Transformations

Transform coordinates between various coordinate systems used in Bulgaria.

Contents

• Info
• How to use
• API
  • IPoint
  • IExtent
  • Ellipsoids
  • Projections
  • Transformation methods
• 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
  • Transform by calculating transformation parameters for an extent
  • 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 Spline (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.

Optionally you can calculate transformation parameters for affine transformation valid for specific region and use them to calculate points more quickly, but with less precission.

The library is available in JavaScript too: transformations.

How to use

1. Install with Nuget:

Install-Package Transformations.NET

2. Implement IPoint and/or IExtent interfaces:

using BojkoSoft.Transformations;
...
class Point : IPoint
{
    public double N { get; set; }
    public double E { get; set; }
    public double Z { get; set; }

    public TestPoint(double x, double y, double z)
    {
        ...
    }

    public IPoint Clone()
        => new Point(this.N, this.E, this.Z);
}

class Extent : IExtent
{
    public double MinN { get; set; }
    public double MinE { get; set; }
    public double MaxN { get; set; }
    public double MaxE { get; set; }
    public double Width => this.MaxE - this.MinE;
    public double Height => this.MaxN - this.MinN;
    public bool IsEmpty => this.Width <= 0 && this.Height <= 0;

    public TestExtent(double northingMax, double northingMin, double eastingMax, double eastingMin)
    {
        ...
    }

    public void Expand(double meters)
    {
        ...
    }

    public IExtent Clone()
        => new TestExtent(this.MaxN, this.MinN, this.MaxE, this.MinE);
}

2. Instantiate Transformations class. When instatiating the class you can pass a boolean parameter whether the control points must be initialized (default is true - control points are initialized). If you plan to transform between BGS coordinate systems the contrl points MUST BE initialized otherwisee you wont be able to transform coordinates. If you don't plan to transform between BGS coordinate systems you can pass false and the control points wont be added to the memory.

using BojkoSoft.Transformations;
...
Transformations tr = new Transformations(/* pass false and control points won't ne initialized */);

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

A posible solution is to create a singleton class, simmilar to this one:

using BojkoSoft.Transformations;
using BojkoSoft.Transformations.Constants;

namespace YourNamespace
{
  sealed class TransformationUtils
  {
    public static TransformationUtils Instance => _instance;
    public enumProjection SourceProjection { get; set; }
    public enumProjection TargetProjection { get; set; }
    public bool NeedsTransformation
    {
      get
      {
        return this.SourceProjection != enumProjection.Unknown
            && this.TargetProjection != enumProjection.Unknown
            && this.SourceProjection != this.TargetProjection;
      }
    }

    private static readonly TransformationUtils _instance = new TransformationUtils();
    private readonly Transformations tr;
    private double[] parameters;

    private TransformationUtils()
    {
      this.tr = new Transformations();
      this.parameters = null;

      this.SourceProjection = enumProjection.Unknown;
      this.TargetProjection = enumProjection.Unknown;
    }

    public void CalculateTransformationParameters(IExtent extent)
    {
      // ensure that the extent is big enough to include more control points
      // for calculating better transformation parameters
      if (extent.IsEmpty || extent.Height < 20000 || extent.Width < 20000)
        extent.Expand(20000);
      this.parameters = this.tr.CalculateAffineTransformationParameters(
        extent, this.SourceProjection, this.TargetProjection);
    }

    public IPoint TransformPoint(IPoint sourcePoint)
    {
      IPoint outputPoint = null;
      switch (this.SourceProjection)
      {
        case enumProjection.BGS_1970_K9:
        {
          switch (this.TargetProjection)
          {
            case enumProjection.BGS_2005_KK:
            {
              outputPoint = this.tr.TransformBGSCoordinates(
                sourcePoint, this.parameters,
                (int)this.SourceProjection,
                (int)this.TargetProjection);
              break;
            }
            case enumProjection.WGS84_GEOGRAPHIC:
            {
              outputPoint = this.tr.TransformBGSCoordinates(
                sourcePoint,
                this.parameters,
                (int)this.SourceProjection,
                (int)enumProjection.BGS_2005_KK);
              outputPoint = this.tr.TransformLambertToGeographic(outputPoint);
              break;
            }
          }
          break;
        }
      }
      return outputPoint;
    }
  }
}

TransformationUtils.TransformPoint() is the main method used for transforming points using the above singleton class. You can implement one or more transformations between enumProjection projections in the switch.

Using a singleton class

TransformationUtils.Instance.SourceProjection = enumProjection.BGS_1970_K9;
TransformationUtils.Instance.TargetProjection = enumProjection.WGS84_GEOGRAPHIC;

// calculate transformation parameters if you plan to process more points
TransformationUtils.Instance.CalculateTransformationParameters(new IExtent(...));

Point bgs1970k9 = new Point(4547844.976, 8508858.179);
Point wgs84 = TransformationUtils.Instance.TransformPoint(bgs1970k9);
// result is: 42.195768, 23.448409

API

This library exposes several objects for easier integration. Main workflows for transforming coordinates are:

Without calculating transformation parameters

This method can be used if you don't transform between BGS coordinate systems:

Transformations tr = new Transformations(false);  // false means no control points will be added to memory
IPoint input = new Point(4735953.349, 490177.508);
IPoint result = tr.TransformLambertToGeographic(input);

Or if you plan to transform few points:

Transformations tr = new Transformations();
IPoint transformed = tr.TransformBGSCoordinates(inputPoint, BGS_1970_K9, WGS84_GEOGRAPHIC);

With calculating transformation parameters

If you plan to transform more than few points it is suggested to calculate transformation parameters for the whole area where your coordiantes are located and then use them to calculate all points in the area:

IExtent extent = new Extent(...);
Transformations tr = new Transformations();
double[] parameters = tr.CalculateAffineTransformationParameters(extent, ...);
IPoint transformed = tr.TransformBGSCoordinates(inputPoint, parameters, BGS_1970_K9, WGS84_GEOGRAPHIC)

This will make the process run faster as the parameters will be calculated only once.

IPoint

Represents a point geometry, ready for transformation. Coordinates hold different values for different coordinate systems:

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

IExtent

Represents an extent. Implement this interface if you transform between BGS coordinate systems and plan to transform more coordinates. You can create an extent for the area where the coordinates are located and then calculate transformation parameters for that area. Make sure the area is big enough to contain more control points - in most cases area with diameter of ~20km is more than enough. This will make the transformation run faster:

IExtent extent = new Extent(...);
Transformations tr = new Transformations();
double[] parameters = tr.CalculateAffineTransformationParameters(extent, ...);
IPoint transformed = tr.TransformBGSCoordinates(inputPoint, parameters, ...);

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
• Unknown - unknown projection (coordinate system)

Transformation methods

• Transform geographic coordinates to projected in Lambert projection

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

• Transform projected coordinates in Lambert projection to geographic

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

• Transform geographic coordinates to projected in UTM

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

• Transform projected coordinates in UTM to geographic

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

• Transform geographic coordinates to projected in Gauss–Krüger

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

• Transform projected coordinates in Gauss–Krüger to geographic

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

• Transform geographic coordinates to projected in Web Mercator

public IPoint TransformGeographicToWebMercator(IPoint inputPoint)

• Transform projected coordinates in Web Mercator to geographic

public IPoint TransformWebMercatorToGeographic(IPoint inputPoint)

• Transform geographic coordinates to geocentric

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

• Transform geocentric coordinates to geographic

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

• Transform projected coordinates between BGS coordinate systems

public IPoint TransformBGSCoordinates(IPoint 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)

• Calculate Affine transformation parameters for a region

public double[] CalculateAffineTransformationParameters(IExtent inputExtent, enumProjection inputProjection = enumProjection.BGS_1970_K9, enumProjection outputProjection = enumProjection.BGS_2005_KK)

Examples

Transform between geographic coordinates and projected in Lambert projection

Transformations tr = new Transformations();

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

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

Transform between geographic coordinates and projected in UTM

Transformations tr = new Transformations();

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

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

Transform between geographic coordinates and projected in Gauss–Krüger

Transformations tr = new Transformations();

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

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

Transform between geographic coordinates and projected in Web Mercator

Transformations tr = new Transformations();

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

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

Transform between geographic and geocentric coordinates

Transformations tr = new Transformations();

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

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

Transform between BGS coordinates

Transformations between BGS coordinate systems are than by calculating transformation parameters using predefined set of control points. Control points are available for following coordinate systems: BGS_1930_24, BGS_1930_27, BGS_1950_3_24, BGS_1950_3_27, BGS_1950_6_21, BGS_1950_6_27, BGS_1970_K3, BGS_1970_K5, BGS_1970_K7, BGS_1970_K9, BGS_2005_KK. If you need to transform for example from BGS_1970_K9 to WGS84_GEOGRAPHIC here is the workflow to do so:

Transformations tr = new Transformations();
// first transform to BGS_2005_KK using control points
IPoint outputPoint = tr.TransformBGSCoordinates(sourcePoint, BGS_1970_K9, BGS_2005_KK);
// then transform to WGS84_GEOGRAPHIC
outputPoint = this.tr.TransformLambertToGeographic(outputPoint);

• BGS 1930

Transformations tr = new Transformations();

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

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

• BGS 1950

Transformations tr = new Transformations();

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

IPoint input = new Point(4728401.432, 483893.508);
IPoint 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();

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

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

• BGS 1970

Transformations tr = new Transformations();

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

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

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

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

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

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

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

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

Transform by calculating transformation parameters for an extent

• You first provide the extent and calculate transformation parameters usi.......................

IExtent extent = new Extent(4590706, 4556298, 8561889, 8519105);
// optionaly you can expand the provided extent:
// extent.Expand(20000);

Transformations tr = new Transformations();

// calculate transformation parameters
double[] parameters = tr.CalculateAffineTransformationParameters(extent, enumProjection.BGS_1970_K9, enumProjection.BGS_2005_KK);

// transform input point with calculated parameters
IPoint input = new Point(4573488, 8539465);
IPoint result = tr.TransformBGSCoordinates(input, parameters, enumProjection.BGS_1970_K9, enumProjection.BGS_2005_KK);
// result is: 4700322.190, 361795.526

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 IPoint constructor when used like: new Point(int id, double X, double Y)
• Implement Polynomial transformation

Tests

Check Tests project for more information.

License

Transformations.NET is MIT License @ bojko108