C++实现高斯坐标转经纬度坐标的函数

以下是C++实现高斯坐标转经纬度坐标的函数：

#include <cmath>

// 定义常量
const double PI = 3.14159265358979323846;
const double a = 6378137.0; // 长半轴
const double b = 6356752.3142; // 短半轴
const double f = 1.0 / 298.257223563; // 扁率
const double e2 = f * (2 - f); // 第一偏心率的平方
const double ee2 = e2 / (1 - e2); // 第二偏心率的平方

// 高斯投影正算
void GaussForward(double B, double L, double &X, double &Y, double L0, double K0)
{
    double L1 = L - L0;
    double l = L1 * PI / 180;
    double b = B * PI / 180;
    double N = a / sqrt(1 - e2 * sin(b) * sin(b));
    double t = tan(b);
    double g = sqrt(ee2) * cos(b);
    double m = cos(b) * l;
    double s = sin(b);
    double n = sqrt(ee2) * s;
    double t1 = t * t;
    double g2 = g * g;
    double N2 = N * N;
    double cos3 = cos(b) * cos(b) * cos(b);
    double sin2 = sin(b) * sin(b);
    double x = K0 * N * (m + (1 - t1 + g2) * m * m * m / 6.0 + (5 - 18 * t1 + t1 * t1 + 72 * g2 - 58 * ee2) * m * m * m * m * m / 120.0);
    double y = K0 * (N * t + N * (9 * ee2 + 4 * g2 - 12) * t * t * t / 24.0 + N * (61 - 58 * t1 + t1 * t1 + 600 * g2 - 330 * ee2) * t * t * t * t * t / 720.0);
    X = x + 500000;
    Y = y;
}

// 高斯投影反算
void GaussInverse(double X, double Y, double &B, double &L, double L0, double K0)
{
    Y = Y / K0;
    double x = X - 500000;
    double e1 = (1 - sqrt(1 - e2)) / (1 + sqrt(1 - e2));
    double xx = x / (a * K0);
    double m = xx / cos(B);
    double m2 = m * m;
    double m3 = m2 * m;
    double m4 = m3 * m;
    double m5 = m4 * m;
    double n = (e2 * cos(B) * cos(B)) / (1 - e2);
    double n2 = n * n;
    double t = tan(B);
    double t2 = t * t;
    double t4 = t2 * t2;
    double t6 = t4 * t2;
    double cos3 = cos(B) * cos(B) * cos(B);
    double cos5 = cos3 * cos(B) * cos(B);
    double eta = ee2 * cos(B) * cos(B);
    double eta2 = eta * eta;
    double eta3 = eta2 * eta;
    double eta4 = eta3 * eta;

    B = B - t * xx * xx / (2 * a * a * N) + t * (5 + 3 * t2 + n - 9 * eta) * xx * xx * xx * xx / (24 * a * a * a * a * N * N * N)
        - t * (61 + 90 * t2 + 45 * t4) * xx * xx * xx * xx * xx * xx / (720 * a * a * a * a * a * a * N * N * N * N * N)
        + t * xx * xx * xx * xx * xx * xx * (1385 + 3633 * t2 + 4095 * t4 + 1575 * t6) / (40320 * a * a * a * a * a * a * a * a * N * N * N * N * N * N);

    L = L0 + m - (1 + 2 * t2 + n) * m3 / 6 + (5 - 2 * n + 28 * t2 - 3 * n2 + 8 * eta + 24 * t4) * m5 / 120;

    B = B * 180 / PI;
    L = L * 180 / PI;
}

其中，高斯投影正算函数`GaussForward`的参数为输入的经度`L`和纬度`B`，输出的高斯坐标`X`和`Y`，以及中央子午线经度`L0`和比例因子`K0`；高斯投影反算函数`GaussInverse`的参数为输入的高斯坐标`X`和`Y`，输出的经度`L`和纬度`B`，以及中央子午线经度`L0`和比例因子`K0`。