surf_pos_of_ray_first_intersection

Ellipsoid.surf_pos_of_ray_first_intersection(self, r_source: ndarray[double], u_ray: ndarray[double]) → ndarray[double]

Compute the first ellipsoid‐surface intersection of a ray.

Given a ray starting at ECEF point \(\mathbf{r}_0\) and traveling in unit‐direction \(\hat{\mathbf{u}}\), find the closest intersection point(s) with the reference ellipsoid surface.

Parameters:

r_sourcefloat or ndarray of float, shape (3,)

Ray origin in ECEF coordinates [\(x\), \(y\), \(z\)] (metres).

u_rayndarray of float, shape (3,) or (N, 3)

Unit direction vector(s) of the ray in ECEF coordinates.

Returns:

r_surfndarray of float, shape (3,) or (N, 3)

ECEF coordinate(s) of the first intersection point(s) on the ellipsoid.

Raises:

AssertionError

If r_source is not shape (3,), or if u_ray is not shape (3,) or (N, 3).

See also

c_surf_pos_of_ray_first_intersection

Core C implementation (nogil) for a single ray.

Notes

Solve for the parameter \(t\) in the quadratic

\[\]

rac{igl(r_{0,x} + t,u_xigr)^2}{a^2}

rac{igl(r_{0,y} + t,u_yigr)^2}{a^2}

rac{igl(r_{0,z} + t,u_zigr)^2}{b^2}

= 1,

where \(a\) is the semi-major axis, \(b = a\,(1 - f)\) the semi-minor axis, and the smallest positive root is chosen. The intersection is then \(\mathbf{r}_ ext{surf} = \mathbf{r}_0 + t\,\hat{\mathbf{u}}\).