Find the limb of a triaxial ellipsoid, viewed from a specified 
   point. 

   ELLIPSES 

   Variable  I/O  Description 
   --------  ---  -------------------------------------------------- 
   a          I   Length of ellipsoid semi-axis lying on the x-axis. 
   b          I   Length of ellipsoid semi-axis lying on the y-axis. 
   c          I   Length of ellipsoid semi-axis lying on the z-axis. 
   viewpt     I   Location of viewing point. 
   limb       O   Limb of ellipsoid as seen from viewing point. 

   a, 
   b, 
   c              are the lengths of the semi-axes of a triaxial 
                  ellipsoid.  The ellipsoid is centered at the 
                  origin and oriented so that its axes lie on the 
                  x, y and z axes.  a, b, and c are the lengths of 
                  the semi-axes that point in the x, y, and z 
                  directions respectively. 

   viewpt         is a point from which the ellipsoid is viewed. 
                  viewpt must be outside of the ellipsoid. 

   limb           is a CSPICE ellipse that represents the limb of 
                  the ellipsoid. 

   None. 

   The limb of a body, as seen from a viewing point, is the boundary 
   of the portion of the body's surface that is visible from that 
   viewing point.  In this definition, we consider a surface point 
   to be `visible' if it can be connected to the viewing point by a 
   line segment that doen't pass through the body.  This is a purely 
   geometrical definition that ignores the matter of which portions 
   of the surface are illuminated, or whether the view is obscured by 
   any additional objects. 

   If a body is modelled as a triaxial ellipsoid, the limb is always 
   an ellipse.  The limb is determined by its center, a semi-major 
   axis vector, and a semi-minor axis vector. 

   We note that the problem of finding the limb of a triaxial 
   ellipsoid is mathematically identical to that of finding its 
   terminator, if one makes the simplifying assumption that the 
   terminator is the limb of the body as seen from the vertex of the 
   umbra.  So, this routine can be used to solve this simplified 
   version of the problem of finding the terminator. 

   1)  We'd like to find the apparent limb of Jupiter, corrected for 
       light time and stellar aberration, as seen from a spacecraft's 
       position at time ET. 


          /.
          Find the viewing point in Jupiter-fixed coordinates.  To do 
          this, find the apparent position of Jupiter as seen from the
          spacecraft in Jupiter-fixed coordinates and negate this 
          vector.  In this case we'll use light time and stellar 
          aberration corrections to arrive at the apparent limb. jstat 
          is the Jupiter's state (position and velocity) as seen
          from the spacecraft.  scpos is the spacecraft's
          position relative to Jupiter.
          ./
          spkez_c( jupid, et, "IAU_JUPITER", "LT+S", scid, scstat, &lt);

          vminus_c ( scstat, scpos );

          /.
          Get Jupiter's semi-axis lengths.
          ./
          bodvcd_c ( jupid, "RADII", 3, &n, rad );

          /.
          Find the apparent limb.  limb is a CSPICE ellipse
          representing the limb.
          ./
          edlimb_c ( rad[0], rad[1], rad[2], scpos, &limb );

          /.
          lcentr, smajor, and sminor are the limb's center,
          semi-major axis, and semi-minor axis. 
          ./
          el2cgv_c ( &limb, center, smajor, sminor );

   None. 

   1)  If the length of any semi-axis of the ellipsoid is 
       non-positive, the error DEGENERATECASE is signaled. 
       limb is not modified. 

   2)  If the length of any semi-axis of the ellipsoid is zero after 
       the semi-axis lengths are scaled by the reciprocal of the 
       magnitude of the longest semi-axis and then squared, the error 
       SPICE(DEGENERATECASE) is signaled.  limb is not modified. 

   3)  If the viewing point viewpt is inside the ellipse, the error 
       SPICE(INVALIDPOINT) is signaled.  limb is not modified. 

   4)  If the geometry defined by the input ellipsoid and viewing 
       point is so extreme that the limb cannot be found, the error 
       SPICE(DEGENERATECASE) is signaled. 

   5)  If the shape of the ellipsoid and the viewing geometry are 
       such that the limb is an excessively flat ellipsoid, the 
       limb may be a degenerate ellipse.  You must determine whether 
       this possibility poses a problem for your application. 

   None. 

   N.J. Bachman   (JPL) 

   None. 

   -CSPICE Version 1.0.1, 24-OCT-2005 (NJB)

       Header update: reference to bodvar_c was replaced with
       reference to bodvcd_c.

   -CSPICE Version 1.0.0, 13-JUN-1999 (NJB)

   ellipsoid limb