public override Coordinate ProjectInverse(double xyx, double xyy, Coordinate lp)
{
xyy /= C_y;
lp.Y = ProjectionMath.Asin(Math.Sin(xyy) / n);
lp.X = xyx / (C_x * Math.Cos(xyy));
return(lp);
}
public override Coordinate Project(double lplam, double lpphi, Coordinate xy)
{
xy.Y = ProjectionMath.Asin(n * Math.Sin(lpphi));
xy.X = C_x * lplam * Math.Cos(lpphi);
xy.Y = C_y * lpphi;
return(xy);
}
public override Coordinate ProjectInverse(double xyx, double xyy, Coordinate lp)
{
double V;
int i;
if (n != 0)
{
lp.Y = xyy;
for (i = MaxIter; i > 0; --i)
{
lp.Y -= V = (n * lp.Y + n1 * Math.Sin(lp.Y) - xyy) /
(n + n1 * Math.Cos(lp.Y));
if (Math.Abs(V) < LoopTolerance)
{
break;
}
}
if (i == 0)
{
lp.Y = xyy < 0.0 ? -ProjectionMath.PiHalf : ProjectionMath.PiHalf;
}
}
else
{
lp.Y = ProjectionMath.Asin(xyy);
}
V = Math.Cos(lp.Y);
lp.X = xyx * (n + n1 * V) / V;
return(lp);
}
public override Coordinate ProjectInverse(double xyx, double xyy, Coordinate lp)
{
lp.Y = xyy / C_y;
lp.X = xyx / (C_x * Math.Cos(lp.Y));
lp.Y = ProjectionMath.Asin(Math.Sin(lp.Y) / C_p1) / C_p2;
return(lp);
}
public override Coordinate Project(double lplam, double lpphi, Coordinate xy)
{
lpphi = ProjectionMath.Asin(0.883883476 * Math.Sin(lpphi));
xy.X = C_x * lplam * Math.Cos(lpphi);
xy.X /= Math.Cos(lpphi *= 0.333333333333333);
xy.Y = C_y * Math.Sin(lpphi);
return(xy);
}
public override Coordinate ProjectInverse(double xyx, double xyy, Coordinate lp)
{
double th, s;
lp.X = 2.0 * xyx / (1.0 + Math.Cos(xyy));
lp.Y = ProjectionMath.Asin(0.5 * (xyy + Math.Sin(xyy)));
return(lp);
}
public override Coordinate ProjectInverse(double xyx, double xyy, Coordinate lp)
{
lp.Y = ProjectionMath.Asin(xyy / C_y);
lp.X = xyx * Math.Cos(lp.Y) / C_x;
lp.Y *= 3.0;
lp.X /= Math.Cos(lp.Y);
lp.Y = ProjectionMath.Asin(1.13137085 * Math.Sin(lp.Y));
return(lp);
}
public override Coordinate ProjectInverse(double xyx, double xyy, Coordinate lp)
{
double c;
lp.Y = ProjectionMath.Asin(xyy / C_y);
lp.X = xyx / (C_x * (1.0 + (c = Math.Cos(lp.Y))));
lp.Y = ProjectionMath.Asin((lp.Y + Math.Sin(lp.Y) * (c + 2.0)) / C_p);
return(lp);
}
public override Coordinate ProjectInverse(double xyx, double xyy, Coordinate lp)
{
double t, s;
lp.Y = C2 * (t = ProjectionMath.Asin(xyy / C_y));
lp.X = xyx / (C_x * (1.0 + 3.0 * Math.Cos(lp.Y) / Math.Cos(t)));
lp.Y = ProjectionMath.Asin((C1 * Math.Sin(t) + Math.Sin(lp.Y)) / C3);
return(lp);
}
public override Coordinate ProjectInverse(double x, double y, Coordinate coord)
{
if (_spherical)
{
double h = Math.Exp(x / _scaleFactor);
double g = 0.5 * (h - 1.0 / h);
h = Math.Cos(_projectionLatitude + y / _scaleFactor);
coord.Y = ProjectionMath.Asin(Math.Sqrt((1.0 - h * h) / (1.0 + g * g)));
if (y < 0)
{
coord.Y = -coord.Y;
}
coord.X = Math.Atan2(g, h);
}
else
{
double n, con, cosphi, d, ds, sinphi, t;
coord.Y = ProjectionMath.inv_mlfn(_ml0 + y / _scaleFactor, _es, _en);
if (Math.Abs(y) >= ProjectionMath.PiHalf)
{
coord.Y = y < 0.0 ? -ProjectionMath.PiHalf : ProjectionMath.PiHalf;
coord.X = 0.0;
}
else
{
sinphi = Math.Sin(coord.Y);
cosphi = Math.Cos(coord.Y);
t = Math.Abs(cosphi) > 1e-10 ? sinphi / cosphi : 0.0;
n = _esp * cosphi * cosphi;
d = x * Math.Sqrt(con = 1.0 - _es * sinphi * sinphi) / _scaleFactor;
con *= t;
t *= t;
ds = d * d;
coord.Y -= (con * ds / (1.0 - _es)) * FC2 * (1.0 -
ds * FC4 * (5.0 + t * (3.0 - 9.0 * n) + n * (1.0 - 4 * n) -
ds * FC6 * (61.0 + t * (90.0 - 252.0 * n +
45.0 * t) + 46.0 * n
- ds * FC8 * (1385.0 + t * (3633.0 + t * (4095.0 + 1574.0 * t)))
)));
coord.X = d * (FC1 -
ds * FC3 * (1.0 + 2.0 * t + n -
ds * FC5 * (5.0 + t * (28.0 + 24.0 * t + 8.0 * n) + 6.0 * n
- ds * FC7 * (61.0 + t * (662.0 + t * (1320.0 + 720.0 * t)))
))) / cosphi;
}
}
return(coord);
}
public override Coordinate ProjectInverse(double xyx, double xyy, Coordinate lp)
{
double c;
xyy /= _cY;
c = Math.Cos(lp.Y = _tanMode ? Math.Atan(xyy) : ProjectionMath.Asin(xyy));
lp.Y /= _cP;
lp.X = xyx / (_cX * Math.Cos(lp.Y /= _cP));
if (_tanMode)
{
lp.X /= c * c;
}
else
{
lp.X *= c;
}
return(lp);
}
public override Coordinate Project(double lam, double phi, Coordinate xy)
{
if (Spherical)
{
double coslam, cosphi, sinphi;
sinphi = Math.Sin(phi);
cosphi = Math.Cos(phi);
coslam = Math.Cos(lam);
switch (Mode)
{
case AzimuthalMode.Equator:
case AzimuthalMode.Oblique:
if (Mode == AzimuthalMode.Equator)
{
xy.Y = cosphi * coslam;
}
else
{
xy.Y = _sinphi0 * sinphi + _cosphi0 * cosphi * coslam;
}
if (Math.Abs(Math.Abs(xy.Y) - 1.0) < Tolerance)
{
if (xy.Y < 0.0)
{
throw new ProjectionException();
}
else
{
xy.X = xy.Y = 0.0;
}
}
else
{
xy.Y = Math.Acos(xy.Y);
xy.Y /= Math.Sin(xy.Y);
xy.X = xy.Y * cosphi * Math.Sin(lam);
xy.Y *= (Mode == AzimuthalMode.Equator) ? sinphi :
_cosphi0 * sinphi - _sinphi0 * cosphi * coslam;
}
break;
case AzimuthalMode.NorthPole:
case AzimuthalMode.SouthPole:
if (Mode == AzimuthalMode.NorthPole)
{
phi = -phi;
coslam = -coslam;
}
if (Math.Abs(phi - ProjectionMath.PiHalf) < EPS10)
{
throw new ProjectionException();
}
xy.X = (xy.Y = (ProjectionMath.PiHalf + phi)) * Math.Sin(lam);
xy.Y *= coslam;
break;
}
}
else
{
double coslam, cosphi, sinphi, rho, s, H, H2, c, Az, t, ct, st, cA, sA;
coslam = Math.Cos(lam);
cosphi = Math.Cos(phi);
sinphi = Math.Sin(phi);
switch (Mode)
{
case AzimuthalMode.NorthPole:
case AzimuthalMode.SouthPole:
if (Mode == AzimuthalMode.NorthPole)
{
coslam = -coslam;
}
xy.X = (rho = Math.Abs(_mp - ProjectionMath.mlfn(phi, sinphi, cosphi, _en))) *
Math.Sin(lam);
xy.Y = rho * coslam;
break;
case AzimuthalMode.Equator:
case AzimuthalMode.Oblique:
if (Math.Abs(lam) < EPS10 && Math.Abs(phi - ProjectionLatitude) < EPS10)
{
xy.X = xy.Y = 0.0;
break;
}
t = Math.Atan2(_oneEs * sinphi + EccentricitySquared * _n1 * _sinphi0 *
Math.Sqrt(1.0 - EccentricitySquared * sinphi * sinphi), cosphi);
ct = Math.Cos(t); st = Math.Sin(t);
Az = Math.Atan2(Math.Sin(lam) * ct, _cosphi0 * st - _sinphi0 * coslam * ct);
cA = Math.Cos(Az); sA = Math.Sin(Az);
s = ProjectionMath.Asin(Math.Abs(sA) < Tolerance ?
(_cosphi0 * st - _sinphi0 * coslam * ct) / cA :
Math.Sin(lam) * ct / sA);
H = _he * cA;
H2 = H * H;
c = _n1 * s * (1.0 + s * s * (-H2 * (1.0 - H2) / 6.0 +
s * (_g * H * (1.0 - 2.0 * H2 * H2) / 8.0 +
s * ((H2 * (4.0 - 7.0 * H2) - 3.0 * _g * _g * (1.0 - 7.0 * H2)) /
120.0 - s * _g * H / 48.0))));
xy.X = c * sA;
xy.Y = c * cA;
break;
}
}
return(xy);
}
public override Coordinate ProjectInverse(double x, double y, Coordinate lp)
{
if (Spherical)
{
double cosc, c_rh, sinc;
if ((c_rh = ProjectionMath.Distance(x, y)) > Math.PI)
{
if (c_rh - EPS10 > Math.PI)
{
throw new ProjectionException();
}
c_rh = Math.PI;
}
else if (c_rh < EPS10)
{
lp.Y = ProjectionLatitude;
lp.X = 0.0;
return(lp);
}
if (Mode == AzimuthalMode.Oblique || Mode == AzimuthalMode.Equator)
{
sinc = Math.Sin(c_rh);
cosc = Math.Cos(c_rh);
if (Mode == AzimuthalMode.Equator)
{
lp.Y = ProjectionMath.Asin(y * sinc / c_rh);
x *= sinc;
y = cosc * c_rh;
}
else
{
lp.Y = ProjectionMath.Asin(cosc * _sinphi0 + y * sinc * _cosphi0 /
c_rh);
y = (cosc - _sinphi0 * Math.Sin(lp.Y)) * c_rh;
x *= sinc * _cosphi0;
}
lp.X = y == 0.0 ? 0.0 : Math.Atan2(x, y);
}
else if (Mode == AzimuthalMode.NorthPole)
{
lp.Y = ProjectionMath.PiHalf - c_rh;
lp.X = Math.Atan2(x, -y);
}
else
{
lp.Y = c_rh - ProjectionMath.PiHalf;
lp.X = Math.Atan2(x, y);
}
}
else
{
double c, Az, cosAz, A, B, D, E, F, psi, t;
int i;
if ((c = ProjectionMath.Distance(x, y)) < EPS10)
{
lp.Y = ProjectionLatitude;
lp.X = 0.0;
return(lp);
}
if (Mode == AzimuthalMode.Oblique || Mode == AzimuthalMode.Equator)
{
cosAz = Math.Cos(Az = Math.Atan2(x, y));
t = _cosphi0 * cosAz;
B = EccentricitySquared * t / _oneEs;
A = -B * t;
B *= 3.0 * (1.0 - A) * _sinphi0;
D = c / _n1;
E = D * (1.0 - D * D * (A * (1.0 + A) / 6.0 + B * (1.0 + 3.0 * A) * D / 24.0));
F = 1.0 - E * E * (A / 2.0 + B * E / 6.0);
psi = ProjectionMath.Asin(_sinphi0 * Math.Cos(E) + t * Math.Sin(E));
lp.X = ProjectionMath.Asin(Math.Sin(Az) * Math.Sin(E) / Math.Cos(psi));
if ((t = Math.Abs(psi)) < EPS10)
{
lp.Y = 00.0;
}
else if (Math.Abs(t - ProjectionMath.PiHalf) < 0.0)
{
lp.Y = ProjectionMath.PiHalf;
}
else
{
lp.Y = Math.Atan((1.0 - EccentricitySquared * F * _sinphi0 / Math.Sin(psi)) * Math.Tan(psi) / _oneEs);
}
}
else
{
lp.Y = ProjectionMath.inv_mlfn(Mode == AzimuthalMode.NorthPole ? _mp - c : _mp + c, EccentricitySquared, _en);
lp.X = Math.Atan2(x, Mode == AzimuthalMode.NorthPole ? -y : y);
}
}
return(lp);
}
public override Coordinate Project(double lplam, double lpphi, Coordinate xy)
{
int l, nn;
double lamt = 0, xlam, sdsq, c, d, s, lamdp = 0, phidp, lampp, tanph,
lamtp, cl, sd, sp, fac, sav, tanphi;
if (lpphi > ProjectionMath.PiHalf)
{
lpphi = ProjectionMath.PiHalf;
}
else if (lpphi < -ProjectionMath.PiHalf)
{
lpphi = -ProjectionMath.PiHalf;
}
lampp = lpphi >= 0.0 ? ProjectionMath.PiHalf : PI_HALFPI;
tanphi = Math.Tan(lpphi);
for (nn = 0; ;)
{
sav = lampp;
lamtp = lplam + p22 * lampp;
cl = Math.Cos(lamtp);
if (Math.Abs(cl) < Tolerance)
{
lamtp -= Tolerance;
}
fac = lampp - Math.Sin(lampp) * (cl < 0.0 ? -ProjectionMath.PiHalf : ProjectionMath.PiHalf);
for (l = 50; l > 0; --l)
{
lamt = lplam + p22 * sav;
if (Math.Abs(c = Math.Cos(lamt)) < Tolerance)
{
lamt -= Tolerance;
}
xlam = (_oneEs * tanphi * sa + Math.Sin(lamt) * ca) / c;
lamdp = Math.Atan(xlam) + fac;
if (Math.Abs(Math.Abs(sav) - Math.Abs(lamdp)) < Tolerance)
{
break;
}
sav = lamdp;
}
if (l == 0 || ++nn >= 3 || (lamdp > rlm && lamdp < rlm2))
{
break;
}
if (lamdp <= rlm)
{
lampp = TWOPI_HALFPI;
}
else if (lamdp >= rlm2)
{
lampp = ProjectionMath.PiHalf;
}
}
if (l != 0)
{
sp = Math.Sin(lpphi);
phidp = ProjectionMath.Asin((_oneEs * ca * sp - sa * Math.Cos(lpphi) *
Math.Sin(lamt)) / Math.Sqrt(1.0 - EccentricitySquared * sp * sp));
tanph = Math.Log(Math.Tan(ProjectionMath.PiFourth + .5 * phidp));
sd = Math.Sin(lamdp);
sdsq = sd * sd;
s = p22 * sa * Math.Cos(lamdp) * Math.Sqrt((1.0 + t * sdsq)
/ ((1.0 + w * sdsq) * (1.0 + q * sdsq)));
d = Math.Sqrt(xj * xj + s * s);
xy.X = b * lamdp + a2 * Math.Sin(2.0 * lamdp) + a4 *
Math.Sin(lamdp * 4.0) - tanph * s / d;
xy.Y = c1 * sd + c3 * Math.Sin(lamdp * 3.0) + tanph * xj / d;
}
else
{
xy.X = xy.Y = Double.PositiveInfinity;
}
return(xy);
}