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Required Reading


   CSPICE_NPELPT calculates the location on an ellipse closest
   to a specified point, both in three-dimensional space,
   and the distance between the ellipse and the point.



      point     a 3-vector defining a location in 3-dimensional space.

                [3,1] = size(point); double = class(point)

      ellipse   a SPICE ellipse.

                [1,1] = size(ellipse); struct = class(ellipse)

                The structure has the fields:

                center:    [3,1] = size(center); double = class(center)
                semiMinor: [3,1] = size(semiMinor); double = class(semiMinor)
                semiMajor: [3,1] = size(semiMajor); double = class(semiMajor)

   the call:

      [ pnear, dist ] = cspice_npelpt( point, ellipse )


      pnear   the 3-vector defining the location on the ellipse nearest
              to 'point'.

              [3,1] = size(point); double = class(point)

      dist    the distance between the calculated point 'pnear' 
              and 'point'.

              dist = || pnear - point ||

              [1,1] = size(dist); double = class(dist)


   Any numerical results shown for this example may differ between
   platforms as the results depend on the SPICE kernels used as input
   and the machine specific arithmetic implementation.


   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 Mice routine cspice_nearpt.  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
   cspice_nearpt, the input point is on, inside, or outside the ellipsoid,
   so it makes sense to speak of its altitude.

Required Reading

   For important details concerning this module's function, please refer to
   the CSPICE routine npelpt_c.



   -Mice Version 1.0.0, 14-NOV-2014, EDW (JPL)


   nearest point on ellipse to point

Wed Apr  5 18:00:33 2017