internal static PolarGeoCoordinate Convert(PolarGeoCoordinate source, CoordinateSystems destination)
{
PolarGeoCoordinate retVal;
if (source.CoordinateSystem == CoordinateSystems.OSGB36 && destination == CoordinateSystems.WGS84)
{
retVal = Convert(
source,
EllipseParameter.GetEllipseParameters(EllipseParameter.Ellipses.Airy1830),
HelmertTransform.GetTransform(HelmertTransform.HelmertTransformType.OSGB36toWGS84),
EllipseParameter.GetEllipseParameters(EllipseParameter.Ellipses.WGS84));
}
else if (source.CoordinateSystem == CoordinateSystems.WGS84 && destination == CoordinateSystems.OSGB36)
{
retVal = Convert(
source,
EllipseParameter.GetEllipseParameters(EllipseParameter.Ellipses.WGS84),
HelmertTransform.GetTransform(HelmertTransform.HelmertTransformType.WGS84toOSGB36),
EllipseParameter.GetEllipseParameters(EllipseParameter.Ellipses.Airy1830));
}
else
{
throw new NotImplementedException("Requested source and destination are not currently supported");
}
retVal.AlignSigFigs(source);
return retVal;
}
public static PolarGeoCoordinate ChangeUnits(PolarGeoCoordinate original, AngleUnit changeTo)
{
if (original.Units == changeTo)
{
return new PolarGeoCoordinate(
original.Lat, original.Lon, original.Height, original.Units, original.CoordinateSystem);
}
if (original.Units == AngleUnit.Degrees && changeTo == AngleUnit.Radians)
{
return new PolarGeoCoordinate(
Converter.DegToRad(original.Lat),
Converter.DegToRad(original.Lon),
original.Height,
AngleUnit.Radians,
original.CoordinateSystem);
}
if (original.Units == AngleUnit.Radians && changeTo == AngleUnit.Degrees)
{
return new PolarGeoCoordinate(
Converter.RadToDeg(original.Lat),
Converter.RadToDeg(original.Lon),
original.Height,
AngleUnit.Degrees,
original.CoordinateSystem);
}
throw new NotImplementedException("Invalid conversion requested");
}
public static GridReference ChangeToGridReference(PolarGeoCoordinate original)
{
PolarGeoCoordinate convertible = original.CoordinateSystem != CoordinateSystems.OSGB36
? ChangeCoordinateSystem(original, CoordinateSystems.OSGB36)
: original;
return Converter.GeodesicToGridReference(convertible);
}
private static PolarGeoCoordinate Convert(
PolarGeoCoordinate originalCoord, EllipseParameter e1, HelmertTransform t, EllipseParameter e2)
{
// -- convert polar to cartesian coordinates (using ellipse 1)
PolarGeoCoordinate p1 = PolarGeoCoordinate.ChangeUnits(originalCoord, AngleUnit.Radians);
double sinPhi = Math.Sin(p1.Lat);
double cosPhi = Math.Cos(p1.Lat);
double sinLambda = Math.Sin(p1.Lon);
double cosLambda = Math.Cos(p1.Lon);
double H = p1.Height;
double eSq = (Math.Pow(e1.SemimajorAxis, 2) - Math.Pow(e1.SemiMinorAxis, 2)) / Math.Pow(e1.SemimajorAxis, 2);
double nu = e1.SemimajorAxis / Math.Sqrt(1 - eSq * sinPhi * sinPhi);
double x1 = (nu + H) * cosPhi * cosLambda;
double y1 = (nu + H) * cosPhi * sinLambda;
double z1 = ((1 - eSq) * nu + H) * sinPhi;
// -- apply helmert transform using appropriate params
double tx = t.tx, ty = t.ty, tz = t.tz;
double rx = t.rx / 3600 * Math.PI / 180; // normalise seconds to radians
double ry = t.ry / 3600 * Math.PI / 180;
double rz = t.rz / 3600 * Math.PI / 180;
double s1 = t.s / 1e6 + 1; // normalise ppm to (s+1)
// apply transform
double x2 = tx + x1 * s1 - y1 * rz + z1 * ry;
double y2 = ty + x1 * rz + y1 * s1 - z1 * rx;
double z2 = tz - x1 * ry + y1 * rx + z1 * s1;
// -- convert cartesian to polar coordinates (using ellipse 2)
double a = e2.SemimajorAxis;
double precision = 4 / e2.SemimajorAxis; // results accurate to around 4 metres
eSq = (Math.Pow(e2.SemimajorAxis, 2) - Math.Pow(e2.SemiMinorAxis, 2)) / Math.Pow(e2.SemimajorAxis, 2);
double p = Math.Sqrt(x2 * x2 + y2 * y2);
double phi = Math.Atan2(z2, p * (1 - eSq)), phiP = 2 * Math.PI;
while (Math.Abs(phi - phiP) > precision)
{
nu = a / Math.Sqrt(1 - eSq * Math.Sin(phi) * Math.Sin(phi));
phiP = phi;
phi = Math.Atan2(z2 + eSq * nu * Math.Sin(phi), p);
}
double lambda = Math.Atan2(y2, x2);
H = p / Math.Cos(phi) - nu;
return(new PolarGeoCoordinate(
RadToDeg(phi), RadToDeg(lambda), H, AngleUnit.Degrees, t.outputCoordinateSystem));
}
internal static PolarGeoCoordinate GridReferenceToGeodesic(GridReference g)
{
double lat = _NatGridTrueOrigin.Lat;
double M = 0;
do
{
lat = (g.Northing - _NatNETrueOrigin.Northing - M) / (_Airy1830.SemimajorAxis * _NatGridScaleFactor) + lat;
double Ma = (1 + _n + (5d / 4d) * _n2 + (5d / 4d) * _n3) * (lat - _NatGridTrueOrigin.Lat);
double Mb = (3 * _n + 3 * _n * _n + (21d / 8d) * _n3) * Math.Sin(lat - _NatGridTrueOrigin.Lat) * Math.Cos(lat + _NatGridTrueOrigin.Lat);
double Mc = ((15d / 8d) * _n2 + (15d / 8d) * _n3) * Math.Sin(2 * (lat - _NatGridTrueOrigin.Lat)) * Math.Cos(2 * (lat + _NatGridTrueOrigin.Lat));
double Md = (35d / 24d) * _n3 * Math.Sin(3 * (lat - _NatGridTrueOrigin.Lat)) * Math.Cos(3 * (lat + _NatGridTrueOrigin.Lat));
M = _Airy1830.SemiMinorAxis * _NatGridScaleFactor * (Ma - Mb + Mc - Md); // meridional arc
} while (g.Northing - _NatNETrueOrigin.Northing - M >= 0.00001); // ie until < 0.01mm
double cosLat = Math.Cos(lat), sinLat = Math.Sin(lat);
double nu = _Airy1830.SemimajorAxis * _NatGridScaleFactor / Math.Sqrt(1 - _e2 * sinLat * sinLat); // transverse radius of curvature
double rho = _Airy1830.SemimajorAxis * _NatGridScaleFactor * (1 - _e2) / Math.Pow(1 - _e2 * sinLat * sinLat, 1.5); // meridional radius of curvature
double eta2 = nu / rho - 1;
double tanLat = Math.Tan(lat);
double tan2lat = tanLat * tanLat, tan4lat = tan2lat * tan2lat, tan6lat = tan4lat * tan2lat;
double secLat = 1 / cosLat;
double nu3 = nu * nu * nu, nu5 = nu3 * nu * nu, nu7 = nu5 * nu * nu;
double VII = tanLat / (2 * rho * nu);
double VIII = tanLat / (24 * rho * nu3) * (5 + 3 * tan2lat + eta2 - 9 * tan2lat * eta2);
double IX = tanLat / (720 * rho * nu5) * (61 + 90 * tan2lat + 45 * tan4lat);
double X = secLat / nu;
double XI = secLat / (6 * nu3) * (nu / rho + 2 * tan2lat);
double XII = secLat / (120 * nu5) * (5 + 28 * tan2lat + 24 * tan4lat);
double XIIA = secLat / (5040 * nu7) * (61 + 662 * tan2lat + 1320 * tan4lat + 720 * tan6lat);
double dE = (g.Easting - _NatNETrueOrigin.Easting);
double dE2 = dE * dE;
double dE3 = dE2 * dE;
double dE4 = dE2 * dE2;
double dE5 = dE3 * dE2;
double dE6 = dE4 * dE2;
double dE7 = dE5 * dE2;
lat = lat - VII * dE2 + VIII * dE4 - IX * dE6;
double lon = _NatGridTrueOrigin.Lon + X * dE - XI * dE3 + XII * dE5 - XIIA * dE7;
PolarGeoCoordinate retVal = new PolarGeoCoordinate(lat, lon, 0, AngleUnit.Radians, CoordinateSystems.OSGB36);
retVal = PolarGeoCoordinate.ChangeUnits(retVal, AngleUnit.Degrees);
retVal.SetSigFigs(7);
return(retVal);
}
public static GridReference ChangeToGridReference(PolarGeoCoordinate original)
{
PolarGeoCoordinate convertible;
if (original.CoordinateSystem != CoordinateSystems.OSGB36)
{
convertible = ChangeCoordinateSystem(original, CoordinateSystems.OSGB36);
}
else
{
convertible = original;
}
return(Converter.GeodesicToGridReference(convertible));
}
internal static GridReference GeodesicToGridReference(PolarGeoCoordinate originalCoords)
{
PolarGeoCoordinate originalRads = PolarGeoCoordinate.ChangeUnits(originalCoords, AngleUnit.Radians);
double cosLat = Math.Cos(originalRads.Lat);
double sinLat = Math.Sin(originalRads.Lat);
double nu = _Airy1830.SemimajorAxis * _NatGridScaleFactor / Math.Sqrt(1 - _e2 * sinLat * sinLat);
// transverse radius of curvature
double rho = _Airy1830.SemimajorAxis * _NatGridScaleFactor * (1 - _e2)
/ Math.Pow(1 - _e2 * sinLat * sinLat, 1.5); // meridional radius of curvature
double eta2 = nu / rho - 1;
double Ma = (1 + _n + (5d / 4d) * _n2 + (5d / 4d) * _n3) * (originalRads.Lat - _NatGridTrueOrigin.Lat);
double Mb = (3 * _n + 3 * _n * _n + (21d / 8d) * _n3) * Math.Sin(originalRads.Lat - _NatGridTrueOrigin.Lat)
* Math.Cos(originalRads.Lat + _NatGridTrueOrigin.Lat);
double Mc = ((15d / 8d) * _n2 + (15d / 8d) * _n3)
* Math.Sin(2 * (originalRads.Lat - _NatGridTrueOrigin.Lat))
* Math.Cos(2 * (originalRads.Lat + _NatGridTrueOrigin.Lat));
double Md = (35d / 24d) * _n3 * Math.Sin(3 * (originalRads.Lat - _NatGridTrueOrigin.Lat))
* Math.Cos(3 * (originalRads.Lat + _NatGridTrueOrigin.Lat));
double M = _Airy1830.SemiMinorAxis * _NatGridScaleFactor * (Ma - Mb + Mc - Md); // meridional arc
double cos3lat = cosLat * cosLat * cosLat;
double cos5lat = cos3lat * cosLat * cosLat;
double tan2lat = Math.Tan(originalRads.Lat) * Math.Tan(originalRads.Lat);
double tan4lat = tan2lat * tan2lat;
double I = M + _NatNETrueOrigin.Northing;
double II = (nu / 2) * sinLat * cosLat;
double III = (nu / 24) * sinLat * cos3lat * (5 - tan2lat + 9 * eta2);
double IIIA = (nu / 720) * sinLat * cos5lat * (61 - 58 * tan2lat + tan4lat);
double IV = nu * cosLat;
double V = (nu / 6) * cos3lat * (nu / rho - tan2lat);
double VI = (nu / 120) * cos5lat * (5 - 18 * tan2lat + tan4lat + 14 * eta2 - 58 * tan2lat * eta2);
double dLon = originalRads.Lon - _NatGridTrueOrigin.Lon;
double dLon2 = dLon * dLon,
dLon3 = dLon2 * dLon,
dLon4 = dLon3 * dLon,
dLon5 = dLon4 * dLon,
dLon6 = dLon5 * dLon;
double N = I + II * dLon2 + III * dLon4 + IIIA * dLon6;
double E = _NatNETrueOrigin.Easting + IV * dLon + V * dLon3 + VI * dLon5;
return new GridReference((int)E, (int)N);
}
internal static GridReference GeodesicToGridReference(PolarGeoCoordinate originalCoords)
{
PolarGeoCoordinate originalRads = PolarGeoCoordinate.ChangeUnits(originalCoords, AngleUnit.Radians);
double cosLat = Math.Cos(originalRads.Lat);
double sinLat = Math.Sin(originalRads.Lat);
double nu = _Airy1830.SemimajorAxis * _NatGridScaleFactor / Math.Sqrt(1 - _e2 * sinLat * sinLat);
// transverse radius of curvature
double rho = _Airy1830.SemimajorAxis * _NatGridScaleFactor * (1 - _e2)
/ Math.Pow(1 - _e2 * sinLat * sinLat, 1.5); // meridional radius of curvature
double eta2 = nu / rho - 1;
double Ma = (1 + _n + (5d / 4d) * _n2 + (5d / 4d) * _n3) * (originalRads.Lat - _NatGridTrueOrigin.Lat);
double Mb = (3 * _n + 3 * _n * _n + (21d / 8d) * _n3) * Math.Sin(originalRads.Lat - _NatGridTrueOrigin.Lat)
* Math.Cos(originalRads.Lat + _NatGridTrueOrigin.Lat);
double Mc = ((15d / 8d) * _n2 + (15d / 8d) * _n3)
* Math.Sin(2 * (originalRads.Lat - _NatGridTrueOrigin.Lat))
* Math.Cos(2 * (originalRads.Lat + _NatGridTrueOrigin.Lat));
double Md = (35d / 24d) * _n3 * Math.Sin(3 * (originalRads.Lat - _NatGridTrueOrigin.Lat))
* Math.Cos(3 * (originalRads.Lat + _NatGridTrueOrigin.Lat));
double M = _Airy1830.SemiMinorAxis * _NatGridScaleFactor * (Ma - Mb + Mc - Md); // meridional arc
double cos3lat = cosLat * cosLat * cosLat;
double cos5lat = cos3lat * cosLat * cosLat;
double tan2lat = Math.Tan(originalRads.Lat) * Math.Tan(originalRads.Lat);
double tan4lat = tan2lat * tan2lat;
double I = M + _NatNETrueOrigin.Northing;
double II = (nu / 2) * sinLat * cosLat;
double III = (nu / 24) * sinLat * cos3lat * (5 - tan2lat + 9 * eta2);
double IIIA = (nu / 720) * sinLat * cos5lat * (61 - 58 * tan2lat + tan4lat);
double IV = nu * cosLat;
double V = (nu / 6) * cos3lat * (nu / rho - tan2lat);
double VI = (nu / 120) * cos5lat * (5 - 18 * tan2lat + tan4lat + 14 * eta2 - 58 * tan2lat * eta2);
double dLon = originalRads.Lon - _NatGridTrueOrigin.Lon;
double dLon2 = dLon * dLon,
dLon3 = dLon2 * dLon,
dLon4 = dLon3 * dLon,
dLon5 = dLon4 * dLon,
dLon6 = dLon5 * dLon;
double N = I + II * dLon2 + III * dLon4 + IIIA * dLon6;
double E = _NatNETrueOrigin.Easting + IV * dLon + V * dLon3 + VI * dLon5;
return(new GridReference((int)E, (int)N));
}
internal static PolarGeoCoordinate ReduceSigFigsBy1(PolarGeoCoordinate source)
{
double Lat = Converter.SetSigFigs(
source.Lat,
Converter.GetSigFigs(source.Lat) - 1);
double Lon = Converter.SetSigFigs(
source.Lon,
Converter.GetSigFigs(source.Lon) - 1);
double Height = Converter.SetSigFigs(
source.Height,
Converter.GetSigFigs(source.Height) - 1);
return(new PolarGeoCoordinate(Lat, Lon, Height, source.Units, source.CoordinateSystem));
}
internal void AlignSigFigs(PolarGeoCoordinate source)
{
int SigFigsSrc = Converter.GetSigFigs(source.Lat);
int SigFigsDest = Converter.GetSigFigs(this.Lat);
this.Lat = Converter.SetSigFigs(this.Lat, SigFigsDest < SigFigsSrc ? SigFigsDest : SigFigsSrc);
SigFigsSrc = Converter.GetSigFigs(source.Lon);
SigFigsDest = Converter.GetSigFigs(this.Lon);
this.Lon = Converter.SetSigFigs(this.Lon, SigFigsDest < SigFigsSrc ? SigFigsDest : SigFigsSrc);
SigFigsSrc = Converter.GetSigFigs(source.Height);
SigFigsDest = Converter.GetSigFigs(this.Height);
this.Height = Converter.SetSigFigs(this.Height, SigFigsDest < SigFigsSrc ? SigFigsDest : SigFigsSrc);
}
public bool IsTheSameAs(PolarGeoCoordinate compareTo)
{
if (
compareTo.CoordinateSystem != this.CoordinateSystem ||
compareTo.Height != this.Height ||
compareTo.Lat != this.Lat ||
compareTo.Lon != this.Lon ||
compareTo.Units != this.Units
)
{
return(false);
}
else
{
return(true);
}
}
// overload of IsTheSameAs to ignore rounding errors on final digit and align the sigfigs on both coords
public bool IsTheSameAs(PolarGeoCoordinate compareTo, bool ignoreFinalDigit, bool alignSigFigs)
{
if (alignSigFigs)
{
this.AlignSigFigs(compareTo);
}
if (ignoreFinalDigit)
{
compareTo = ReduceSigFigsBy1(compareTo);
PolarGeoCoordinate comparer = ReduceSigFigsBy1(this);
bool retVal = comparer.IsTheSameAs(compareTo);
return(retVal);
}
return(this.IsTheSameAs(compareTo));
}
public void TestDegreesToRadians()
{
PolarGeoCoordinate deg = new PolarGeoCoordinate(180, 180, 0, AngleUnit.Degrees, CoordinateSystems.OSGB36);
PolarGeoCoordinate rad = new PolarGeoCoordinate(Math.PI, Math.PI, 0, AngleUnit.Radians, CoordinateSystems.OSGB36);
Assert.IsTrue(rad.IsTheSameAs(PolarGeoCoordinate.ChangeUnits(deg, AngleUnit.Radians)));
}
// overload of IsTheSameAs to ignore rounding errors on final digit and align the sigfigs on both coords
public bool IsTheSameAs(PolarGeoCoordinate compareTo, bool ignoreFinalDigit, bool alignSigFigs)
{
if (alignSigFigs)
{
this.AlignSigFigs(compareTo);
}
if (ignoreFinalDigit)
{
compareTo = ReduceSigFigsBy1(compareTo);
PolarGeoCoordinate comparer = ReduceSigFigsBy1(this);
bool retVal = comparer.IsTheSameAs(compareTo);
return retVal;
}
return this.IsTheSameAs(compareTo);
}
public static PolarGeoCoordinate ChangeCoordinateSystem(
PolarGeoCoordinate original, CoordinateSystems destination)
{
PolarGeoCoordinate retVal = Converter.Convert(original, destination);
return retVal;
}
internal void AlignSigFigs(PolarGeoCoordinate source)
{
int SigFigsSrc = Converter.GetSigFigs(source.Lat);
int SigFigsDest = Converter.GetSigFigs(this.Lat);
this.Lat = Converter.SetSigFigs(this.Lat, SigFigsDest < SigFigsSrc ? SigFigsDest : SigFigsSrc);
SigFigsSrc = Converter.GetSigFigs(source.Lon);
SigFigsDest = Converter.GetSigFigs(this.Lon);
this.Lon = Converter.SetSigFigs(this.Lon, SigFigsDest < SigFigsSrc ? SigFigsDest : SigFigsSrc);
SigFigsSrc = Converter.GetSigFigs(source.Height);
SigFigsDest = Converter.GetSigFigs(this.Height);
this.Height = Converter.SetSigFigs(this.Height, SigFigsDest < SigFigsSrc ? SigFigsDest : SigFigsSrc);
}
internal static PolarGeoCoordinate ReduceSigFigsBy1(PolarGeoCoordinate source)
{
double Lat = Converter.SetSigFigs(source.Lat, Converter.GetSigFigs(source.Lat) - 1);
double Lon = Converter.SetSigFigs(source.Lon, Converter.GetSigFigs(source.Lon) - 1);
double Height = Converter.SetSigFigs(source.Height, Converter.GetSigFigs(source.Height) - 1);
return new PolarGeoCoordinate(Lat, Lon, Height, source.Units, source.CoordinateSystem);
}
public bool IsTheSameAs(PolarGeoCoordinate compareTo)
{
if (compareTo.CoordinateSystem != this.CoordinateSystem || compareTo.Height != this.Height
|| compareTo.Lat != this.Lat || compareTo.Lon != this.Lon || compareTo.Units != this.Units)
{
return false;
}
return true;
}
public static PolarGeoCoordinate ChangeCoordinateSystem(PolarGeoCoordinate original, CoordinateSystems destination)
{
PolarGeoCoordinate retVal = Converter.Convert(original, destination);
return(retVal);
}
private static PolarGeoCoordinate Convert(
PolarGeoCoordinate originalCoord, EllipseParameter e1, HelmertTransform t, EllipseParameter e2)
{
// -- convert polar to cartesian coordinates (using ellipse 1)
PolarGeoCoordinate p1 = PolarGeoCoordinate.ChangeUnits(originalCoord, AngleUnit.Radians);
double sinPhi = Math.Sin(p1.Lat);
double cosPhi = Math.Cos(p1.Lat);
double sinLambda = Math.Sin(p1.Lon);
double cosLambda = Math.Cos(p1.Lon);
double H = p1.Height;
double eSq = (Math.Pow(e1.SemimajorAxis, 2) - Math.Pow(e1.SemiMinorAxis, 2)) / Math.Pow(e1.SemimajorAxis, 2);
double nu = e1.SemimajorAxis / Math.Sqrt(1 - eSq * sinPhi * sinPhi);
double x1 = (nu + H) * cosPhi * cosLambda;
double y1 = (nu + H) * cosPhi * sinLambda;
double z1 = ((1 - eSq) * nu + H) * sinPhi;
// -- apply helmert transform using appropriate params
double tx = t.tx, ty = t.ty, tz = t.tz;
double rx = t.rx / 3600 * Math.PI / 180; // normalise seconds to radians
double ry = t.ry / 3600 * Math.PI / 180;
double rz = t.rz / 3600 * Math.PI / 180;
double s1 = t.s / 1e6 + 1; // normalise ppm to (s+1)
// apply transform
double x2 = tx + x1 * s1 - y1 * rz + z1 * ry;
double y2 = ty + x1 * rz + y1 * s1 - z1 * rx;
double z2 = tz - x1 * ry + y1 * rx + z1 * s1;
// -- convert cartesian to polar coordinates (using ellipse 2)
double a = e2.SemimajorAxis;
double precision = 4 / e2.SemimajorAxis; // results accurate to around 4 metres
eSq = (Math.Pow(e2.SemimajorAxis, 2) - Math.Pow(e2.SemiMinorAxis, 2)) / Math.Pow(e2.SemimajorAxis, 2);
double p = Math.Sqrt(x2 * x2 + y2 * y2);
double phi = Math.Atan2(z2, p * (1 - eSq)), phiP = 2 * Math.PI;
while (Math.Abs(phi - phiP) > precision)
{
nu = a / Math.Sqrt(1 - eSq * Math.Sin(phi) * Math.Sin(phi));
phiP = phi;
phi = Math.Atan2(z2 + eSq * nu * Math.Sin(phi), p);
}
double lambda = Math.Atan2(y2, x2);
H = p / Math.Cos(phi) - nu;
return new PolarGeoCoordinate(
RadToDeg(phi), RadToDeg(lambda), H, AngleUnit.Degrees, t.outputCoordinateSystem);
}
internal static PolarGeoCoordinate GridReferenceToGeodesic(GridReference g)
{
double lat = _NatGridTrueOrigin.Lat;
double M = 0;
do
{
lat = (g.Northing - _NatNETrueOrigin.Northing - M) / (_Airy1830.SemimajorAxis * _NatGridScaleFactor)
+ lat;
double Ma = (1 + _n + (5d / 4d) * _n2 + (5d / 4d) * _n3) * (lat - _NatGridTrueOrigin.Lat);
double Mb = (3 * _n + 3 * _n * _n + (21d / 8d) * _n3) * Math.Sin(lat - _NatGridTrueOrigin.Lat)
* Math.Cos(lat + _NatGridTrueOrigin.Lat);
double Mc = ((15d / 8d) * _n2 + (15d / 8d) * _n3) * Math.Sin(2 * (lat - _NatGridTrueOrigin.Lat))
* Math.Cos(2 * (lat + _NatGridTrueOrigin.Lat));
double Md = (35d / 24d) * _n3 * Math.Sin(3 * (lat - _NatGridTrueOrigin.Lat))
* Math.Cos(3 * (lat + _NatGridTrueOrigin.Lat));
M = _Airy1830.SemiMinorAxis * _NatGridScaleFactor * (Ma - Mb + Mc - Md); // meridional arc
}
while (g.Northing - _NatNETrueOrigin.Northing - M >= 0.00001); // ie until < 0.01mm
double cosLat = Math.Cos(lat), sinLat = Math.Sin(lat);
double nu = _Airy1830.SemimajorAxis * _NatGridScaleFactor / Math.Sqrt(1 - _e2 * sinLat * sinLat);
// transverse radius of curvature
double rho = _Airy1830.SemimajorAxis * _NatGridScaleFactor * (1 - _e2)
/ Math.Pow(1 - _e2 * sinLat * sinLat, 1.5); // meridional radius of curvature
double eta2 = nu / rho - 1;
double tanLat = Math.Tan(lat);
double tan2lat = tanLat * tanLat, tan4lat = tan2lat * tan2lat, tan6lat = tan4lat * tan2lat;
double secLat = 1 / cosLat;
double nu3 = nu * nu * nu, nu5 = nu3 * nu * nu, nu7 = nu5 * nu * nu;
double VII = tanLat / (2 * rho * nu);
double VIII = tanLat / (24 * rho * nu3) * (5 + 3 * tan2lat + eta2 - 9 * tan2lat * eta2);
double IX = tanLat / (720 * rho * nu5) * (61 + 90 * tan2lat + 45 * tan4lat);
double X = secLat / nu;
double XI = secLat / (6 * nu3) * (nu / rho + 2 * tan2lat);
double XII = secLat / (120 * nu5) * (5 + 28 * tan2lat + 24 * tan4lat);
double XIIA = secLat / (5040 * nu7) * (61 + 662 * tan2lat + 1320 * tan4lat + 720 * tan6lat);
double dE = g.Easting - _NatNETrueOrigin.Easting;
double dE2 = dE * dE;
double dE3 = dE2 * dE;
double dE4 = dE2 * dE2;
double dE5 = dE3 * dE2;
double dE6 = dE4 * dE2;
double dE7 = dE5 * dE2;
lat = lat - VII * dE2 + VIII * dE4 - IX * dE6;
double lon = _NatGridTrueOrigin.Lon + X * dE - XI * dE3 + XII * dE5 - XIIA * dE7;
var retVal = new PolarGeoCoordinate(lat, lon, 0, AngleUnit.Radians, CoordinateSystems.OSGB36);
retVal = PolarGeoCoordinate.ChangeUnits(retVal, AngleUnit.Degrees);
retVal.SetSigFigs(7);
return retVal;
}