你帮我写一个基于QT C++的大地转投影坐标的函数代码。用高斯克吕格投影方法，已知投影参数如下 double centralMeridian = 116.0; // 中央经线 double scaleFactor = 1.0; // 比例因子 double falseEasting = 500000.0; // 东偏移 double falseNorthing = 0.0; // 北偏移 椭球参数 double a = ellipsoid.semi_major_axis; double f = ellipsoid.oblateness; double b = a * (1 - f); double e2 = (a*a - b*b) / (a*a);

以下是基于QT C++的大地转投影坐标的函数代码，使用高斯克吕格投影方法，输入参数为经度和纬度，输出参数为投影坐标的x和y值。其中，输入的ellipsoid为椭球参数，包含长半轴和扁率。代码中使用了cmath库中的一些数学函数，如sin、cos、sqrt等，需要在代码开头添加#include <cmath>。

#include <cmath>

void geodeticToProjected(double lon, double lat, double& x, double& y, Ellipsoid ellipsoid, double centralMeridian, double scaleFactor, double falseEasting, double falseNorthing)
{
    // 计算投影带号
    int zone_number = static_cast<int>((lon - 1.5) / 3.0) + 1;

    // 计算中央经线经度
    double central_meridian = (zone_number - 1) * 3 + 1.5;

    // 将经度和纬度转换为弧度
    double rad_lon = lon * M_PI / 180.0;
    double rad_lat = lat * M_PI / 180.0;

    // 计算子午线弧长
    double a = ellipsoid.semi_major_axis;
    double f = ellipsoid.oblateness;
    double b = a * (1 - f);
    double e2 = (a*a - b*b) / (a*a);
    double B = atan((1 - f) * tan(rad_lat));
    double N = a / sqrt(1 - e2 * sin(rad_lat) * sin(rad_lat));
    double T = tan(rad_lat) * tan(rad_lat);
    double C = e2 * cos(rad_lat) * cos(rad_lat);
    double M = a * ((1 - e2 / 4 - 3 * e2*e2 / 64 - 5 * e2*e2*e2 / 256) * B
        - (3 * e2 / 8 + 3 * e2*e2 / 32 + 45 * e2*e2*e2 / 1024) * sin(2 * B)
        + (15 * e2*e2 / 256 + 45 * e2*e2*e2 / 1024) * sin(4 * B)
        - (35 * e2*e2*e2 / 3072) * sin(6 * B)
        + (315 * e2*e2*e2*e2 / 131072) * sin(8 * B));

    // 计算投影坐标
    double k0 = scaleFactor;
    double x0 = falseEasting;
    double y0 = falseNorthing;
    double x = k0 * N * (rad_lon - central_meridian * M_PI / 180.0) + x0;
    double y = k0 * (M + N * tan(rad_lat) * (1 + (T - C) * (T - C) / 6
        + (5 - 18 * T + T * T + 72 * C - 58 * e2) * (T - C) * (T - C) * (T - C) / 120)) + y0;

    // 将结果赋值给输出参数
    x = round(x * 1000) / 1000;
    y = round(y * 1000) / 1000;
}

使用示例：

// 定义椭球参数
Ellipsoid ellipsoid;
ellipsoid.semi_major_axis = 6378137;
ellipsoid.oblateness = 1.0 / 298.257223563;

// 定义投影参数
double centralMeridian = 116.0;
double scaleFactor = 1.0;
double falseEasting = 500000.0;
double falseNorthing = 0.0;

// 输入经度和纬度
double lon = 116.5;
double lat = 39.5;

// 定义输出变量
double x, y;

// 调用函数计算投影坐标
geodeticToProjected(lon, lat, x, y, ellipsoid, centralMeridian, scaleFactor, falseEasting, falseNorthing);

// 输出结果
qDebug() << "x = " << x << ", y = " << y;