Determine the intersection of a line-of-sight vector with the surface of an ellipsoid.
VARIABLE I/O DESCRIPTION -------- --- -------------------------------------------------- positn I Position of the observer in body-fixed frame. u I Vector from the observer in some direction. a I Length of the ellipsoid semi-axis along the x-axis. b I Length of the ellipsoid semi-axis along the y-axis. c I Length of the ellipsoid semi-axis along the z-axis. point O Point on the ellipsoid pointed to by u. found O Flag indicating if u points at the ellipsoid.
positn 3-vector giving the position of an observer with respect to the center of an ellipsoid. The vector is expressed in a body-fixed reference frame. The semi-axes of the ellipsoid are aligned with the x, y, and z-axes of the body-fixed frame. u Direction vector emanating from the observer. a Length of the semi-axis of the ellipsoid that is parallel to the x-axis of the body-fixed reference frame. b Length of the semi-axis of the ellipsoid that is parallel to the y-axis of the body-fixed reference frame. c Length of the semi-axis of the ellipsoid that is parallel to the z-axis of the body-fixed reference frame.
point If the ray with direction vector u emanating from positn intersects the ellipsoid, point will be returned with the body-fixed coordinates of the point where the ray first meets the ellipsoid. Otherwise, point will be returned as (0, 0, 0). found A logical flag indicating whether or not the ray from positn with direction u actually intersects the ellipsoid. If the ray does intersect the ellipsoid, found will be returned as SPICETRUE. If the ray misses the ellipsoid, found will be returned as SPICEFALSE.
This routine assumes that an ellipsoid having semi-axes of length a, b and c is given. Moreover, it is assumed that these axes are parallel to the x-, y-, and z-axes of a coordinate system whose origin is the geometric center of the ellipsoid---this is called the body-fixed coordinate frame.
A typical use of surfpt_c would be to obtain the the planetocentric coordinates of the point at which the optic axis of a spacecraft-mounted instrument intersects the surface of a target body, given the following items. 1) The epoch (et) of observation, and the inertial pointing (vpnt) of the instrument at this epoch. 2) The apparent position (vtarg) of the center of the target body as seen from the spacecraft at the epoch of observation, and the one-way light time (tau) from the target to the spacecraft. In order to find the point of intersection, the following items are also needed. 3) The transformation (tibf) from inertial to body-fixed coordinates at epoch et-tau. 4) The radii (r) of the tri-axial ellipsoid used to model the target body. These may be obtained from the kernel pool via calls to pxform_c and bodvrd_c or bodvcd_c respectively. The position of the observer is just the negative of the spacecraft-target vector, vtarg, computed using the vminus_c module. (Note that this is NOT the same as the apparent position of the spacecraft as seen from the target!) Both vectors must be in body-fixed coordinates. The point of intersection is found as follows. vminus_c ( vtarg, vpos ); mxv_c ( tibf, vpos, vpos ); mxv_c ( tibf, vpnt, vpnt ); surfpt_c ( vpos, vpnt, r, r, r, vsurf, &found ); Note that vsurf may or may not be a point of intersection, depending on whether found is SPICETRUE or SPICEFALSE. Note also that vsurf is a vector from the center to the surface of the target, in body-fixed coordinates, which may be converted directly to planetocentric latitude, longitude, and radius: reclat_c ( vsurf, &radius, &long, &lat ); To get the inertial vector from the spacecraft to the surface point, you must subtract vpos from vsurf, and rotate the resulting vector back to inertial coordinates: vsub_c ( vsurf, vpos, vsurf ); mtxv_c ( tibf, vsurf, vsurf );
1) If the input vector is the zero vector, the error SPICE(ZEROVECTOR) is signaled. 2) If any of the body's axes is zero, the error SPICE(BADAXISLENGTH) is signaled.
C.H. Acton (JPL) N.J. Bachman (JPL) W.L. Taber (JPL)
-CSPICE Version 1.4.3, 24-OCT-2005 (NJB) Header update: reference to bodvar_c was replaced with references to bodvrd_c and bodvcd_c. -CSPICE Version 1.4.2, 27-JUL-2003 (NJB) (CHA) Various header corrections were made. -CSPICE Version 1.4.1, 28-NOV-2002 (NJB) Made miscellaneous updates to header comments. -CSPICE Version 1.4.0, 27-AUG-1999 (NJB) Now uses local "found" flag of type logical. -CSPICE Version 1.3.0, 22-OCT-1998 (NJB) Made input vectors const. -CSPICE Version 1.2.0, 08-FEB-1998 (NJB) Removed local variables used for temporary capture of outputs. -CSPICE Version 1.0.0, 25-OCT-1997 (NJB) Based on SPICELIB Version 1.1.0, 07-AUG-1996 (WLT)
line of sight intercept with body point of intersection between ray and ellipsoid surface point of intersection of ray and ellipsoid