/// <summary>
/// 高斯引数法反算
/// </summary>
/// <param name="ge">已知元素</param>
public void GaussInverse(GeodeticElement ge)
{
double Bm = Methods.Average(ge.Br1, ge.Br2),
delta_B = ge.Br2 - ge.Br1,
delta_L = ge.Lr2 - ge.Lr1,
Vm = Auxiliary.GetV(ep.data.e2_2, Bm),
Nm = Auxiliary.GetN(ep.data.a, ep.data.e_2, Bm),
tm = Auxiliary.Get_t(Bm),
tm2 = tm * tm,
yita_2 = Auxiliary.GetYita2(ep.data.e2_2, Bm),
cos_Bm = Math.Cos(Bm),
cos_Bm2 = cos_Bm * cos_Bm;
double r01 = Nm * cos_Bm,
r21 = r01 / 24 / Math.Pow(Vm, 4) * (1 + yita_2 - 9 * yita_2 * tm2 + yita_2 * yita_2),
r03 = -r01 / 24 * cos_Bm2 * tm2;
double s10 = Nm / Vm / Vm,
s12 = -s10 * cos_Bm2 / 24 * (2 + 3 * tm2 + 2 * yita_2 * tm2),
s30 = Nm / Math.Pow(Vm, 6) / 8 * (yita_2 - tm2 * yita_2 + yita_2 * yita_2);
double t01 = tm * cos_Bm,
t21 = t01 / 24 / Math.Pow(Vm, 4) * (2 + 7 * yita_2 + 9 * tm2 * yita_2 + 5 * yita_2 * yita_2),
t03 = t01 * cos_Bm2 / 24 * (2 + tm2 + 2 * yita_2);
double S_sinAm = r01 * delta_L + r21 * delta_B * delta_B * delta_L + r03 * Math.Pow(delta_L, 3),
S_cosAm = s10 * delta_B + s12 * delta_B * delta_L * delta_L + s30 * Math.Pow(delta_B, 3),
delta_A = t01 * delta_L + t21 * delta_B * delta_B * delta_L + t03 * Math.Pow(delta_L, 3);
//S_sinAm1=S_sinAm,S_cosAm1=S_cosAm,delta_A1=delta_A;
double Am = _2D_Point.Get_PAngle(new _2D_Point(0, 0), new _2D_Point(S_cosAm, S_sinAm)).ChangeToRad();
//Am1
//do
//{
// S_sinAm = S_sinAm1;
// S_cosAm = S_cosAm1;
// Am = Am1;
// S_sinAm1 = delta_L * Nm * cos_Bm - S_sinAm / 24 / Nm / Nm * (S_sinAm * S_sinAm * tm2 - S_cosAm * S_cosAm * (1 + yita_2 - 9 * yita_2 * tm2 + yita_2 * yita_2));
// S_cosAm1 = delta_B * Nm / Vm / Vm - S_cosAm1 / 24 / Nm / Nm * (S_sinAm1 * S_sinAm1 * (2 + 3 * tm2 + 2 * yita_2 * tm2) + 3 * yita_2 * S_cosAm * S_cosAm1 * (1 + yita_2 - tm2 + 4 * tm2 * yita_2));
// Am1 = _2D_Point.Get_PAngle(new _2D_Point(0, 0), new _2D_Point(S_cosAm1, S_sinAm1)).ChangeToRad();
//} while (Math.Abs(Angle.ChangeToAngle(Am1 - Am).Miao) > 0.0001);
ge.S = ge.Sr = S_sinAm / Math.Sin(Am);
ge.Ar12 = Am - delta_A / 2;
ge.A12 = Angle.ChangeToAngle(ge.Ar12);
if (Am + delta_A >= Math.PI)
{
ge.Ar21 = Am + delta_A / 2 - Math.PI;
}
else
{
ge.Ar21 = Am + delta_A / 2 + Math.PI;
}
ge.A21 = Angle.ChangeToAngle(ge.Ar21);
}
/// <summary>
/// 贝塞尔正算
/// </summary>
/// <param name="ge">已知元素</param>
public void BesselPositive(GeodeticElement ge)
{
double W1 = Auxiliary.GetW(ep.data.e_2, ge.Br1),
sin_u1 = Math.Sin(ge.Br1) * Math.Sqrt(1 - ep.data.e_2) / W1,
cos_u1 = Math.Cos(ge.Br1) / W1,
sinA1 = Math.Sin(ge.Ar12),
cosA1 = Math.Cos(ge.Ar12);
double sinA0 = cos_u1 * sinA1,
cot_xigema1 = cos_u1 * cosA1 / sin_u1,
sin_2xigema1 = 2 * cot_xigema1 / (cot_xigema1 * cot_xigema1 + 1),
cos_2xigema1 = (cot_xigema1 * cot_xigema1 - 1) / (cot_xigema1 * cot_xigema1 + 1);
double cos2A0 = 1 - sinA0 * sinA0,
k_2 = ep.data.e2_2 * cos2A0,
k_4 = k_2 * k_2,
k_6 = k_2 * k_4,
b = ep.data.b,
e_2 = ep.data.e_2,
e_4 = e_2 * e_2,
e_6 = e_2 * e_4,
A = b * (1 + k_2 / 4 - 3 * k_4 / 64 + 5 * k_6 / 256),
B = b * (k_2 / 8 - k_4 / 32 + 15 * k_6 / 1024),
C = b * (k_4 / 128 - 3 * k_6 / 512),
Alph = e_2 / 2 + e_4 / 8 + e_6 / 8 - (e_4 / 16 + e_6 / 16) * cos2A0 + 3 * e_6 / 128 * cos2A0 * cos2A0,
Beta = (e_4 / 32 + e_6 / 32) * cos2A0 - e_6 / 64 * cos2A0 * cos2A0;
double xigema0 = (ge.Sr - (B + C * cos_2xigema1) * sin_2xigema1) / A,
cos_2xigema0 = Math.Cos(2 * xigema0),
sin_2xigema0 = Math.Sin(2 * xigema0),
sin_2xigema10 = sin_2xigema1 * cos_2xigema0 + cos_2xigema1 * sin_2xigema0,
cos_2xigema10 = cos_2xigema1 * cos_2xigema0 - sin_2xigema0 * sin_2xigema1,
xigema = xigema0 + (B + 5 * C * cos_2xigema10) * sin_2xigema10 / A;
double delta = (Alph * xigema + Beta * (sin_2xigema1 * Math.Cos(2 * xigema) + cos_2xigema1 * Math.Sin(2 * xigema) - sin_2xigema1)) * sinA0;
double sin_u2 = sin_u1 * Math.Cos(xigema) + cos_u1 * cosA1 * Math.Sin(xigema),
B2 = Math.Atan(sin_u2 / Math.Sqrt((1 - e_2) * (1 - sin_u2 * sin_u2))),
lamda = Math.Atan2(sinA1, (cos_u1 * Math.Cos(xigema) - sin_u1 * Math.Sin(xigema) * cosA1) / Math.Sin(xigema)),
L2 = ge.Lr1 + lamda - delta;
var A2 = _2D_Point.Get_PAngle(new _2D_Point(0, 0),
new _2D_Point(-(Math.Cos(xigema) * cos_u1 * cosA1 - sin_u1 * Math.Sin(xigema)) / cos_u1, -sinA1));
ge.Br2 = B2; ge.Lr2 = L2;
ge.B2 = Angle.ChangeToAngle(B2); ge.L2 = Angle.ChangeToAngle(L2);
ge.Ar21 = A2.ChangeToRad(); ge.A21 = A2;
}
/// <summary>
/// 贝塞尔反算1
/// </summary>
/// <param name="ge"></param>
public void BesselInverse1(GeodeticElement ge)
{
double W1 = Auxiliary.GetW(ep.data.e_2, ge.Br1),
W2 = Auxiliary.GetW(ep.data.e_2, ge.Br2),
sin_u1 = Math.Sin(ge.Br1) * Math.Sqrt(1 - ep.data.e_2) / W1,
sin_u2 = Math.Sin(ge.Br2) * Math.Sqrt(1 - ep.data.e_2) / W2,
cos_u1 = Math.Cos(ge.Br1) / W1,
cos_u2 = Math.Cos(ge.Br2) / W2,
L = ge.Lr2 - ge.Lr1,
a1 = sin_u1 * sin_u2,
a2 = cos_u1 * cos_u2,
b1 = cos_u1 * sin_u2,
b2 = sin_u1 * cos_u2,
delta0=0,
delta1=delta0,
lamda,
A1,
xigema,xigema1,xigema2,
sin_xigema,
cos_xigema,
sinA0,
cos2A0;
do
{
delta0 = delta1;
lamda = L + delta0;
double sinlamda = Math.Sin(lamda),
coslamda = Math.Cos(lamda);
double p = cos_u2 * sinlamda,
q = b1 - b2 * coslamda;
A1 = _2D_Point.Get_PAngle(_2D_Point.Origin, new _2D_Point(q, p)).ChangeToRad();
sin_xigema = p * Math.Sin(A1) + q * Math.Cos(A1);
cos_xigema = a1 + a2 * Math.Cos(lamda);
xigema = Math.Atan(sin_xigema / cos_xigema);
if (cos_xigema < 0) xigema = Math.PI - Math.Abs(xigema);
else xigema = Math.Abs(xigema);
sinA0 = cos_u1 * Math.Sin(A1);
double sinA1 = Math.Sin(A1),
cosA1 = Math.Cos(A1),
tan_xigema1 = sin_u1 / cos_u1 / cosA1;
xigema1 = Math.Atan(tan_xigema1);
xigema2 = xigema + xigema1;
cos2A0 = 1 - sinA0 * sinA0;
double e_2 = ep.data.e_2,
e_4 = e_2 * e_2,
e_6 = e_2 * e_4,
Alph = e_2 / 2 + e_4 / 8 + e_6 / 8 - (e_4 / 16 + e_6 / 16) * cos2A0 + 3 * e_6 / 128 * cos2A0 * cos2A0,
Beta = (e_4 / 32 + e_6 / 32) * cos2A0 - e_6 / 64 * cos2A0 * cos2A0,
Beta1 = 2 * Beta / cos2A0;
delta1 = sinA0 * (Alph * xigema + Beta * (Math.Sin(2 * xigema2) - Math.Sin(2 * xigema1)));
} while (Math.Abs(delta0 - delta1) * Methods.ρ > 0.0001);
double k_2 = ep.data.e2_2 * cos2A0,
k_4 = k_2 * k_2,
k_6 = k_2 * k_4,
b = ep.data.b,
A = b * (1 + k_2 / 4 - 3 * k_4 / 64 + 5 * k_6 / 256),
B = b * (k_2 / 8 - k_4 / 32 + 15 * k_6 / 1024),
C = b * (k_4 / 128 - 3 * k_6 / 512),
B_pp = 2 * B / cos2A0,
C_pp = 2 * C / cos2A0 / cos2A0;
double S = A * xigema + (B+C*Math.Cos(2*xigema1)) * Math.Sin(2*xigema1)-Math.Sin(2*xigema2)*(B+C*Math.Cos(2*xigema2)),
p1 = cos_u1 * Math.Sin(lamda),
q1 = b1 * Math.Cos(lamda) - b2;
var A21 = _2D_Point.Get_PAngle(_2D_Point.Origin, new _2D_Point(-q1, -p1));
ge.S = ge.Sr = S;
ge.A21 = A21; ge.Ar21 = A21.ChangeToRad();
ge.Ar12 = A1; ge.A12 = Angle.ChangeToAngle(A1);
}
/// <summary>
/// 高斯引数法反算
/// </summary>
/// <param name="ge">已知元素</param>
public void GaussInverse(GeodeticElement ge)
{
double Bm = Methods.Average(ge.Br1, ge.Br2),
delta_B = ge.Br2 - ge.Br1,
delta_L = ge.Lr2 - ge.Lr1,
Vm = Auxiliary.GetV(ep.data.e2_2, Bm),
Nm = Auxiliary.GetN(ep.data.a, ep.data.e_2, Bm),
tm = Auxiliary.Get_t(Bm),
tm2=tm*tm,
yita_2 = Auxiliary.GetYita2(ep.data.e2_2, Bm),
cos_Bm=Math.Cos(Bm),
cos_Bm2=cos_Bm*cos_Bm;
double r01 = Nm * cos_Bm,
r21 = r01 / 24 / Math.Pow(Vm, 4) * (1 + yita_2 - 9 * yita_2 * tm2 + yita_2 * yita_2),
r03 = -r01 / 24 * cos_Bm2 * tm2;
double s10 = Nm / Vm / Vm,
s12 = -s10 * cos_Bm2 / 24 * (2 + 3 * tm2 + 2 * yita_2*tm2),
s30 = Nm /Math.Pow(Vm,6)/ 8 * (yita_2- tm2 * yita_2+yita_2*yita_2);
double t01 = tm * cos_Bm,
t21 = t01 / 24 / Math.Pow(Vm, 4) * (2 + 7 * yita_2 +9*tm2*yita_2 + 5 * yita_2 * yita_2),
t03 = t01 * cos_Bm2 / 24 * (2+tm2 +2* yita_2);
double S_sinAm = r01 * delta_L + r21 * delta_B * delta_B * delta_L + r03 * Math.Pow(delta_L, 3),
S_cosAm = s10 * delta_B + s12 * delta_B * delta_L * delta_L + s30 * Math.Pow(delta_B, 3),
delta_A = t01 * delta_L + t21 * delta_B * delta_B * delta_L + t03 * Math.Pow(delta_L, 3);
//S_sinAm1=S_sinAm,S_cosAm1=S_cosAm,delta_A1=delta_A;
double Am = _2D_Point.Get_PAngle(new _2D_Point(0, 0), new _2D_Point(S_cosAm, S_sinAm)).ChangeToRad();
//Am1
//do
//{
// S_sinAm = S_sinAm1;
// S_cosAm = S_cosAm1;
// Am = Am1;
// S_sinAm1 = delta_L * Nm * cos_Bm - S_sinAm / 24 / Nm / Nm * (S_sinAm * S_sinAm * tm2 - S_cosAm * S_cosAm * (1 + yita_2 - 9 * yita_2 * tm2 + yita_2 * yita_2));
// S_cosAm1 = delta_B * Nm / Vm / Vm - S_cosAm1 / 24 / Nm / Nm * (S_sinAm1 * S_sinAm1 * (2 + 3 * tm2 + 2 * yita_2 * tm2) + 3 * yita_2 * S_cosAm * S_cosAm1 * (1 + yita_2 - tm2 + 4 * tm2 * yita_2));
// Am1 = _2D_Point.Get_PAngle(new _2D_Point(0, 0), new _2D_Point(S_cosAm1, S_sinAm1)).ChangeToRad();
//} while (Math.Abs(Angle.ChangeToAngle(Am1 - Am).Miao) > 0.0001);
ge.S = ge.Sr = S_sinAm / Math.Sin(Am);
ge.Ar12 = Am - delta_A / 2;
ge.A12 = Angle.ChangeToAngle(ge.Ar12);
if (Am + delta_A >= Math.PI)
{
ge.Ar21 = Am + delta_A/2 - Math.PI;
}
else
ge.Ar21 = Am + delta_A/2 + Math.PI;
ge.A21 = Angle.ChangeToAngle(ge.Ar21);
}
/// <summary>
/// 贝塞尔正算
/// </summary>
/// <param name="ge">已知元素</param>
public void BesselPositive(GeodeticElement ge)
{
double W1 = Auxiliary.GetW(ep.data.e_2, ge.Br1),
sin_u1 = Math.Sin(ge.Br1) * Math.Sqrt(1 - ep.data.e_2) / W1,
cos_u1 = Math.Cos(ge.Br1) / W1,
sinA1=Math.Sin(ge.Ar12),
cosA1=Math.Cos(ge.Ar12);
double sinA0 = cos_u1 * sinA1,
cot_xigema1 = cos_u1 * cosA1 / sin_u1,
sin_2xigema1 = 2 * cot_xigema1 / (cot_xigema1 * cot_xigema1 + 1),
cos_2xigema1 = (cot_xigema1 * cot_xigema1 - 1) / (cot_xigema1 * cot_xigema1 + 1);
double cos2A0 = 1 - sinA0 * sinA0,
k_2 = ep.data.e2_2 * cos2A0,
k_4 = k_2 * k_2,
k_6 = k_2 * k_4,
b = ep.data.b,
e_2 = ep.data.e_2,
e_4 = e_2 * e_2,
e_6 = e_2 * e_4,
A = b * (1 + k_2 / 4 - 3 * k_4 / 64 + 5 * k_6 / 256),
B = b * (k_2 / 8 - k_4 / 32 + 15 * k_6 / 1024),
C = b * (k_4 / 128 - 3 * k_6 / 512),
Alph = e_2 / 2 + e_4 / 8 + e_6 / 8 - (e_4 / 16 + e_6 / 16) * cos2A0 + 3 * e_6 / 128 * cos2A0 * cos2A0,
Beta = (e_4 / 32 + e_6 / 32) * cos2A0 - e_6 / 64 * cos2A0 * cos2A0;
double xigema0 = (ge.Sr - (B + C * cos_2xigema1) * sin_2xigema1) / A,
cos_2xigema0 = Math.Cos(2 * xigema0),
sin_2xigema0 = Math.Sin(2 * xigema0),
sin_2xigema10 = sin_2xigema1 * cos_2xigema0 + cos_2xigema1 * sin_2xigema0,
cos_2xigema10 = cos_2xigema1 * cos_2xigema0 - sin_2xigema0 * sin_2xigema1,
xigema = xigema0 + (B + 5 * C * cos_2xigema10) * sin_2xigema10 / A;
double delta = (Alph * xigema + Beta * (sin_2xigema1 * Math.Cos(2 * xigema) + cos_2xigema1 * Math.Sin(2 * xigema) - sin_2xigema1)) * sinA0;
double sin_u2 = sin_u1 * Math.Cos(xigema) + cos_u1 * cosA1 * Math.Sin(xigema),
B2 = Math.Atan(sin_u2 / Math.Sqrt((1 - e_2) * (1 - sin_u2 * sin_u2))),
lamda = Math.Atan2(sinA1, (cos_u1 * Math.Cos(xigema) - sin_u1 * Math.Sin(xigema) * cosA1) / Math.Sin(xigema)),
L2 = ge.Lr1 + lamda - delta;
var A2 = _2D_Point.Get_PAngle(new _2D_Point(0, 0),
new _2D_Point(-(Math.Cos(xigema) * cos_u1 * cosA1 - sin_u1 * Math.Sin(xigema)) / cos_u1, -sinA1));
ge.Br2 = B2; ge.Lr2 = L2;
ge.B2 = Angle.ChangeToAngle(B2); ge.L2 = Angle.ChangeToAngle(L2);
ge.Ar21 = A2.ChangeToRad(); ge.A21 =A2 ;
}
///// <summary>
///// 构造函数，自定义椭球
///// </summary>
///// <param name="a">椭球元素a</param>
///// <param name="b">椭球元素b</param>
//public GeodeticSolution(double a, double b)
//{
// ep = new Ellipsoid(a, b);
//}
/// <summary>
/// 高斯平均引数法正算
/// </summary>
/// <param name="ge">已知条件</param>
public void GaussPositive(GeodeticElement ge)
{
double e2_2 = ep.data.e2_2,
c = ep.data.c,
Vm = Auxiliary.GetV(e2_2, ge.Br1),
Mm = c / Vm / Vm / Vm,
Nm = c / Vm,
delta_B0 = Methods.ρ / Mm * ge.Sr * Math.Cos(ge.Ar12),
delta_L0 = Methods.ρ / Nm * ge.Sr * Math.Sin(ge.Ar12) / Math.Cos(ge.Br1),
delta_A0 = delta_L0 * Math.Sin(ge.Br1),
delta_B1=delta_B0,
delta_L1=delta_L0,
delta_A1=delta_A0,
Bm,
Am,
tm,
yita_2;
#region 迭代法求解
do
{
delta_B0=delta_B1;
delta_L0=delta_L1;
delta_A0=delta_A1;
Bm=ge.Br1+delta_B0/2/Methods.ρ;
Am=ge.Ar12+delta_A0/2/Methods.ρ;
Vm = Auxiliary.GetV(e2_2, Bm);
Nm = c / Vm;
tm=Auxiliary.Get_t(Bm);
yita_2=Auxiliary.GetYita2(e2_2,Bm);
delta_B1 = Vm * Vm / Nm * Methods.ρ * ge.Sr * Math.Cos(Am) *
(1 + ge.Sr * ge.Sr / 24 / Nm / Nm *
(Math.Sin(Am) * Math.Sin(Am) * (2 + 3 * tm * tm + 3 * yita_2*tm*tm) +
3 * yita_2 * Math.Cos(Am) * Math.Cos(Am) * (-1 +tm*tm- yita_2 - 4 * yita_2 * tm * tm)));
delta_L1 = Methods.ρ / Nm * ge.Sr * Math.Sin(Am) /Math.Cos(Bm)*
(1 + ge.Sr * ge.Sr / 24 / Nm / Nm *
(Math.Sin(Am) * Math.Sin(Am) * tm * tm -
Math.Cos(Am) * Math.Cos(Am) * (1 + yita_2 - 9 * yita_2 * tm * tm+yita_2*yita_2)));
delta_A1 = Methods.ρ / Nm * ge.Sr * Math.Sin(Am) *tm*
(1 + ge.Sr * ge.Sr / 24 / Nm / Nm *
(Math.Cos(Am) * Math.Cos(Am) * (2 + 7*yita_2 + 9 * yita_2 * tm * tm+5*yita_2*yita_2) +
Math.Sin(Am) * Math.Sin(Am) * (2 + tm*tm + 2 * yita_2)));
}while(Math.Abs(delta_B1-delta_B0)>0.0001||
Math.Abs(delta_L1-delta_L0)>0.0001||
Math.Abs(delta_A1-delta_A0)>0.0001);
#endregion
ge.Br2 = ge.Br1 + delta_B1 / Methods.ρ;
ge.B2 = Angle.ChangeToAngle(ge.Br2);
ge.Lr2 = ge.Lr1 + delta_L1 / Methods.ρ;
ge.L2 = Angle.ChangeToAngle(ge.Lr2);
if(ge.Ar12+delta_A1/Methods.ρ>=Math.PI)
{
ge.Ar21 = ge.Ar12 + delta_A1 / Methods.ρ - Math.PI;
}
else
ge.Ar21 = ge.Ar12 + delta_A1 / Methods.ρ + Math.PI;
ge.A21 = Angle.ChangeToAngle(ge.Ar21);
}
/// <summary>
/// 贝塞尔反算1
/// </summary>
/// <param name="ge"></param>
public void BesselInverse1(GeodeticElement ge)
{
double W1 = Auxiliary.GetW(ep.data.e_2, ge.Br1),
W2 = Auxiliary.GetW(ep.data.e_2, ge.Br2),
sin_u1 = Math.Sin(ge.Br1) * Math.Sqrt(1 - ep.data.e_2) / W1,
sin_u2 = Math.Sin(ge.Br2) * Math.Sqrt(1 - ep.data.e_2) / W2,
cos_u1 = Math.Cos(ge.Br1) / W1,
cos_u2 = Math.Cos(ge.Br2) / W2,
L = ge.Lr2 - ge.Lr1,
a1 = sin_u1 * sin_u2,
a2 = cos_u1 * cos_u2,
b1 = cos_u1 * sin_u2,
b2 = sin_u1 * cos_u2,
delta0 = 0,
delta1 = delta0,
lamda,
A1,
xigema, xigema1, xigema2,
sin_xigema,
cos_xigema,
sinA0,
cos2A0;
do
{
delta0 = delta1;
lamda = L + delta0;
double sinlamda = Math.Sin(lamda),
coslamda = Math.Cos(lamda);
double p = cos_u2 * sinlamda,
q = b1 - b2 * coslamda;
A1 = _2D_Point.Get_PAngle(_2D_Point.Origin, new _2D_Point(q, p)).ChangeToRad();
sin_xigema = p * Math.Sin(A1) + q * Math.Cos(A1);
cos_xigema = a1 + a2 * Math.Cos(lamda);
xigema = Math.Atan(sin_xigema / cos_xigema);
if (cos_xigema < 0)
{
xigema = Math.PI - Math.Abs(xigema);
}
else
{
xigema = Math.Abs(xigema);
}
sinA0 = cos_u1 * Math.Sin(A1);
double sinA1 = Math.Sin(A1),
cosA1 = Math.Cos(A1),
tan_xigema1 = sin_u1 / cos_u1 / cosA1;
xigema1 = Math.Atan(tan_xigema1);
xigema2 = xigema + xigema1;
cos2A0 = 1 - sinA0 * sinA0;
double e_2 = ep.data.e_2,
e_4 = e_2 * e_2,
e_6 = e_2 * e_4,
Alph = e_2 / 2 + e_4 / 8 + e_6 / 8 - (e_4 / 16 + e_6 / 16) * cos2A0 + 3 * e_6 / 128 * cos2A0 * cos2A0,
Beta = (e_4 / 32 + e_6 / 32) * cos2A0 - e_6 / 64 * cos2A0 * cos2A0,
Beta1 = 2 * Beta / cos2A0;
delta1 = sinA0 * (Alph * xigema + Beta * (Math.Sin(2 * xigema2) - Math.Sin(2 * xigema1)));
} while (Math.Abs(delta0 - delta1) * Methods.ρ > 0.0001);
double k_2 = ep.data.e2_2 * cos2A0,
k_4 = k_2 * k_2,
k_6 = k_2 * k_4,
b = ep.data.b,
A = b * (1 + k_2 / 4 - 3 * k_4 / 64 + 5 * k_6 / 256),
B = b * (k_2 / 8 - k_4 / 32 + 15 * k_6 / 1024),
C = b * (k_4 / 128 - 3 * k_6 / 512),
B_pp = 2 * B / cos2A0,
C_pp = 2 * C / cos2A0 / cos2A0;
double S = A * xigema + (B + C * Math.Cos(2 * xigema1)) * Math.Sin(2 * xigema1) - Math.Sin(2 * xigema2) * (B + C * Math.Cos(2 * xigema2)),
p1 = cos_u1 * Math.Sin(lamda),
q1 = b1 * Math.Cos(lamda) - b2;
var A21 = _2D_Point.Get_PAngle(_2D_Point.Origin, new _2D_Point(-q1, -p1));
ge.S = ge.Sr = S;
ge.A21 = A21; ge.Ar21 = A21.ChangeToRad();
ge.Ar12 = A1; ge.A12 = Angle.ChangeToAngle(A1);
}
///// <summary>
///// 构造函数，自定义椭球
///// </summary>
///// <param name="a">椭球元素a</param>
///// <param name="b">椭球元素b</param>
//public GeodeticSolution(double a, double b)
//{
// ep = new Ellipsoid(a, b);
//}
/// <summary>
/// 高斯平均引数法正算
/// </summary>
/// <param name="ge">已知条件</param>
public void GaussPositive(GeodeticElement ge)
{
double e2_2 = ep.data.e2_2,
c = ep.data.c,
Vm = Auxiliary.GetV(e2_2, ge.Br1),
Mm = c / Vm / Vm / Vm,
Nm = c / Vm,
delta_B0 = Methods.ρ / Mm * ge.Sr * Math.Cos(ge.Ar12),
delta_L0 = Methods.ρ / Nm * ge.Sr * Math.Sin(ge.Ar12) / Math.Cos(ge.Br1),
delta_A0 = delta_L0 * Math.Sin(ge.Br1),
delta_B1 = delta_B0,
delta_L1 = delta_L0,
delta_A1 = delta_A0,
Bm,
Am,
tm,
yita_2;
#region 迭代法求解
do
{
delta_B0 = delta_B1;
delta_L0 = delta_L1;
delta_A0 = delta_A1;
Bm = ge.Br1 + delta_B0 / 2 / Methods.ρ;
Am = ge.Ar12 + delta_A0 / 2 / Methods.ρ;
Vm = Auxiliary.GetV(e2_2, Bm);
Nm = c / Vm;
tm = Auxiliary.Get_t(Bm);
yita_2 = Auxiliary.GetYita2(e2_2, Bm);
delta_B1 = Vm * Vm / Nm * Methods.ρ * ge.Sr * Math.Cos(Am) *
(1 + ge.Sr * ge.Sr / 24 / Nm / Nm *
(Math.Sin(Am) * Math.Sin(Am) * (2 + 3 * tm * tm + 3 * yita_2 * tm * tm) +
3 * yita_2 * Math.Cos(Am) * Math.Cos(Am) * (-1 + tm * tm - yita_2 - 4 * yita_2 * tm * tm)));
delta_L1 = Methods.ρ / Nm * ge.Sr * Math.Sin(Am) / Math.Cos(Bm) *
(1 + ge.Sr * ge.Sr / 24 / Nm / Nm *
(Math.Sin(Am) * Math.Sin(Am) * tm * tm -
Math.Cos(Am) * Math.Cos(Am) * (1 + yita_2 - 9 * yita_2 * tm * tm + yita_2 * yita_2)));
delta_A1 = Methods.ρ / Nm * ge.Sr * Math.Sin(Am) * tm *
(1 + ge.Sr * ge.Sr / 24 / Nm / Nm *
(Math.Cos(Am) * Math.Cos(Am) * (2 + 7 * yita_2 + 9 * yita_2 * tm * tm + 5 * yita_2 * yita_2) +
Math.Sin(Am) * Math.Sin(Am) * (2 + tm * tm + 2 * yita_2)));
}while(Math.Abs(delta_B1 - delta_B0) > 0.0001 ||
Math.Abs(delta_L1 - delta_L0) > 0.0001 ||
Math.Abs(delta_A1 - delta_A0) > 0.0001);
#endregion
ge.Br2 = ge.Br1 + delta_B1 / Methods.ρ;
ge.B2 = Angle.ChangeToAngle(ge.Br2);
ge.Lr2 = ge.Lr1 + delta_L1 / Methods.ρ;
ge.L2 = Angle.ChangeToAngle(ge.Lr2);
if (ge.Ar12 + delta_A1 / Methods.ρ >= Math.PI)
{
ge.Ar21 = ge.Ar12 + delta_A1 / Methods.ρ - Math.PI;
}
else
{
ge.Ar21 = ge.Ar12 + delta_A1 / Methods.ρ + Math.PI;
}
ge.A21 = Angle.ChangeToAngle(ge.Ar21);
}
