EGM96海拔高度转椭球高度，c语言实现

EGM96 是一个用于计算地球重力场的模型，它可以用来将海拔高度转换为椭球高度或者反过来。

要在 C 语言中实现 EGM96 的海拔高度转椭球高度功能，您需要先准备好 EGM96 的数据文件。这些数据文件可以从国家地球物理数据中心（NGDC）的网站上下载。下载链接为：https://www.ngdc.noaa.gov/geomag/EMM/egm96/egm96.html

下载后，您需要将数据文件读入内存中，并根据算法计算出椭球高度。以下是一个简单的 C 语言实现示例：

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>

#define EGM96_DATA_FILE "WW15MGH.DAC"

typedef struct {
    double c, s;
} coeff_t;

coeff_t* read_egm96_data() {
    FILE* fp = fopen(EGM96_DATA_FILE, "rb");
    if (!fp) {
        perror("Failed to open EGM96 data file");
        return NULL;
    }

    // Skip the header
    fseek(fp, 0x20c, SEEK_SET);

    // Read the coefficients
    coeff_t* coeffs = calloc(2190, sizeof(coeff_t));
    if (!coeffs) {
        perror("Failed to allocate memory for EGM96 coefficients");
        fclose(fp);
        return NULL;
    }

    for (int n = 0; n <= 2160; n++) {
        for (int m = 0; m <= n; m++) {
            int i = n*(n+1)/2 + m;
            double c, s;
            if (fscanf(fp, "%lf %lf", &c, &s) != 2) {
                fprintf(stderr, "Failed to read EGM96 coefficient (%d, %d)\n", n, m);
                fclose(fp);
                free(coeffs);
                return NULL;
            }
            coeffs[i].c = c;
            coeffs[i].s = s;
        }
    }

    fclose(fp);
    return coeffs;
}

void free_egm96_data(coeff_t* coeffs) {
    free(coeffs);
}

double egm96_height_to_ellipsoid(double lat, double lon, double h, coeff_t* coeffs) {
    const double a = 6378137.0; // Equatorial radius
    const double b = 6356752.3142; // Polar radius
    const double GM = 3986004.418e8; // Gravitational constant times mass of Earth

    // Convert latitude and longitude to radians
    lat = lat * M_PI / 180.0;
    lon = lon * M_PI / 180.0;

    // Compute the geocentric distance
    const double r = sqrt(pow(a*a*cos(lat), 2) + pow(b*b*sin(lat), 2)) / sqrt(pow(a*cos(lat), 2) + pow(b*sin(lat), 2)) + h;

    // Compute the geocentric latitude
    const double phi = atan2(b*b*cos(lat), a*a*sin(lat));

    // Compute the spherical harmonics
    double sum = 0.0;
    for (int n = 2; n <= 2160; n++) {
        for (int m = 0; m <= n; m++) {
            int i = n*(n+1)/2 + m;
            double Pnm = legendre(n, m, sin(phi));
            sum += (a / r) * pow(GM / pow(r, 2), n) * (coeffs[i].c*cos(m*lon) + coeffs[i].s*sin(m*lon)) * Pnm;
        }
    }

    // Return the ellipsoid height
    return r - sum;
}

double legendre(int n, int m, double x) {
    if (n == m) {
        return pow(-1, m) * fact(2*m-1) * pow(sqrt(1-x*x), m);
    }
    if (n == m+1) {
        return x*(2*m+1)*legendre(m, m, x);
    }
    double Pnm1m1 = legendre(n-1, m-1, x);
    double Pnm2m1 = legendre(n-2, m-1, x);
    return ((2*n-1)*x*Pnm1m1 - (n+m-1)*Pnm2m1) / (n-m);
}

double fact(int n) {
    double f = 1.0;
    for (int i = 2; i <= n; i++) {
        f *= i;
    }
    return f;
}

int main() {
    // Read EGM96 data
    coeff_t* coeffs = read_egm96_data();
    if (!coeffs) {
        return 1;
    }

    // Compute the ellipsoid height
    double lat = 40.0;
    double lon = -105.0;
    double h = 1609.344; // 1 mile in meters
    double ellipsoid_height = egm96_height_to_ellipsoid(lat, lon, h, coeffs);
    printf("Ellipsoid height = %.3lf meters\n", ellipsoid_height);

    // Free EGM96 data
    free_egm96_data(coeffs);

    return 0;
}

请注意，这只是一个简单的示例，实际应用中，您需要根据自己的需求进行修改和优化。