Procedure

   npelpt_c ( Nearest point on ellipse to point ) 

   void npelpt_c ( ConstSpiceDouble      point  [3],
                   ConstSpiceEllipse   * ellips,
                   SpiceDouble           pnear  [3],
                   SpiceDouble         * dist       )

Abstract

   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.

Required_Reading

   ELLIPSES

Keywords

   CONIC
   ELLIPSE
   GEOMETRY
   MATH

Brief_I/O

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

Detailed_Input

   point       is a point in 3-dimensional space.

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

Detailed_Output

   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.

Parameters

   None.

Exceptions

   1)  If the input ellipse `ellips' has one or both semi-axis lengths
       equal to zero, the error SPICE(DEGENERATECASE) is signaled.

   2)  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'.

   3)  If a ratio of non-zero ellipse radii violates the constraints
       imposed by nearpt_c, an error is signaled by a routine in the
       call tree of this routine.

   4)  The routine does not check for overflow when scaling or
       translating the input point.

Files

   None.

Particulars

   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.

Examples

   1)  For planetary rings that can be modeled 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 SPICE 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.

Restrictions

   None.

Literature_References

   None.

Author_and_Institution

   N.J. Bachman        (JPL)
   J. Diaz del Rio     (ODC Space)

Version

   -CSPICE Version 1.0.1, 24-AUG-2021 (JDR)

       Edited the header to comply with NAIF standard.

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

Index_Entries

   nearest point on ellipse to point