/// <summary>
/// The inverse transform from linear units to geodetic units
/// </summary>
/// <param name="xy">The double values for the input x and y values stored in an array</param>
/// <param name="lp">The double values for the output lambda and phi values stored in an array</param>
protected override void OnInverse(double[] xy, double[] lp)
{
int i;
double phipp = 2 * (Math.Atan(Math.Exp(xy[Y] / _kR)) - FortPi);
double lampp = xy[X] / _kR;
double cp = Math.Cos(phipp);
double phip = Proj.Aasin(_cosp0 * Math.Sin(phipp) + _sinp0 * cp * Math.Cos(lampp));
double lamp = Proj.Aasin(cp * Math.Sin(lampp) / Math.Cos(phip));
double con = (_k - Math.Log(Math.Tan(FortPi + 0.5 * phip))) / _c;
for (i = Niter; i > 0; --i)
{
double esp = E * Math.Sin(phip);
double delp = (con + Math.Log(Math.Tan(FortPi + 0.5 * phip)) - _hlfE *
Math.Log((1 + esp) / (1 - esp))) *
(1 - esp * esp) * Math.Cos(phip) * ROneEs;
phip -= delp;
if (Math.Abs(delp) < EPS)
{
break;
}
}
if (i <= 0)
{
throw new ProjectionException(20);
}
lp[Phi] = phip;
lp[Lambda] = lamp / _c;
}
/// <summary>
/// The inverse transform from linear units to geodetic units
/// </summary>
/// <param name="xy">The double values for the input x and y values stored in an array</param>
/// <param name="lp">The double values for the output lambda and phi values stored in an array</param>
protected override void OnInverse(double[] xy, double[] lp)
{
lp[Phi] = Proj.Aasin(xy[Y] / _cY);
lp[Lambda] = xy[X] / (_cX * Math.Cos(lp[Phi]));
lp[Phi] += lp[Phi];
lp[Phi] = Proj.Aasin((lp[Phi] + Math.Sin(lp[Phi])) / _cP);
}
/// <summary>
/// The inverse transform from linear units to geodetic units
/// </summary>
/// <param name="xy">The double values for the input x and y values stored in an array</param>
/// <param name="lp">The double values for the output lambda and phi values stored in an array</param>
protected override void OnInverse(double[] xy, double[] lp)
{
double c;
lp[Phi] = Proj.Aasin(xy[Y] / Cy);
lp[Lambda] = xy[X] / (Cx * (1 + (c = Math.Cos(lp[Phi]))));
lp[Phi] = Proj.Aasin((lp[Phi] + Math.Sin(lp[Phi]) * (c + 2)) / CP);
}
/// <summary>
/// Performs the inverse transform from a single coordinate of linear units to the same coordinate in geodetic lambda and
/// phi units in the special case where the shape of the earth is being approximated as a perfect sphere.
/// </summary>
/// <param name="xy">The double linear input x and y values organized into a 1 dimensional array</param>
/// <param name="lp">The double geodetic output lambda and phi values organized into a 1 dimensional array</param>
protected override void SphericalInverse(double[] xy, double[] lp)
{
xy[Y] /= _cY;
lp[Phi] = _m > 0
? Proj.Aasin((_m * xy[Y] + Math.Sin(xy[Y])) / _n)
:
(_n != 1 ? Proj.Aasin(Math.Sin(xy[Y]) / _n) : xy[Y]);
lp[Lambda] = xy[X] / (_cX * (_m + Math.Cos(xy[Y])));
}
/// <summary>
/// The forward transform from geodetic units to linear units
/// </summary>
/// <param name="lp">The array of lambda, phi coordinates</param>
/// <param name="xy">The array of x, y coordinates</param>
protected override void OnForward(double[] lp, double[] xy)
{
double sp = E * Math.Sin(lp[Phi]);
double phip = 2 * Math.Atan(Math.Exp(_c * (
Math.Log(Math.Tan(FortPi + 0.5 * lp[Phi])) - _hlfE * Math.Log((1 + sp) / (1 - sp)))
+ _k)) - HalfPi;
double lamp = _c * lp[Lambda];
double cp = Math.Cos(phip);
double phipp = Proj.Aasin(_cosp0 * Math.Sin(phip) - _sinp0 * cp * Math.Cos(lamp));
double lampp = Proj.Aasin(cp * Math.Sin(lamp) / Math.Cos(phipp));
xy[X] = _kR * lampp;
xy[Y] = _kR * Math.Log(Math.Tan(FortPi + 0.5 * phipp));
}
/// <summary>
/// Performs the inverse transfrom from a single coordinate of linear units to the same coordinate in geodetic units
/// </summary>
/// <param name="xy">The double linear input x and y values organized into a 1 dimensional array</param>
/// <param name="lp">The double geodetic output lambda and phi values organized into a 1 dimensional array</param>
protected override void EllipticalInverse(double[] xy, double[] lp)
{
if (_isGuam)
{
GuamInverse(xy, lp);
}
double c;
if ((c = Proj.Hypot(xy[X], xy[Y])) < EPS10)
{
lp[Phi] = Phi0;
lp[Lambda] = 0;
return;
}
if (_mode == Modes.Oblique || _mode == Modes.Equitorial)
{
double az;
double cosAz = Math.Cos(az = Math.Atan2(xy[X], xy[Y]));
double t = _cosph0 * cosAz;
double b = Es * t / OneEs;
double a = -b * t;
b *= 3 * (1 - a) * _sinph0;
double d = c / _N1;
double e = d * (1 - d * d * (a * (1 + a) / 6 + b * (1 + 3 * a) * d / 24));
double f = 1 - e * e * (a / 2 + b * e / 6);
double psi = Proj.Aasin(_sinph0 * Math.Cos(e) + t * Math.Sin(e));
lp[Lambda] = Proj.Aasin(Math.Sin(az) * Math.Sin(e) / Math.Cos(psi));
if ((t = Math.Abs(psi)) < EPS10)
{
lp[Phi] = 0;
}
else if (Math.Abs(t - HalfPi) < 0)
{
lp[Phi] = HalfPi;
}
else
{
lp[Phi] = Math.Atan((1 - Es * f * _sinph0 / Math.Sin(psi)) * Math.Tan(psi) /
OneEs);
}
}
else
{
/* Polar */
lp[Phi] = Proj.InvMlfn(_mode == Modes.NorthPole ? _Mp - c : _Mp + c,
Es, _en);
lp[Lambda] = Math.Atan2(xy[X], _mode == Modes.NorthPole ? -xy[Y] : xy[Y]);
}
}
/// <summary>
/// Performs the inverse transform from a single coordinate of linear units to the same coordinate in geodetic lambda and
/// phi units in the special case where the shape of the earth is being approximated as a perfect sphere.
/// </summary>
/// <param name="xy">The double linear input x and y values organized into a 1 dimensional array</param>
/// <param name="lp">The double geodetic output lambda and phi values organized into a 1 dimensional array</param>
protected override void SphericalInverse(double[] xy, double[] lp)
{
double cRh;
if ((cRh = Proj.Hypot(xy[X], xy[Y])) > Math.PI)
{
if (cRh - EPS10 > Math.PI)
{
throw new ProjectionException(20);
}
cRh = Math.PI;
}
else if (cRh < EPS10)
{
lp[Phi] = Phi0;
lp[Lambda] = 0;
return;
}
if (_mode == Modes.Oblique || _mode == Modes.Equitorial)
{
double sinc = Math.Sin(cRh);
double cosc = Math.Cos(cRh);
if (_mode == Modes.Equitorial)
{
lp[Phi] = Proj.Aasin(xy[Y] * sinc / cRh);
xy[X] *= sinc;
xy[Y] = cosc * cRh;
}
else
{
lp[Phi] = Proj.Aasin(cosc * _sinph0 + xy[Y] * sinc * _cosph0 /
cRh);
xy[Y] = (cosc - _sinph0 * Math.Sin(lp[Phi])) * cRh;
xy[X] *= sinc * _cosph0;
}
lp[Lambda] = xy[Y] == 0 ? 0 : Math.Atan2(xy[X], xy[Y]);
}
else if (_mode == Modes.NorthPole)
{
lp[Phi] = HalfPi - cRh;
lp[Lambda] = Math.Atan2(xy[X], -xy[Y]);
}
else
{
lp[Phi] = cRh - HalfPi;
lp[Lambda] = Math.Atan2(xy[X], xy[Y]);
}
}
/// <summary>
/// The inverse transform from linear units to geodetic units
/// </summary>
/// <param name="xy">The double values for the input x and y values stored in an array</param>
/// <param name="lp">The double values for the output lambda and phi values stored in an array</param>
protected override void OnInverse(double[] xy, double[] lp)
{
xy[Y] /= _cY;
double c = Math.Cos(lp[Phi] = _tanMode ? Math.Atan(xy[Y]) : Proj.Aasin(xy[Y]));
lp[Phi] /= _cP;
lp[Lambda] = xy[X] / (_cX * Math.Cos(lp[Phi] /= _cP));
if (_tanMode)
{
lp[Lambda] /= c * c;
}
else
{
lp[Lambda] *= c;
}
}
/// <summary>
/// Initializes the transform using the parameters from the specified coordinate system information
/// </summary>
/// <param name="projInfo">A ProjectionInfo class contains all the standard and custom parameters needed to initialize this transform</param>
protected override void OnInit(ProjectionInfo projInfo)
{
double phip0;
_hlfE = 0.5 * E;
double cp = Math.Cos(Phi0);
cp *= cp;
_c = Math.Sqrt(1 + Es * cp * cp * ROneEs);
double sp = Math.Sin(Phi0);
_cosp0 = Math.Cos(phip0 = Proj.Aasin(_sinp0 = sp / _c));
sp *= E;
_k = Math.Log(Math.Tan(FortPi + 0.5 * phip0)) - _c * (
Math.Log(Math.Tan(FortPi + 0.5 * Phi0)) - _hlfE *
Math.Log((1 + sp) / (1 - sp)));
_kR = K0 * Math.Sqrt(OneEs) / (1 - sp * sp);
}
/// <summary>
/// The inverse transform from linear units to geodetic units
/// </summary>
/// <param name="xy">The double values for the input x and y values stored in an array</param>
/// <param name="lp">The double values for the output lambda and phi values stored in an array</param>
protected override void OnInverse(double[] xy, double[] lp)
{
double cz1 = Math.Cos(Proj.Hypot(xy[Y], xy[X] + _hz0));
double cz2 = Math.Cos(Proj.Hypot(xy[Y], xy[X] - _hz0));
double s = cz1 + cz2;
double d = cz1 - cz2;
lp[Lambda] = -Math.Atan2(d, (s * _thz0));
lp[Phi] = Proj.Aacos(Proj.Hypot(_thz0 * s, d) * _rhshz0);
if (xy[Y] < 0)
{
lp[Phi] = -lp[Phi];
}
/* lam--phi now in system relative to P1--P2 base equator */
double sp = Math.Sin(lp[Phi]);
double cp = Math.Cos(lp[Phi]);
lp[Phi] = Proj.Aasin(_sa * sp + _ca * cp * (s = Math.Cos(lp[Lambda] -= _lp)));
lp[Lambda] = Math.Atan2(cp * Math.Sin(lp[Lambda]), _sa * cp * s - _ca * sp) + _lamc;
}
/// <summary>
/// Initializes the transform using the parameters from the specified coordinate system information
/// </summary>
/// <param name="projInfo">A ProjectionInfo class contains all the standard and custom parameters needed to initialize this transform</param>
protected override void OnInit(ProjectionInfo projInfo)
{
double pp;
/* get control point locations */
double phi1 = projInfo.GetPhi1();
double lam1 = projInfo.GetLam1();
double phi2 = projInfo.GetPhi2();
double lam2 = projInfo.GetLam2();
if (phi1 == phi2 && lam1 == lam2)
{
throw new ProjectionException(-25);
}
Lam0 = Proj.Adjlon(0.5 * (lam1 + lam2));
_dlam2 = Proj.Adjlon(lam2 - lam1);
_cp1 = Math.Cos(phi1);
_cp2 = Math.Cos(phi2);
_sp1 = Math.Sin(phi1);
_sp2 = Math.Sin(phi2);
_cs = _cp1 * _sp2;
_sc = _sp1 * _cp2;
_ccs = _cp1 * _cp2 * Math.Sin(_dlam2);
_z02 = Proj.Aacos(_sp1 * _sp2 + _cp1 * _cp2 * Math.Cos(_dlam2));
_hz0 = .5 * _z02;
double A12 = Math.Atan2(_cp2 * Math.Sin(_dlam2),
_cp1 * _sp2 - _sp1 * _cp2 * Math.Cos(_dlam2));
_ca = Math.Cos(pp = Proj.Aasin(_cp1 * Math.Sin(A12)));
_sa = Math.Sin(pp);
_lp = Proj.Adjlon(Math.Atan2(_cp1 * Math.Cos(A12), _sp1) - _hz0);
_dlam2 *= .5;
_lamc = HalfPi - Math.Atan2(Math.Sin(A12) * _sp1, Math.Cos(A12)) - _dlam2;
_thz0 = Math.Tan(_hz0);
_rhshz0 = .5 / Math.Sin(_hz0);
_r2z0 = 0.5 / _z02;
_z02 *= _z02;
}
