/// <summary>
/// Rotates a point around another around point with a given angle clockwise.
/// </summary>
/// <returns>The around point.</returns>
/// <param name="angle">Angle.</param>
/// <param name="center">Center.</param>
/// <param name="point">Point.</param>
public static PointF2D RotateAroundPoint(Radian angle, PointF2D center, PointF2D point)
{
double sin = System.Math.Sin (angle.Value);
double cos = System.Math.Cos (angle.Value);
double newX = center [0] + (cos * (point [0] - center[0]) + sin * (point [1] - center [1]));
double newY = center [1] + (-sin * (point [0] - center[0]) + cos * (point [1] - center [1]));
return new PointF2D (newX, newY);
}
/// <summary>
/// Rotates a set of points around another around point with a given angle clockwise.
/// </summary>
/// <returns>The around point.</returns>
/// <param name="angle">Angle.</param>
/// <param name="center">Center.</param>
/// <param name="points">Points.</param>
public static PointF2D[] RotateAroundPoint(Radian angle, PointF2D center, PointF2D[] points)
{
double sin = System.Math.Sin (angle.Value);
double cos = System.Math.Cos (angle.Value);
PointF2D[] rotated = new PointF2D[points.Length];
for (int idx = 0; idx < points.Length; idx++) {
double newX = center [0] + (cos * (points[idx] [0] - center[0]) + sin * (points[idx] [1] - center [1]));
double newY = center [1] + (-sin * (points[idx] [0] - center[0]) + cos * (points[idx] [1] - center [1]));
rotated[idx] = new PointF2D (newX, newY);
}
return rotated;
}
/// <summary>
/// Rotates this view around it's center with a given angle and returns the modified version.
/// </summary>
/// <returns>The around center.</returns>
/// <param name="angle">Angle.</param>
public View2D RotateAroundCenter(Radian angle)
{
RectangleF2D rotated = this.Rectangle.RotateAroundCenter (angle);
return new View2D (rotated, _invertX, _invertY);
}
/// <summary>
/// Converts the given lambert coordinates to mercator coordinates.
/// </summary>
/// <param name="x"></param>
/// <param name="y"></param>
/// <returns></returns>
public GeoCoordinate ConvertToWGS84(double x, double y)
{
double latitude;
double longitude;
double r = (System.Math.Sqrt(
System.Math.Pow(x - _x_origin, 2.0) +
System.Math.Pow((_r_0 - (y - _y_origin)), 2.0))
);
double t = System.Math.Pow((r / (_ellipsoid.SemiMajorAxis * _g)), 1.0 / _n);
double phi = System.Math.Atan((x - _x_origin) /
(_r_0 - (y - _y_origin)));
longitude = ((phi / _n) + _longitude_origin_radians);
latitude = (System.Math.PI / 2.0 - 2.0 * System.Math.Atan(t));
double e = _ellipsoid.Eccentricity;
double new_latitude = 0;
while (new_latitude != latitude)
{ // iterate 100 times.
new_latitude = latitude;
latitude = (System.Math.PI / 2.0 - 2.0 *
System.Math.Atan(t *
System.Math.Pow(
((1.0 - e * System.Math.Sin(latitude)) / (1.0 + e * System.Math.Sin(latitude))),
e / 2.0)));
}
Hayford1924Ellipsoid hayford = new Hayford1924Ellipsoid();
double phi_72 = latitude; // phi = latitude!
double lambda_72 = longitude; // lambda = longitude!
double h_72 = 100;
double a_72 = hayford.SemiMajorAxis;
double e_72 = hayford.Eccentricity;
double es_72 = e_72 * e_72;
double sin_phi_72 = System.Math.Sin(phi_72);
double cos_phi_72 = System.Math.Cos(phi_72);
double sin_lambda_72 = System.Math.Sin(lambda_72);
double cos_lambda_72 = System.Math.Cos(lambda_72);
double v_72 = a_72 / System.Math.Sqrt(1 - (es_72 * sin_phi_72 * sin_phi_72));
double X_72 = (v_72 + h_72) * cos_phi_72 * cos_lambda_72;
double Y_72 = (v_72 + h_72) * cos_phi_72 * sin_lambda_72;
double Z_72 = ((1 - es_72) * v_72 + h_72) * sin_phi_72;
// ALL OK
//X_72 = X_72 * (1 / 1.0000012747);
//Y_72 = Y_72 * (1 / 1.0000012747);
//Z_72 = Z_72 * (1 / 1.0000012747);
// translations.
double x_trans = 106.868628;
double y_trans = 52.297783;
double z_trans = 103.723893;
double X_89 = X_72 - x_trans;
double Y_89 = Y_72 + y_trans;
double Z_89 = Z_72 - z_trans;
// rotations.
double x_angle = ((Radian)new Degree(0.336570 / 3600)).Value;
double sin_x_angle = System.Math.Sin(x_angle);
double cos_x_angle = System.Math.Cos(x_angle);
double y_angle = ((Radian)new Degree(-0.456955 / 3600)).Value;
double sin_y_angle = System.Math.Sin(y_angle);
double cos_y_angle = System.Math.Cos(y_angle);
double z_angle = ((Radian)new Degree(1.842183 / 3600)).Value;
double sin_z_angle = System.Math.Sin(z_angle);
double cos_z_angle = System.Math.Cos(z_angle);
// rotate around x.
//X_89 = X_89;
Y_89 = Y_89 * cos_x_angle - Z_89 * sin_x_angle;
Z_89 = Y_89 * sin_x_angle + Z_89 * cos_x_angle;
// rotate around y.
X_89 = X_89 * cos_y_angle + Z_89 * sin_y_angle;
//Y_89 = Y_89;
Z_89 = X_89 * (-sin_y_angle) + Z_89 * cos_y_angle;
// rotate around Z.
X_89 = X_89 * cos_z_angle - Y_89 * sin_z_angle;
Y_89 = X_89 * sin_z_angle + Y_89 * cos_z_angle;
//Z_89 = Z_89;
Wgs1984Ellipsoid wgs1984 = new Wgs1984Ellipsoid();
e = wgs1984.Eccentricity;
double es = e * e;
double ps = X_89 * X_89 + Y_89 * Y_89;
double p = System.Math.Sqrt(ps);
r = System.Math.Sqrt(ps + Z_89 * Z_89);
double f = wgs1984.Flattening;
double a = wgs1984.SemiMajorAxis;
double u = System.Math.Atan((Z_89 / p) * ((1 - f) + (es * a / r)));
double lambda = System.Math.Atan(Y_89 / X_89);
phi = System.Math.Atan((Z_89 * (1 - f) + (es * a * System.Math.Pow(System.Math.Sin(u), 3)))
/
((1 - f) * (p - (es * a * System.Math.Pow(System.Math.Cos(u), 3)))));
Degree longitude_84 = new Radian(lambda);
Degree latitude_84 = new Radian(phi);
return new GeoCoordinate(latitude_84.Value, longitude_84.Value);
}
/// <summary>
/// Creates a new angle in radians.
/// </summary>
/// <param name="value"></param>
public Radian(double value)
: base(Radian.Normalize(value))
{
}