private void ForwardByRadian(double φ, double λ, out double E, out double N)
{
double h1 = n / 2 - 2.0 / 3.0 * Math.Pow(n, 2) + 5.0 / 16.0 * Math.Pow(n, 3) + 41.0 / 180.0 * Math.Pow(n, 4);
double h2 = 13.0 / 48.0 * Math.Pow(n, 2) - 3.0 / 4.0 * Math.Pow(n, 3) + 557.0 / 1440.0 * Math.Pow(n, 4);
double h3 = 61.0 / 240.0 * Math.Pow(n, 3) - 103.0 / 140.0 * Math.Pow(n, 4);
double h4 = 49561.0 / 161280.0 * Math.Pow(n, 4);
double Q = InverseHyperbolic.Asinh(Math.Tan(φ)) - (Ellipsoid.e * InverseHyperbolic.Atanh(Ellipsoid.e * Math.Sin(φ)));
double β = Math.Atan(Math.Sinh(Q));
double η0 = InverseHyperbolic.Atanh(Math.Cos(β) * Math.Sin(λ - λ0));
double ξ0 = Math.Asin(Math.Sin(β) * Math.Cosh(η0));
double ξ1 = h1 * Math.Sin(2 * ξ0) * Math.Cosh(2 * η0);
double ξ2 = h2 * Math.Sin(4 * ξ0) * Math.Cosh(4 * η0);
double ξ3 = h3 * Math.Sin(6 * ξ0) * Math.Cosh(6 * η0);
double ξ4 = h4 * Math.Sin(8 * ξ0) * Math.Cosh(8 * η0);
double ξ = ξ0 + ξ1 + ξ2 + ξ3 + ξ4;
double η1 = h1 * Math.Cos(2 * ξ0) * Math.Sinh(2 * η0);
double η2 = h2 * Math.Cos(4 * ξ0) * Math.Sinh(4 * η0);
double η3 = h3 * Math.Cos(6 * ξ0) * Math.Sinh(6 * η0);
double η4 = h4 * Math.Cos(8 * ξ0) * Math.Sinh(8 * η0);
double η = η0 + η1 + η2 + η3 + η4;
E = FE + k0 * B * η;
N = FN + k0 * (B * ξ - M0);
}
private void ReverseByRadian(double E, double N, out double φ, out double λ)
{
double h1ˊ = n / 2.0 - 2.0 / 3.0 * Math.Pow(n, 2) + 37.0 / 96.0 * Math.Pow(n, 3) - 1 / 360.0 * Math.Pow(n, 4);
double h2ˊ = 1 / 48.0 * Math.Pow(n, 2) + 1 / 15.0 * Math.Pow(n, 3) - 437.0 / 1440.0 * Math.Pow(n, 4);
double h3ˊ = 17.0 / 480.0 * Math.Pow(n, 3) - 37.0 / 840.0 * Math.Pow(n, 4);
double h4ˊ = 4397.0 / 161280.0 * Math.Pow(n, 4);
double ηˊ = (E - FE) / (B * k0);
double ξˊ = ((N - FN) + k0 * M0) / (B * k0);
double ξ1ˊ = h1ˊ * Math.Sin(2 * ξˊ) * Math.Cosh(2 * ηˊ);
double ξ2ˊ = h2ˊ * Math.Sin(4 * ξˊ) * Math.Cosh(4 * ηˊ);
double ξ3ˊ = h3ˊ * Math.Sin(6 * ξˊ) * Math.Cosh(6 * ηˊ);
double ξ4ˊ = h4ˊ * Math.Sin(8 * ξˊ) * Math.Cosh(8 * ηˊ);
double ξ0ˊ = ξˊ - (ξ1ˊ + ξ2ˊ + ξ3ˊ + ξ4ˊ);
double η1ˊ = h1ˊ * Math.Cos(2 * ξˊ) * Math.Sinh(2 * ηˊ);
double η2ˊ = h2ˊ * Math.Cos(4 * ξˊ) * Math.Sinh(4 * ηˊ);
double η3ˊ = h3ˊ * Math.Cos(6 * ξˊ) * Math.Sinh(6 * ηˊ);
double η4ˊ = h4ˊ * Math.Cos(8 * ξˊ) * Math.Sinh(8 * ηˊ);
double η0ˊ = ηˊ - (η1ˊ + η2ˊ + η3ˊ + η4ˊ);
double βˊ = Math.Asin(Math.Sin(ξ0ˊ) / Math.Cosh(η0ˊ));
double Qˊ = InverseHyperbolic.Asinh(Math.Tan(βˊ));
double Qˊˊ = Qˊ + (e * InverseHyperbolic.Atanh(e * Math.Tanh(Qˊ)));
double q = Qˊ + (e * InverseHyperbolic.Atanh(e * Math.Tanh(Qˊˊ)));
while (Math.Abs(Qˊˊ - q) > 0.0000000001)
{
Qˊˊ = q;
q = Qˊ + (e * InverseHyperbolic.Atanh(e * Math.Tanh(Qˊˊ)));
}
φ = Math.Atan(Math.Sinh(Qˊˊ));
λ = λ0 + Math.Asin(Math.Tanh(η0ˊ) / Math.Cos(βˊ));
}
