/// <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>
/// 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)
{
if ((_rho = _c - (IsElliptical ? _n * Proj.Qsfn(Math.Sin(lp[Phi]),
E, OneEs) : _n2 *Math.Sin(lp[Phi]))) < 0)
{
xy[X] = double.NaN;
xy[Y] = double.NaN;
//throw new ProjectionException(20);
return;
}
_rho = _dd * Math.Sqrt(_rho);
xy[X] = _rho * Math.Sin(lp[Lambda] *= _n);
xy[Y] = _rho0 - _rho * Math.Cos(lp[Lambda]);
}
/// <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>
/// 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 sinphi;
if (projInfo.StandardParallel1 != null)
{
_phi1 = projInfo.StandardParallel1.Value * Math.PI / 180;
}
if (projInfo.StandardParallel2 != null)
{
_phi2 = projInfo.StandardParallel2.Value * Math.PI / 180;
}
if (Math.Abs(_phi1 + _phi2) < EPS10)
{
throw new ProjectionException(-21);
}
_en = Proj.Enfn(Es);
_n = sinphi = Math.Sin(_phi1);
double cosphi = Math.Cos(_phi1);
bool secant = Math.Abs(_phi1 - _phi2) >= EPS10;
if (IsElliptical)
{
double m1 = Proj.Msfn(sinphi, cosphi, Es);
double ml1 = Proj.Mlfn(_phi1, sinphi, cosphi, _en);
if (secant)
{
/* secant cone */
sinphi = Math.Sin(_phi2);
cosphi = Math.Cos(_phi2);
_n = (m1 - Proj.Msfn(sinphi, cosphi, Es)) /
(Proj.Mlfn(_phi2, sinphi, cosphi, _en) - ml1);
}
_c = ml1 + m1 / _n;
_rho0 = _c - Proj.Mlfn(Phi0, Math.Sin(Phi0),
Math.Cos(Phi0), _en);
}
else
{
if (secant)
{
_n = (cosphi - Math.Cos(_phi2)) / (_phi2 - _phi1);
}
_c = _phi1 + Math.Cos(_phi1) / _n;
_rho0 = _c - Phi0;
}
}
/// <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)
{
double ph1 = Proj.InvMlfn(_m0 + xy[Y], Es, _en);
_tn = Math.Tan(ph1); _t = _tn * _tn;
_n = Math.Sin(ph1);
_r = 1 / (1 - Es * _n * _n);
_n = Math.Sqrt(_r);
_r *= (1 - Es) * _n;
_dd = xy[X] / _n;
_d2 = _dd * _dd;
lp[Phi] = ph1 - (_n * _tn / _r) * _d2 *
(.5 - (1 + 3 * _t) * _d2 * C3);
lp[Lambda] = _dd * (1 + _t * _d2 *
(-C4 + (1 + 3 * _t) * _d2 * C5)) / Math.Cos(ph1);
}
private void GuamInverse(double[] xy, double[] lp)
{
double t = 0;
int i;
double x2 = 0.5 * xy[X] * xy[X];
lp[Phi] = Phi0;
for (i = 0; i < 3; ++i)
{
t = E * Math.Sin(lp[Phi]);
lp[Phi] = Proj.InvMlfn(_M1 + xy[Y] -
x2 * Math.Tan(lp[Phi]) * (t = Math.Sqrt(1 - t * t)), Es, _en);
}
lp[Lambda] = xy[X] * t / Math.Cos(lp[Phi]);
}
/// <summary>
/// The forward transform where the spheroidal model of the earth has a flattening factor,
/// matching more closely with the oblique spheroid of the actual earth
/// </summary>
/// <param name="lp">The double values for geodetic lambda and phi organized into a one dimensional array</param>
/// <param name="xy">The double values for linear x and y organized into a one dimensional array</param>
protected override void EllipticalForward(double[] lp, double[] xy)
{
if (Math.Abs(lp[Phi]) <= TOL)
{
xy[X] = lp[Lambda]; xy[Y] = -_ml0;
}
else
{
double sp = Math.Sin(lp[Phi]);
double cp;
double ms = Math.Abs(cp = Math.Cos(lp[Phi])) > TOL?Proj.Msfn(sp, cp, Es) / sp : 0;
xy[X] = ms * Math.Sin(lp[Lambda] *= sp);
xy[Y] = (Proj.Mlfn(lp[Phi], sp, cp, _en) - _ml0) + ms * (1 - Math.Cos(lp[Lambda]));
}
}
/// <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>
/// 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[] p = new double[2];
lp[Phi] = (lp[Phi] - Phi0) * RadToSec5;
p[R] = _tpsi[Ntpsi];
for (int i = Ntpsi - 1; i >= 0; i--)
{
p[R] = _tpsi[i] + lp[Phi] * p[R];
}
p[R] *= lp[Phi];
p[I] = lp[Lambda];
p = Proj.Zpoly1(p, _bf, Nbf);
xy[X] = p[I];
xy[Y] = p[R];
}
/// <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 ul, us;
double vl = Math.Sin(_bl * lp[Lambda]);
if (Math.Abs(Math.Abs(lp[Phi]) - Math.PI / 2) <= EPS10)
{
ul = lp[Phi] < 0 ? -_singam : _singam;
us = _al * lp[Phi] / _bl;
}
else
{
double q = _el / (_ellips ? Math.Pow(Proj.Tsfn(lp[Phi], Math.Sin(lp[Phi]), E), _bl) : TSFN0(lp[Phi]));
double s = .5 * (q - 1 / q);
ul = 2 * (s * _singam - vl * _cosgam) / (q + 1 / q);
double con = Math.Cos(_bl * lp[Lambda]);
if (Math.Abs(con) >= Tol)
{
us = _al * Math.Atan((s * _cosgam + vl * _singam) / con) / _bl;
if (con < 0)
{
us += Math.PI * _al / _bl;
}
}
else
{
us = _al * _bl * lp[Lambda];
}
}
if (Math.Abs(Math.Abs(ul) - 1) <= EPS10)
{
throw new ProjectionException(20);
}
double vs = .5 * _al * Math.Log((1 - ul) / (1 + ul)) / _bl;
us -= _u0;
if (!_rot)
{
xy[X] = us;
xy[Y] = vs;
}
else
{
xy[X] = vs * _cosrot + us * _sinrot;
xy[Y] = us * _cosrot - vs * _sinrot;
}
}
/// <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 t, dl1, dl2;
double sp = Math.Sin(lp[Phi]);
double cp = Math.Cos(lp[Phi]);
double z1 = Proj.Aacos(_sp1 * sp + _cp1 * cp * Math.Cos(dl1 = lp[Lambda] + _dlam2));
double z2 = Proj.Aacos(_sp2 * sp + _cp2 * cp * Math.Cos(dl2 = lp[Lambda] - _dlam2));
z1 *= z1;
z2 *= z2;
xy[X] = _r2z0 * (t = z1 - z2);
t = _z02 - t;
xy[Y] = _r2z0 * Proj.Asqrt(4 * _z02 * z2 - t * t);
if ((_ccs * sp - cp * (_cs * Math.Sin(dl1) - _sc * Math.Sin(dl2))) < 0)
{
xy[Y] = -xy[Y];
}
}
/// <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)
{
double s;
if ((s = Math.Abs(lp[Phi] = Proj.InvMlfn(xy[Y], Es, _en))) < HalfPi)
{
s = Math.Sin(lp[Phi]);
lp[Lambda] = xy[X] * Math.Sqrt(1 - Es * s * s) / Math.Cos(lp[Phi]);
}
else if ((s - EPS10) < HalfPi)
{
lp[Lambda] = 0;
}
else
{
throw new ProjectionException(20);
}
}
/// <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 rh = Proj.Hypot(xy[X], xy[Y] = _cphi1 - xy[Y]);
lp[Phi] = _cphi1 + _phi1 - rh;
if (Math.Abs(lp[Phi]) > HalfPi)
{
throw new ProjectionException(20);
}
if (Math.Abs(Math.Abs(lp[Phi]) - HalfPi) <= EPS10)
{
lp[Lambda] = 0;
}
else
{
lp[Lambda] = rh * Math.Atan2(xy[X], xy[Y]) / Math.Cos(lp[Phi]);
}
}
/// <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>
/// 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)
{
xy[Y] += _ml0;
if (Math.Abs(xy[Y]) <= TOL)
{
lp[Lambda] = xy[X];
lp[Phi] = 0;
}
else
{
double c;
int i;
double r = xy[Y] * xy[Y] + xy[X] * xy[X];
for (lp[Phi] = xy[Y], i = I_ITER; i > 0; --i)
{
double sp = Math.Sin(lp[Phi]);
double cp;
double s2ph = sp * (cp = Math.Cos(lp[Phi]));
if (Math.Abs(cp) < ITOL)
{
throw new ProjectionException(20);
}
double mlp;
c = sp * (mlp = Math.Sqrt(1 - Es * sp * sp)) / cp;
double ml = Proj.Mlfn(lp[Phi], sp, cp, _en);
double mlb = ml * ml + r;
mlp = OneEs / (mlp * mlp * mlp);
double dPhi;
lp[Phi] += (dPhi =
(ml + ml + c * mlb - 2 * xy[Y] * (c * ml + 1)) / (Es * s2ph * (mlb - 2 * xy[Y] * ml) / c +
2 * (xy[Y] - ml) * (c * mlp - 1 / s2ph) - mlp - mlp));
if (Math.Abs(dPhi) <= ITOL)
{
break;
}
}
if (i == 0)
{
throw new ProjectionException(20);
}
c = Math.Sin(lp[Phi]);
lp[Lambda] = Math.Asin(xy[X] * Math.Tan(lp[Phi]) * Math.Sqrt(1 - Es * c * c)) / Math.Sin(lp[Phi]);
}
}
/// <summary>
/// The forward transform where the spheroidal model of the earth has a flattening factor,
/// matching more closely with the oblique spheroid of the actual earth
/// </summary>
/// <param name="lp">The double values for geodetic lambda and phi organized into a one dimensional array</param>
/// <param name="xy">The double values for linear x and y organized into a one dimensional array</param>
protected override void EllipticalForward(double[] lp, double[] xy)
{
double sinX = 0.0, cosX = 0.0;
double coslam = Math.Cos(lp[Lambda]);
double sinlam = Math.Sin(lp[Lambda]);
double sinphi = Math.Sin(lp[Phi]);
if (_mode == Modes.Oblique || _mode == Modes.Equitorial)
{
double x;
sinX = Math.Sin(x = 2 * Math.Atan(Ssfn(lp[Phi], sinphi, E)) - HalfPi);
cosX = Math.Cos(x);
}
if (_mode == Modes.Oblique || _mode == Modes.Equitorial)
{
double a;
if (_mode == Modes.Oblique)
{
a = _akm1 / (_cosX1 * (1 + _sinX1 * sinX +
_cosX1 * cosX * coslam));
xy[Y] = a * (_cosX1 * sinX - _sinX1 * cosX * coslam);
}
else
{
a = 2 * _akm1 / (1 + cosX * coslam);
xy[Y] = a * sinX;
}
xy[X] = a * cosX;
}
else
{
if (_mode == Modes.SouthPole)
{
lp[Phi] = -lp[Phi];
coslam = -coslam;
sinphi = -sinphi;
}
xy[X] = _akm1 * Proj.Tsfn(lp[Phi], sinphi, E);
xy[Y] = -xy[X] * coslam;
}
xy[X] = xy[X] * sinlam;
}
/// <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 us, vs;
if (!_rot)
{
us = xy[X];
vs = xy[Y];
}
else
{
vs = xy[X] * _cosrot - xy[Y] * _sinrot;
us = xy[Y] * _cosrot + xy[X] * _sinrot;
}
us += _u0;
double q = Math.Exp(-_bl * vs / _al);
double s = .5 * (q - 1 / q);
double vl = Math.Sin(_bl * us / _al);
double ul = 2 * (vl * _cosgam + s * _singam) / (q + 1 / q);
if (Math.Abs(Math.Abs(ul) - 1) < EPS10)
{
lp[Lambda] = 0;
lp[Phi] = ul < 0 ? -HalfPi : HalfPi;
}
else
{
lp[Phi] = _el / Math.Sqrt((1 + ul) / (1 - ul));
if (_ellips)
{
if ((lp[Phi] = Proj.Phi2(Math.Pow(lp[Phi], 1 / _bl), E)) == double.MaxValue)
{
throw new ProjectionException(20);
}
}
else
{
lp[Phi] = HalfPi - 2 * Math.Atan(lp[Phi]);
}
lp[Lambda] = -Math.Atan2((s * _cosgam - vl * _singam), Math.Cos(_bl * us / _al)) / _bl;
}
}
/// <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 cosz = 0, sinz = 0;
double x = xy[X];
double y = xy[Y];
double rh = Proj.Hypot(x, y);
if ((lp[Phi] = rh * .5) > 1)
{
throw new ProjectionException(20);
}
lp[Phi] = 2 * Math.Asin(lp[Phi]);
if (_mode == Modes.Oblique || _mode == Modes.Equitorial)
{
sinz = Math.Sin(lp[Phi]);
cosz = Math.Cos(lp[Phi]);
}
switch (_mode)
{
case Modes.Equitorial:
lp[Phi] = Math.Abs(rh) <= EPS10 ? 0 : Math.Asin(y * sinz / rh);
x *= sinz;
y = cosz * rh;
break;
case Modes.Oblique:
lp[Phi] = Math.Abs(rh) <= EPS10 ? Phi0 : Math.Asin(cosz * _sinb1 + y * sinz * _sinb1 / rh);
x *= sinz * _cosb1;
y = (cosz - Math.Sin(lp[Phi]) * _sinb1) * rh;
break;
case Modes.NorthPole:
y = -y;
lp[Phi] = HalfPi - lp[Phi];
break;
case Modes.SouthPole:
lp[Phi] -= HalfPi;
break;
}
lp[Lambda] = (y == 0 && (_mode == Modes.Equitorial || _mode == Modes.Oblique)) ? 0 : Math.Atan2(x, 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)
{
if ((_rho = Proj.Hypot(xy[X], xy[Y] = _rho0 - xy[Y])) != 0.0)
{
if (_n < 0)
{
_rho = -_rho;
xy[X] = -xy[X];
xy[Y] = -xy[Y];
}
lp[Phi] = _rho / _dd;
if (IsElliptical)
{
lp[Phi] = (_c - lp[Phi] * lp[Phi]) / _n;
if (Math.Abs(_ec - Math.Abs(lp[Phi])) > TOL7)
{
if ((lp[Phi] = PhiFn(lp[Phi], E, OneEs)) == double.MaxValue)
{
throw new ProjectionException(20);
}
}
else
{
lp[Phi] = lp[Phi] < 0 ? -HalfPi : HalfPi;
}
}
else if (Math.Abs(lp[Phi] = (_c - lp[Phi] * lp[Phi]) / _n2) <= 1)
{
lp[Phi] = Math.Asin(lp[Phi]);
}
else
{
lp[Phi] = lp[Phi] < 0 ? -HalfPi : HalfPi;
}
lp[Lambda] = Math.Atan2(xy[X], xy[Y]) / _n;
}
else
{
lp[Lambda] = 0;
lp[Phi] = _n > 0? HalfPi : -HalfPi;
}
}
/// <summary>
/// Special factor calculations for a factors calculation
/// </summary>
/// <param name="lp">lambda-phi</param>
/// <param name="p">The projection</param>
/// <param name="fac">The Factors</param>
protected override void OnSpecial(double[] lp, ProjectionInfo p, Factors fac)
{
if (Math.Abs(Math.Abs(lp[Phi]) - HalfPi) < EPS10)
{
if ((lp[Phi] * _n) <= 0)
{
return;
}
_rho = 0;
}
else
{
_rho = _c * (_ellipse ? Math.Pow(Proj.Tsfn(lp[Phi], Math.Sin(lp[Phi]),
p.GeographicInfo.Datum.Spheroid.Eccentricity()), _n)
: Math.Pow(Math.Tan(Math.PI / 4 + .5 * lp[Phi]), -_n));
}
fac.code = AnalyticModes.IsAnalHK | AnalyticModes.IsAnalConv;
fac.k = fac.h = p.ScaleFactor * _n * _rho / Proj.Msfn(Math.Sin(lp[Phi]), Math.Cos(lp[Phi]), p.GeographicInfo.Datum.Spheroid.EccentricitySquared());
fac.conv = -_n * lp[Lambda];
}
/// <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>
/// Internal code handling the setup operations for the transform
/// </summary>
protected void Setup()
{
double sinphi;
if (Math.Abs(_phi1 + _phi2) < EPS10)
{
throw new ProjectionException(-21);
}
_n = sinphi = Math.Sin(_phi1);
double cosphi = Math.Cos(_phi1);
bool secant = Math.Abs(_phi1 - _phi2) >= EPS10;
if (IsElliptical)
{
double m1 = Proj.Msfn(sinphi, cosphi, Es);
double ml1 = Proj.Qsfn(sinphi, E, OneEs);
if (secant)
{ /* secant cone */
sinphi = Math.Sin(_phi2);
cosphi = Math.Cos(_phi2);
double m2 = Proj.Msfn(sinphi, cosphi, Es);
double ml2 = Proj.Qsfn(sinphi, E, OneEs);
_n = (m1 * m1 - m2 * m2) / (ml2 - ml1);
}
_ec = 1 - .5 * OneEs * Math.Log((1 - E) / (1 + E)) / E;
_c = m1 * m1 + _n * ml1;
_dd = 1 / _n;
_rho0 = _dd * Math.Sqrt(_c - _n * Proj.Qsfn(Math.Sin(Phi0), E, OneEs));
}
else
{
if (secant)
{
_n = .5 * (_n + Math.Sin(_phi2));
}
_n2 = _n + _n;
_c = cosphi * cosphi + _n2 * sinphi;
_dd = 1 / _n;
_rho0 = _dd * Math.Sqrt(_c - _n2 * Math.Sin(Phi0));
}
}
/// <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)
{
double s;
double rh = Proj.Hypot(xy[X], xy[Y] = _am1 - xy[Y]);
lp[Phi] = Proj.InvMlfn(_am1 + _m1 - rh, Es, _en);
if ((s = Math.Abs(lp[Phi])) < HalfPi)
{
s = Math.Sin(lp[Phi]);
lp[Lambda] = rh * Math.Atan2(xy[X], xy[Y]) *
Math.Sqrt(1 - Es * s * s) / Math.Cos(lp[Phi]);
}
else if (Math.Abs(s - HalfPi) <= EPS10)
{
lp[Lambda] = 0;
}
else
{
throw new ProjectionException(20);
}
}
/// <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;
}
/// <summary>
/// The forward transform in the special case where there is no flattening of the spherical model of the earth.
/// </summary>
/// <param name="lp">The input lambda and phi geodetic values organized in an array</param>
/// <param name="xy">The output x and y values organized in an array</param>
protected override void SphericalForward(double[] lp, double[] xy)
{
/* Calculation of the three components of the vector from satellite to
** position on earth surface (lon,lat).*/
double tmp = Math.Cos(lp[Phi]);
double vx = Math.Cos(lp[Lambda]) * tmp;
double vy = Math.Sin(lp[Lambda]) * tmp;
double vz = Math.Sin(lp[Phi]);
/* Check visibility.*/
if (((_radiusG - vx) * vx - vy * vy - vz * vz) < 0)
{
xy[X] = double.NaN;
xy[Y] = double.NaN;
//throw new ProjectionException(20);
return;
}
/* Calculation based on view angles from satellite.*/
tmp = _radiusG - vx;
xy[X] = _radiusG1 * Math.Atan(vy / tmp);
xy[Y] = _radiusG1 * Math.Atan(vz / Proj.Hypot(vy, tmp));
}
/// <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)
{
if ((_rho = Proj.Hypot(xy[X], xy[Y] = _rho0 - xy[Y])) != 0.0)
{
if (_n < 0)
{
_rho = -_rho;
xy[X] = -xy[X];
xy[Y] = -xy[Y];
}
lp[Phi] = _c - _rho;
if (IsElliptical)
{
lp[Phi] = Proj.InvMlfn(lp[Phi], Es, _en);
}
lp[Lambda] = Math.Atan2(xy[X], xy[Y]) / _n;
}
else
{
lp[Lambda] = 0;
lp[Phi] = _n > 0 ? HalfPi : -HalfPi;
}
}
/// <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 t = 0;
if (projInfo.StandardParallel1 != null)
{
t = projInfo.StandardParallel1.Value * Math.PI / 180;
}
t = projInfo.ParamD("lat_ts") * Math.PI / 180;
if ((K0 = Math.Cos(t)) < 0)
{
throw new ProjectionException(-24);
}
if (!IsElliptical)
{
return;
}
t = Math.Sin(t);
K0 /= Math.Sqrt(1 - Es * t * t);
E = Math.Sqrt(Es);
_apa = Proj.Authset(Es);
_qp = Proj.Qsfn(1, E, OneEs);
}
/// <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 nn;
double[] p = new double[2];
double[] dp = new double[2];
p[R] = xy[Y];
p[I] = xy[X];
for (nn = 20; nn > 0; --nn)
{
double[] fp;
double[] f = Proj.Zpolyd1(p, _bf, Nbf, out fp);
f[R] -= xy[Y];
f[I] -= xy[X];
double den = fp[R] * fp[R] + fp[I] * fp[I];
p[R] += dp[R] = -(f[R] * fp[R] + f[I] * fp[I]) / den;
p[I] += dp[I] = -(f[I] * fp[R] - f[R] * fp[I]) / den;
if ((Math.Abs(dp[R]) + Math.Abs(dp[I])) <= EPS10)
{
break;
}
}
if (nn > 0)
{
lp[Lambda] = p[I];
lp[Phi] = _tphi[Ntphi];
for (int i = Ntphi - 1; i > 0; i++)
{
lp[Phi] = _tphi[i] + p[R] * lp[Phi];
}
lp[Phi] = Phi0 + p[R] * lp[Phi] * Sec5ToRad;
}
else
{
lp[Lambda] = lp[Phi] = double.MaxValue;
}
}
/// <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 rho;
xy[X] /= K0;
xy[Y] /= K0;
if ((rho = Proj.Hypot(xy[X], xy[Y])) > 0)
{
double c = 2 * Math.Atan2(rho, _r2);
double sinc = Math.Sin(c);
double cosc = Math.Cos(c);
lp[Phi] = Math.Asin(cosc * _sinc0 + xy[Y] * sinc * _cosc0 / rho);
lp[Lambda] = Math.Atan2(xy[X] * sinc, rho * _cosc0 * cosc -
xy[Y] * _sinc0 * sinc);
}
else
{
lp[Phi] = _phic0;
lp[Lambda] = 0;
}
double[] temp = _gauss.Inverse(lp);
lp[Phi] = temp[Phi];
lp[Lambda] = temp[Lambda];
}
