBGSCoordinates(input, enumProjection.BGS_1970_K5, enumProjection.BGS_2005_KK);
// result is: 4679669.824, 569554.912

GeoPoint input = new GeoPoint(4679669.825, 569554.918);
GeoPoint result = tr.TransformBGSCoordinates(input, enumProjection.BGS_2005_KK, enumProjection.BGS_1970_K5);
// result is: 4613479.193, 9493233.639

GeoPoint input = new GeoPoint(4708089.898, 9570974.988);
GeoPoint result = tr.TransformBGSCoordinates(input, enumProjection.BGS_1970_K7, enumProjection.BGS_2005_KK);
// result is: 4810276.410, 626498.618

GeoPoint input = new GeoPoint(4810276.431, 626498.611);
GeoPoint result = tr.TransformBGSCoordinates(input, enumProjection.BGS_2005_KK, enumProjection.BGS_1970_K7);
// result is: 4708089.919, 9570974.981

GeoPoint input = new GeoPoint(4547844.976, 8508858.179);
GeoPoint result = tr.TransformBGSCoordinates(input, enumProjection.BGS_1970_K9, enumProjection.BGS_2005_KK);
// result is: 4675440.859, 330568.410

GeoPoint input = new GeoPoint(4675440.847, 330568.434);
GeoPoint result = tr.TransformBGSCoordinates(input, enumProjection.BGS_2005_KK, enumProjection.BGS_1970_K9);
// result is: 4547844.965, 8508858.203

Format decimal degrees from/to degrees, minutes and seconds

Transformations tr = new Transformations();

double latitude = 42.336542;
string dms = tr.ConvertDecimalDegreesToDMS(latitude);
// result is: "422011.5512000000052"

string dms = "422011.5512000000052";
double result = tr.ConvertDMStoDecimalDegrees(dms);
// result is: 42.336542

TODO

• Transform array of points
• Fix GeoPoint constructor when used like: new GeoPoint(int id, double X, double Y)
• Implement Polynomial transformation

Dependencies

This project depends on KDBush project for fast searching in control points classes.

Tests

Check Tests project for more information.

License

Transformations is MIT License @ bojko108