在C++中 利用白塞尔方法编写代码进行大地主题反算

以下是一个使用白塞尔方法进行大地主题反算的 C++ 代码示例：

#include <iostream>
#include <cmath>

#define PI 3.14159265358979323846
#define a 6378137.0
#define b 6356752.3142
#define f (a - b) / a
#define e sqrt(2 * f - pow(f, 2))

using namespace std;

double rad2deg(double rad) {
    return rad / PI * 180.0;
}

double deg2rad(double deg) {
    return deg * PI / 180.0;
}

double calcM(double lat) {
    double W = sqrt(1 - pow(e * sin(lat), 2));
    return a * (1 - pow(e, 2)) / pow(W, 3);
}

double calcN(double lat) {
    double W = sqrt(1 - pow(e * sin(lat), 2));
    return a / W;
}

double calcT(double lat) {
    return pow(tan(lat), 2);
}

double calcC(double lat) {
    double W = sqrt(1 - pow(e * sin(lat), 2));
    return pow(e * cos(lat) / W, 2);
}

double calcA(double lat) {
    double W = sqrt(1 - pow(e * sin(lat), 2));
    return (a / W) * (1 - pow(e, 2)) / pow(W, 2);
}

double calcS(double lat1, double lon1, double lat2, double lon2) {
    double dx = lon2 - lon1;
    double dy = lat2 - lat1;

    double lat1_rad = deg2rad(lat1);
    double lat2_rad = deg2rad(lat2);
    double dx_rad = deg2rad(dx);

    double N1 = calcN(lat1_rad);
    double M1 = calcM(lat1_rad);
    double T1 = calcT(lat1_rad);
    double C1 = calcC(lat1_rad);
    double A1 = calcA(lat1_rad);

    double W1 = sqrt(1 - pow(e * sin(lat1_rad), 2));
    double cos_lat1 = cos(lat1_rad);
    double sin_lat1 = sin(lat1_rad);
    double sin2_lat1 = pow(sin_lat1, 2);
    double cos2_lat1 = pow(cos_lat1, 2);

    double W2 = sqrt(1 - pow(e * sin(lat2_rad), 2));
    double cos_lat2 = cos(lat2_rad);
    double sin_lat2 = sin(lat2_rad);
    double sin2_lat2 = pow(sin_lat2, 2);
    double cos2_lat2 = pow(cos_lat2, 2);

    double Wx = W2 - W1;
    double Wx2 = pow(Wx, 2);
    double Wy = (cos_lat2 * dx_rad);
    double Wy2 = pow(Wy, 2);

    double M2 = calcM(lat2_rad);
    double N2 = calcN(lat2_rad);
    double T2 = calcT(lat2_rad);
    double C2 = calcC(lat2_rad);
    double A2 = calcA(lat2_rad);

    double M = (M1 + M2) / 2.0;

    double mx = dx_rad * cos_lat1 * M;
    double my = dy * M;

    double m = sqrt(pow(mx, 2) + pow(my, 2));

    double latm = lat1_rad + (dy - (T1 + C1) * (pow(dy, 3) / 6.0) + (5.0 - 18.0 * T1 + pow(T1, 2) + 72.0 * C1 - 58.0 * A1) * (pow(dy, 5) / 120.0)) / M;
    double Wm = sqrt(1 - pow(e * sin(latm), 2));
    double Nm = a / Wm;
    double Tm = pow(tan(latm), 2);
    double Cm = pow(e * cos(latm) / Wm, 2);
    double Am = (a / Wm) * (1 - pow(e, 2)) / pow(Wm, 2);

    double theta = atan(mx / my);
    if (my < 0) {
        theta += PI;
    }

    double s = m * cos(theta) + (Wx2 - Wy2) / (2.0 * Nm);

    return s;
}

double calcAzimuth(double lat1, double lon1, double lat2, double lon2) {
    double lat1_rad = deg2rad(lat1);
    double lat2_rad = deg2rad(lat2);
    double dLon_rad = deg2rad(lon2 - lon1);

    double y = sin(dLon_rad) * cos(lat2_rad);
    double x = cos(lat1_rad) * sin(lat2_rad) - sin(lat1_rad) * cos(lat2_rad) * cos(dLon_rad);
    double azimuth_rad = atan2(y, x);

    return rad2deg(azimuth_rad);
}

int main() {
    double lat1 = 22.331;
    double lon1 = 114.264;
    double lat2 = 22.351;
    double lon2 = 114.162;

    double s = calcS(lat1, lon1, lat2, lon2);
    double azimuth = calcAzimuth(lat1, lon1, lat2, lon2);

    cout << "S = " << s << " m" << endl;
    cout << "Azimuth = " << azimuth << " deg" << endl;

    return 0;
}

在这个示例中，我们定义了一些常量，例如地球椭球体的长半轴 `a`、短半轴 `b`、扁率 `f` 和第一偏心率 `e`。然后，我们实现了一些函数来计算需要用到的各个参数，例如子午线曲率半径 `M`、卯酉圈曲率半径 `N`、子午线弧长公式中的参数 `T`、`C` 和 `A`，以及两点之间的大地线长度 `S` 和方位角 `azimuth`。最后，我们在 `main` 函数中调用这些函数来计算两点之间的大地线长度和方位角，并将它们输出到控制台上。

需要注意的是，在实现白塞尔方法时，需要将角度转换为弧度计算。在本示例中，我们使用了 `deg2rad` 和 `rad2deg` 两个函数来进行角度和弧度的转换。同时，为了方便起见，我们将计算中经常用到的参数都定义为常量，以免在多处使用时出现错误。