/// <summary>
/// 高斯正算
/// </summary>
/// <param name="Geodesy">椭球参数</param>
/// <param name="B">纬度</param>
/// <param name="L">经度</param>
/// <param name="x">横坐标</param>
/// <param name="y">纵坐标</param>
/// <param name="y1"></param>
/// <param name="is3">是否选择3度带</param>
/// <param name="is2">椭球选择参数</param>
/// <param name="is4">经度选择参数</param>
public static void Gauss_P(ell Geodesy, double B, double L, ref double x, ref double y, ref double y1, int is3, int is2, int is4, double L0, int n)
{
try
{
double W;
double N;
double l;
double m;
double t;
double η;
double X = 0;
W = Math.Sqrt(1 - Geodesy.e2 * Math.Sin(B) * Math.Sin(B));
N = Geodesy.a / W;
l = L - L0;
m = Math.Cos(B) * l;
t = Math.Tan(B);
η = Math.Sqrt(Geodesy.e12) * Math.Cos(B);
switch (is2)//判断选择哪个椭球,确定相应的子午线弧长公式
{
case 1: X = 111134.8611 * B * 180 / Math.PI - 16036.4803 * Math.Sin(2 * B) + 16.8281 * Math.Sin(4 * B) - 0.0220 * Math.Sin(6 * B); break;
case 2: X = 111133.0047 * B * 180 / Math.PI - 16038.5282 * Math.Sin(2 * B) + 16.8326 * Math.Sin(4 * B) - 0.0220 * Math.Sin(6 * B); break;
case 3:
X = 111132.95254700 * B * 180 / Math.PI - 16038.508741268 * Math.Sin(2 * B) + 16.832613326622 * Math.Sin(4 * B) - 0.021984374201268 * Math.Sin(6 * B)
+ 3.1141625291648e-5 * Math.Sin(8 * B); break;
default: MessageBox.Show("请选择相应椭球参数！"); break;
}
if (is4 == 1)//选择精度为0.001m时的高斯投影正算公式
{
x = X + N * t * (1.0 / 2 * m * m + 1.0 / 24 * (5 - t * t + 9 * η * η + 4 * Math.Pow(η, 4)) * Math.Pow(m, 4)
+ 1.0 / 720 * (61 - 58 * t * t + Math.Pow(t, 4)) * Math.Pow(m, 6));
y = N * (m + 1.0 / 6 * (1 - t * t + η * η) * Math.Pow(m, 3) +
1.0 / 120 * (5 - 18 * t * t + Math.Pow(t, 4) + 14 * η * η - 58 * η * η * t * t) * Math.Pow(m, 5));
}
else if (is4 == 2)
{
x = X + N * t * (1.0 / 2 * m * m + 1.0 / 24 * (5 - t * t + 9 * η * η + 4 * Math.Pow(η, 4)) * Math.Pow(m, 4));
y = N * (m + 1.0 / 6 * (1 - t * t + η * η) * Math.Pow(m, 3) + 1.0 / 120 * (5 - 18 * t * t + Math.Pow(t, 4)) * Math.Pow(m, 5));
}
if (L == 0 && is3 == 6)
{
y1 = 60 * 1000000 + 500000 + y;
}
if (L <= 1.5 && L >= 0 && is3 == 3)
{
y1 = 120 * 1000000 + 500000 + y;
}
else
{
y1 = n * 1000000 + 500000 + y;
}
}
catch (System.Exception e)
{
MessageBox.Show(e.ToString());
return;
}
}
/// <summary>
/// 高斯正算
/// </summary>
/// <param name="Geodesy">椭球参数</param>
/// <param name="B">唯、维度</param>
/// <param name="L">经度</param>
/// <param name="x"></param>
/// <param name="y"></param>
/// <param name="L0">中央子午线经度</param>
public static void To_Gauss(ell Geodesy, double B, double L, ref double x, ref double y, double L0)
{
double AA, BB, CC, DD, EE, X, e, e1;
double dl, n, t, N;
double a = Geodesy.a;
e = Math.Sqrt(Geodesy.e2);
e1 = Math.Sqrt(Geodesy.e12);
AA = 1 + 3.0 / 4.0 * Math.Pow(e, 2.0) + 45.0 / 64.0 * Math.Pow(e, 4.0) + 175.0 / 256.0 * Math.Pow(e, 6.0);
AA += 11025.0 / 16384.0 * Math.Pow(e, 8.0);
BB = 3.0 / 4.0 * Math.Pow(e, 2.0) + 15.0 / 16.0 * Math.Pow(e, 4.0) + 525.0 / 512.0 * Math.Pow(e, 6.0);
BB += 2205.0 / 2048.0 * Math.Pow(e, 8.0);
CC = 15.0 / 64.0 * Math.Pow(e, 4.0) + 105.0 / 256.0 * Math.Pow(e, 6.0) + 2205.0 / 4096.0 * Math.Pow(e, 8.0);
DD = 35.0 / 512.0 * Math.Pow(e, 6.0) + 315.0 / 2048.0 * Math.Pow(e, 8.0);
EE = 315.0 / 16384.0 * Math.Pow(e, 8.0);
X = a * (1 - Math.Pow(e, 2.0)) * (AA * B - BB / 2 * Math.Sin(2 * B) + CC / 4 * Math.Sin(4 * B)
- DD / 6 * Math.Sin(6 * B) + EE / 8 * Math.Sin(8 * B));
dl = L - L0;
n = e1 * Math.Cos(B);
t = Math.Tan(B);
N = a / Math.Sqrt(1 - e * e * Math.Pow(Math.Sin(B), 2.0));
x = X;
x += N / 2 * Math.Sin(B) * Math.Cos(B) * Math.Pow(dl, 2.0);
x += N / 24 * Math.Sin(B) * Math.Pow(Math.Cos(B), 3.0) * (5 - t * t + 9 * n * n + 4 * Math.Pow(n, 4.0)) * Math.Pow(dl, 4.0);
x += N / 720 * Math.Sin(B) * Math.Pow(Math.Cos(B), 5.0) * (61 - 58 * Math.Pow(t, 2.0) + Math.Pow(t, 4.0)) * Math.Pow(dl, 6.0);
y = N * Math.Cos(B) * dl;
y += N / 6 * Math.Pow(Math.Cos(B), 3.0) * (1 - t * t + n * n) * Math.Pow(dl, 3.0);
y += N / 120 * Math.Pow(Math.Cos(B), 5.0) * (5 - 18 * t * t + Math.Pow(t, 4.0) + 14 * n * n - 58 * n * n * t * t) * Math.Pow(dl, 5.0);
}
/// <summary>
/// 高斯反算
/// </summary>
/// <param name="Geodesy">椭球参数</param>
/// <param name="B"></param>
/// <param name="L"></param>
/// <param name="x"></param>
/// <param name="y"></param>
/// <param name="L0"></param>
public static void Gauss_To(ell Geodesy, ref double B, ref double L, double x, double y, double L0)
{
double AA, BB, CC, DD, EE, e, e1;
double Bf, Bf0, b, dl, nf, tf, Nf, Mf, Wf;
double a = Geodesy.a;
e = Math.Sqrt(Geodesy.e2);
e1 = Math.Sqrt(Geodesy.e12);
AA = 1 + 3.0 / 4.0 * Math.Pow(e, 2.0) + 45.0 / 64.0 * Math.Pow(e, 4.0) + 175.0 / 256.0 * Math.Pow(e, 6.0);
AA += 11025.0 / 16384.0 * Math.Pow(e, 8.0);
BB = 3.0 / 4.0 * Math.Pow(e, 2.0) + 15.0 / 16.0 * Math.Pow(e, 4.0) + 525.0 / 512.0 * Math.Pow(e, 6.0);
BB += 2205.0 / 2048.0 * Math.Pow(e, 8.0);
CC = 15.0 / 64.0 * Math.Pow(e, 4.0) + 105.0 / 256.0 * Math.Pow(e, 6.0) + 2205.0 / 4096.0 * Math.Pow(e, 8.0);
DD = 35.0 / 512.0 * Math.Pow(e, 6.0) + 315.0 / 2048.0 * Math.Pow(e, 8.0);
EE = 315.0 / 16384.0 * Math.Pow(e, 8.0);
Bf0 = x / AA / a / (1 - e * e);//初值
do
{
Bf = x / a / (1 - e * e) / AA + (BB / 2 * Math.Sin(2 * Bf0) - CC / 4 * Math.Sin(4 * Bf0)
+ DD / 6 * Math.Sin(6 * Bf0) - EE / 8 * Math.Sin(8 * Bf0)) / AA;
if (Math.Abs(Bf - Bf0) < 0.0000000000001)
{
break;
}
Bf0 = Bf;
} while (true);
tf = Math.Tan(Bf);
Wf = Math.Sqrt(1 - e * e * Math.Sin(Bf) * Math.Sin(Bf));
Mf = a * (1 - e * e) / Math.Pow(Wf, 3.0);
Nf = a / Wf;
nf = e1 * Math.Cos(Bf);
B = Bf - tf / 2 / Mf / Nf * y * y;
B += tf / 24 / Mf * (5 + 3 * Math.Pow(tf, 2.0) + nf * nf - 9 * nf * nf * tf * tf) * Math.Pow(y / Nf, 3.0) * y;
B += -tf / 720 / Mf * (61 + 90 * tf * tf + 45 * Math.Pow(tf, 4.0)) * Math.Pow(y / Nf, 5.0) * y;
dl = y / Nf / Math.Cos(Bf);
dl += -Math.Pow(y / Nf, 3.0) / 6 / Math.Cos(Bf) * (1 + 2 * tf * tf + nf * nf);
dl += Math.Pow(y / Nf, 5.0) / 120 / Math.Cos(Bf) * (5 + 28 * tf * tf + 24 * Math.Pow(tf, 4.0) + 6 * nf * nf + 8 * nf * nf * tf * tf);
L = L0 + dl;
}
/// <summary>
/// 高斯反算
/// </summary>
/// <param name="Geodesy">椭球参数</param>
/// <param name="B">纬度</param>
/// <param name="L">经度</param>
/// <param name="x">横坐标</param>
/// <param name="y">纵坐标</param>
/// <param name="y1"></param>
/// <param name="is3">是否选择3度带</param>
/// <param name="is2">椭球选择参数</param>
/// <param name="is4">经度选择参数</param>
public static void Gauss_N(ell Geodesy, ref double B, ref double L, double x, double y, double y1, int is3, int is2, int is4)
{
double s = 0;
double W;
double N;
double V;
double t;
double η;
double Bf0; //迭代初始值
double Bf1 = 0; //迭代值
double FB = 0;
double L0 = 0; //中央经线经度
try
{
switch (is2)//选择迭代首项
{
case 1: s = 111134.8611; break;
case 2: s = 111133.0047; break;
case 3: s = 111132.95254700; break;
default: MessageBox.Show("请选择椭球!"); break;
}
if (is3 == 3)
{
L0 = (Math.Floor(y1 / 1000000.0) * 3) * Math.PI / 180.0;
}
else if (is3 == 6)
{
L0 = (Math.Floor(y1 / 1000000.0) * 6 - 3) * Math.PI / 180.0;
}
Bf0 = x / s * Math.PI / 180.0;
double num = 0;//迭代次数
do//迭代求解纬度Bf
{
if (num != 0)
{
Bf0 = Bf1;
}
switch (is2)
{
case 1:
FB = -(32005.7799 * Math.Sin(Bf0) + 133.9238 * Math.Pow(Math.Sin(Bf0), 3) + 0.6973 * Math.Pow(Math.Sin(Bf0), 5)
+ 0.0039 * Math.Pow(Math.Sin(Bf0), 7)) * Math.Cos(Bf0); break;
case 2: FB = -16038.5282 * Math.Sin(2 * Bf0) + 16.8326 * Math.Sin(4 * Bf0) - 0.022 * Math.Sin(6 * Bf0); break;
case 3:
FB = -16038.508741268 * Math.Sin(2 * Bf0) + 16.832613326622 * Math.Sin(4 * Bf0)
- 0.021984374201268 * Math.Sin(6 * Bf0) + 3.1141625291648e-5 * Math.Sin(8 * Bf0); break;
default: MessageBox.Show("请选择相应椭球参数！"); break;
}
Bf1 = (x - FB) / s * Math.PI / 180.0;
num++;
} while (Math.Abs(Bf1 - Bf0) >= 1e-8);
W = Math.Sqrt(1 - Geodesy.e2 * Math.Sin(Bf1) * Math.Sin(Bf1));
V = Math.Sqrt(1 - Geodesy.e12 * Math.Sin(Bf1) * Math.Sin(Bf1));
N = Geodesy.a / W;
t = Math.Tan(Bf1);
η = Math.Sqrt(Geodesy.e12) * Math.Cos(Bf1);
if (is4 == 3)
{
B = Bf1 - 1.0 / 2 * V * V * t * (Math.Pow(y / N, 2) - 1.0 / 12 * (5 + 3 * t * t + η * η - 9 * η * η * t * t) * Math.Pow(y / N, 4)
+ 1.0 / 360 * (61 + 90 * t * t + 45 * Math.Pow(t, 4)) * Math.Pow(y / N, 6));
L = (y / N - 1.0 / 6 * (1 + 2 * t * t + η * η) * Math.Pow(y / N, 3)
+ 1.0 / 120 * (5 + 28 * t * t + 24 * Math.Pow(t, 4) + 6 * η * η + 8 * η * η * t * t) * Math.Pow(y / N, 5)) / Math.Cos(Bf1);
}
else
{
B = Bf1 - 1.0 / 2 * V * V * t * (Math.Pow(y / N, 2) - 1.0 / 12 * (5 + 3 * t * t + η * η - 9 * η * η * t * t) * Math.Pow(y / N, 4));
L = (y / N - 1.0 / 6 * (1 + 2 * t * t + η * η) * Math.Pow(y / N, 3)
+ 1.0 / 120 * (5 + 28 * t * t + 24 * Math.Pow(t, 4)) * Math.Pow(y / N, 5)) / Math.Cos(Bf1);
}
L += L0;
}
catch
{
}
}
