Find the nearest point on an ellipse to a specified point, both 
   in three-dimensional space, and find the distance between the 
   ellipse and the point. 

   Copyright (1995), California Institute of Technology. 
   U.S. Government sponsorship acknowledged. 

   ELLIPSES 

   Variable  I/O  Description 
   --------  ---  -------------------------------------------------- 
   point      I   Point whose distance to an ellipse is to be found. 
   ellips     I   A CSPICE ellipse. 
   pnear      O   Nearest point on ellipse to input point. 
   dist       O   Distance of input point to ellipse. 

   ellips         is a CSPICE ellipse that represents an ellipse 
                  in three-dimensional space. 

   point          is a point in 3-dimensional space. 

   pnear          is the nearest point on ellips to point. 

   dist           is the distance between point and pnear.  This is 
                  the distance between point and the ellipse. 

   None. 

   Given an ellipse and a point in 3-dimensional space, if the 
   orthogonal projection of the point onto the plane of the ellipse 
   is on or outside of the ellipse, then there is a unique point on 
   the ellipse closest to the original point.  This routine finds 
   that nearest point on the ellipse.  If the projection falls inside 
   the ellipse, there may be multiple points on the ellipse that are 
   at the minimum distance from the original point.  In this case, 
   one such closest point will be returned. 

   This routine returns a distance, rather than an altitude, in 
   contrast to the CSPICE routine nearpt_c.  Because our ellipse is 
   situated in 3-space and not 2-space, the input point is not 
   `inside' or `outside' the ellipse, so the notion of altitude does 
   not apply to the problem solved by this routine.  In the case of 
   nearpt_c, the input point is on, inside, or outside the ellipsoid, 
   so it makes sense to speak of its altitude. 

   1)  For planetary rings that can be modelled as flat disks with 
       elliptical outer boundaries, the distance of a point in 
       space from a ring's outer boundary can be computed using this 
       routine.  Suppose center, smajor, and sminor are the center, 
       semi-major axis, and semi-minor axis of the ring's boundary. 
       Suppose also that scpos is the position of a spacecraft. 
       scpos, center, smajor, and sminor must all be expressed in 
       the same coordinate system.  We can find the distance from 
       the spacecraft to the ring using the code fragment 

          #include "SpiceUsr.h"
               .
               .
               .
          /.
          Make a CSPICE ellipse representing the ring, 
          then use npelpt_c to find the distance between 
          the spacecraft position and RING. 
          ./
          cgv2el_c ( center, smajor, sminor,  ring ); 
          npelpt_c ( scpos,  ring,   pnear,  &dist );



   2)  The problem of finding the distance of a line from a tri-axial 
       ellipsoid can be reduced to the problem of finding the 
       distance between the same line and an ellipse; this problem in 
       turn can be reduced to the problem of finding the distance 
       between an ellipse and a point.  The routine npedln_c carries 
       out this process and uses npelpt_c to find the ellipse-to-point 
       distance. 

   None. 

   1)  Invalid ellipses will be diagnosed by routines called by 
       this routine. 

   2)  Ellipses having one or both semi-axis lengths equal to zero 
       are turned away at the door; the error SPICE(DEGENERATECASE) 
       is signalled. 

   3)  If the geometric ellipse represented by ellips does not 
       have a unique point nearest to the input point, any point 
       at which the minimum distance is attained may be returned 
       in pnear. 

   None. 

   N.J. Bachman   (JPL) 

   None. 

   -CSPICE Version 1.0.0, 02-SEP-1999 (NJB)

   nearest point on ellipse to point