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Index Page npelpt_c

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Procedure Abstract Required_Reading Keywords Brief_I/O Detailed_Input | Detailed_Output Parameters Exceptions Files Particulars Examples | Restrictions Literature_References Author_and_Institution Version Index_Entries

#### 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

#### Link to routine npelpt_c source file npelpt_c.c

    Fri Dec 31 18:41:10 2021