/**
* Convert lat/lon point in WGS84 to OSGB36
*
* @param {LatLon} pWGS84: lat/lon in WGS84 reference frame
* @return {LatLon} lat/lon point in OSGB36 reference frame
*/
private LatLong ConvertOSGB36ToWGS84(double northing, double easting)
{
LatLong LatLongOSGB36 = OSGB36GridToLatLong(northing, easting);
return(ConvertEllipsoidOSGB36ToWGS84(LatLongOSGB36));
}
/**
* Convert lat/lon from one ellipsoidal model to another
*
* q.v. Ordnance Survey 'A guide to coordinate systems in Great Britain' Section 6
* www.ordnancesurvey.co.uk/oswebsite/gps/docs/A_Guide_to_Coordinate_Systems_in_Great_Britain.pdf
*
* @private
* @param {LatLon} point: lat/lon in source reference frame
* @param {Number[]} sourceEllipse: source ellipse parameters
* @param {Number[]} t: Helmert transform parameters
* @param {Number[]} targetEllipse: target ellipse parameters
* @return {Coord} lat/lon in target reference frame
*/
private LatLong ConvertEllipsoidOSGB36ToWGS84(LatLong point)
{
var t = TransformFromOSGB36ToWGS84;
var sourceEllipse = Ellipse[EllipseEnum.Airy1830];
var targetEllipse = Ellipse[EllipseEnum.WGS84];
// -- 1: convert polar to Cartesian coordinates (using ellipse 1)
var lat = ToRadian(point.Lat);
var lon = ToRadian(point.Long);
var a = sourceEllipse.A;
var b = sourceEllipse.B;
var sinPhi = Math.Sin(lat);
var cosPhi = Math.Cos(lat);
var sinLambda = Math.Sin(lon);
var cosLambda = Math.Cos(lon);
var h = 24.7; // for the moment
var eSq = (a * a - b * b) / (a * a);
var nu = a / Math.Sqrt(1 - eSq * sinPhi * sinPhi);
var x1 = (nu + h) * cosPhi * cosLambda;
var y1 = (nu + h) * cosPhi * sinLambda;
var z1 = ((1 - eSq) * nu + h) * sinPhi;
// -- 2: apply Helmert transform using appropriate params
var tx = t.Tx;
var ty = t.Ty;
var tz = t.Tz;
var rx = ToRadian(t.Rx / 3600); // normalise seconds to radians
var ry = ToRadian(t.Ry / 3600);
var rz = ToRadian(t.Rz / 3600);
var s1 = t.S / 1e6 + 1; // normalise ppm to (s+1)
// apply transform
var x2 = tx + x1 * s1 - y1 * rz + z1 * ry;
var y2 = ty + x1 * rz + y1 * s1 - z1 * rx;
var z2 = tz - x1 * ry + y1 * rx + z1 * s1;
// -- 3: convert Cartesian to polar coordinates (using ellipse 2)
a = targetEllipse.A;
b = targetEllipse.B;
var precision = 4 / a; // results accurate to around 4 metres
eSq = (a * a - b * b) / (a * a);
var p = Math.Sqrt(x2 * x2 + y2 * y2);
var phi = Math.Atan2(z2, p * (1 - eSq));
var 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);
}
var lambda = Math.Atan2(y2, x2);
h = p / Math.Cos(phi) - nu;
return new LatLong(ToDegree(phi), ToDegree(lambda), h);
}
/**
* Convert lat/lon from one ellipsoidal model to another
*
* q.v. Ordnance Survey 'A guide to coordinate systems in Great Britain' Section 6
* www.ordnancesurvey.co.uk/oswebsite/gps/docs/A_Guide_to_Coordinate_Systems_in_Great_Britain.pdf
*
* @private
* @param {LatLon} point: lat/lon in source reference frame
* @param {Number[]} sourceEllipse: source ellipse parameters
* @param {Number[]} t: Helmert transform parameters
* @param {Number[]} targetEllipse: target ellipse parameters
* @return {Coord} lat/lon in target reference frame
*/
private LatLong ConvertEllipsoidOSGB36ToWGS84(LatLong point)
{
var t = TransformFromOSGB36ToWGS84;
var sourceEllipse = Ellipse[EllipseEnum.Airy1830];
var targetEllipse = Ellipse[EllipseEnum.WGS84];
// -- 1: convert polar to Cartesian coordinates (using ellipse 1)
var lat = ToRadian(point.Lat);
var lon = ToRadian(point.Long);
var a = sourceEllipse.A;
var b = sourceEllipse.B;
var sinPhi = Math.Sin(lat);
var cosPhi = Math.Cos(lat);
var sinLambda = Math.Sin(lon);
var cosLambda = Math.Cos(lon);
var h = 24.7; // for the moment
var eSq = (a * a - b * b) / (a * a);
var nu = a / Math.Sqrt(1 - eSq * sinPhi * sinPhi);
var x1 = (nu + h) * cosPhi * cosLambda;
var y1 = (nu + h) * cosPhi * sinLambda;
var z1 = ((1 - eSq) * nu + h) * sinPhi;
// -- 2: apply Helmert transform using appropriate params
var tx = t.Tx;
var ty = t.Ty;
var tz = t.Tz;
var rx = ToRadian(t.Rx / 3600); // normalise seconds to radians
var ry = ToRadian(t.Ry / 3600);
var rz = ToRadian(t.Rz / 3600);
var s1 = t.S / 1e6 + 1; // normalise ppm to (s+1)
// apply transform
var x2 = tx + x1 * s1 - y1 * rz + z1 * ry;
var y2 = ty + x1 * rz + y1 * s1 - z1 * rx;
var z2 = tz - x1 * ry + y1 * rx + z1 * s1;
// -- 3: convert Cartesian to polar coordinates (using ellipse 2)
a = targetEllipse.A;
b = targetEllipse.B;
var precision = 4 / a; // results accurate to around 4 metres
eSq = (a * a - b * b) / (a * a);
var p = Math.Sqrt(x2 * x2 + y2 * y2);
var phi = Math.Atan2(z2, p * (1 - eSq));
var 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);
}
var lambda = Math.Atan2(y2, x2);
h = p / Math.Cos(phi) - nu;
return(new LatLong(ToDegree(phi), ToDegree(lambda), h));
}
