c-如何计算大地坐标(ECEF)与本地参考(ENU)之间的直接和反向转换

Question

如何将X、Y、Z从本地引用（ENU）转换为世界引用（ECEF）并反转？？

输入：

(lat,long) = center of the local reference system.
       x,y,z = position of the point,in local system reference.

输出：（lat，long）=WGS84中点的位置。还有：反向坐标。

我想步骤是：

1) convert Xlocal,Ylocal,Zlocal  -> Xecef,Yecef,Zecef
2) convert Xecef,Yecef,Zecef     -> Lat,Long (WGS84)

而且比

1) convert Lat,Long(WGS84)       -> Xecef,Yecef,Zecef
2) convert Xecef,Yecef,Zecef     -> Xlocal,Ylocal,Zlocal

Answer 1

我正在开发一个地理空间AR应用程序，刚刚在objective-C/iOS中亲自解决了这个问题（苹果的示例代码提供了很多帮助）。

下面是将lat-lon到ecef转换为ENU和返回的三个C函数。数学公式来自维基百科的这篇文章。

#define RADIANS_TO_DEGREES(radians) ((radians) * (180.0 / M_PI))
#define DEGREES_TO_RADIANS(degrees)((M_PI * degrees)/180)
#define WGS84_A (6378137.0)             // WGS 84 semi-major axis constant in meters
#define WGS84_E (8.1819190842622e-2)    // WGS 84 eccentricity
// Converts latitude, longitude to ECEF coordinate system
void latLonToEcef(double lat, double lon, double alt, double *x, double *y, double *z)
{
    double clat = cos(DEGREES_TO_RADIANS(lat));
    double slat = sin(DEGREES_TO_RADIANS(lat));
    double clon = cos(DEGREES_TO_RADIANS(lon));
    double slon = sin(DEGREES_TO_RADIANS(lon));
    double N = WGS84_A / sqrt(1.0 - WGS84_E * WGS84_E * slat * slat);
    *x = (N + alt) * clat * clon;
    *y = (N + alt) * clat * slon;
    *z = (N * (1.0 - WGS84_E * WGS84_E) + alt) * slat;
}
// Converts ECEF to ENU coordinates centered at given lat, lon
void ecefToEnu(double lat, double lon, double xRef, double yRef, double zRef, double xPOI, double yPOI, double zPOI, double *e, double *n, double *u)
{
    double clat = cos(DEGREES_TO_RADIANS(lat));
    double slat = sin(DEGREES_TO_RADIANS(lat));
    double clon = cos(DEGREES_TO_RADIANS(lon));
    double slon = sin(DEGREES_TO_RADIANS(lon));
    double dx = xPOI - xRef;
    double dy = yPOI - yRef;
    double dz = zPOI - zRef;
    *e = -slon * dx  + clon * dy;
    *n = -slat * clon * dx - slat * slon * dy + clat * dz;
    *u = clat * clon * dx + clat * slon * dy + slat * dz;
}
// Converts ENU of a POI (in realtion to a reference point) to ECEF coordinates
void enuToEcef(double lat, double lon, double xRef, double yRef, double zRef, double *xPOI, double *yPOI, double *zPOI, double e, double n, double u)
{
    double clat = cos(DEGREES_TO_RADIANS(lat));
    double slat = sin(DEGREES_TO_RADIANS(lat));
    double clon = cos(DEGREES_TO_RADIANS(lon));
    double slon = sin(DEGREES_TO_RADIANS(lon));
    *xPOI = (-slon * e) + (-slat * clon * n) + (clat * clon * u) + xRef;
    *yPOI = (clon * e)  + (-slat * slon * n) + (clat * slon * u) + yRef;
    *zPOI = (0 * e)     + (clat * n)         + (slat * u)        + zRef;
}