Determine the intersection of a line-of-sight vector with the 
   surface of an ellipsoid. 

   None. 

   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.

   None. 

   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[0], r[1], r[2], 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 );

   None. 

    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. 

    None. 

    C.H. Acton      (JPL)
    N.J. Bachman    (JPL)
    W.L. Taber      (JPL) 

    None. 

   -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