Table of contents
CSPICE_NPELPT finds the nearest point on an ellipse to a specified point,
both in three-dimensional space, and finds the distance between the
ellipse and the point.
Given:
point a point in 3-dimensional space.
help, point
DOUBLE = Array[3]
ellips a SPICE ellipse that represents an ellipse in three-dimensional
space.
help, ellips
STRUCT = CSPICE_ELLIPSE
The structure has the fields:
center: [3-array double]
semiMajor: [3-array double]
semiMinor: [3-array double]
the call:
cspice_npelpt, point, ellips, pnear, dist
returns:
pnear the nearest point on `ellips' to `point'.
help, pnear
DOUBLE = Array[3]
dist the distance between `point' and `pnear'.
help, dist
DOUBLE = Scalar
This is the distance between `point' and the ellipse.
None.
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.
1) Create a SPICE ellipse given its center and its semi-major and
semi-minor axes, and calculate the location on that ellipse
which is closest to a defined point, and the distance between
those points.
Example code begins here.
PRO npelpt_ex1
;;
;; Define a center, semimajor and semiminor axis for
;; an ellipse.
;;
;; Also define an arbitrary point in space.
;;
center = [ 1.d, 2.d, -3.d ]
smajor = [ 3.d, 0.d, 0.d ]
sminor = [ 0.d, 2.d, 0.d ]
point = [-4.d, 2.d, 1.d ]
;;
;; Create an ellipse structure using the center, smajor,
;; and sminor axes.
;;
cspice_cgv2el, center, smajor, sminor, ellips
print, 'Input SPICE ellipse:'
print, FORMAT='(A,3F10.6)', ' Semi-minor axis:', $
ellips.semiMinor
print, FORMAT='(A,3F10.6)', ' Semi-major axis:', $
ellips.semiMajor
print, FORMAT='(A,3F10.6)', ' Center :', $
ellips.center
;;
;; Calculate the location on the ellipse closest to
;; the defined point.
;;
cspice_npelpt, point, ellips, pnear, dist
print, FORMAT='(A,3F10.6)', 'Nearest point :', pnear
print, FORMAT='(A,F10.6)', 'Distance :', dist
END
When this program was executed on a Mac/Intel/IDL8.x/64-bit
platform, the output was:
Input SPICE ellipse:
Semi-minor axis: 0.000000 2.000000 0.000000
Semi-major axis: 3.000000 0.000000 0.000000
Center : 1.000000 2.000000 -3.000000
Nearest point : -2.000000 2.000000 -3.000000
Distance : 4.472136
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 Icy 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.
1) If the input ellipse `ellips' has one or both semi-axis lengths
equal to zero, the error SPICE(DEGENERATECASE) is signaled by
a routine in the call tree of this routine.
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 cspice_nearpt, 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.
5) If any of the input arguments, `point' or `ellips', is
undefined, an error is signaled by the IDL error handling
system.
6) If any of the input arguments, `point' or `ellips', is not of
the expected type, or it does not have the expected dimensions
and size, an error is signaled by the Icy interface.
7) If any of the output arguments, `pnear' or `dist', is not a
named variable, an error is signaled by the Icy interface.
None.
None.
ELLIPSES.REQ
ICY.REQ
None.
J. Diaz del Rio (ODC Space)
E.D. Wright (JPL)
-Icy Version 1.0.2, 27-AUG-2021 (JDR)
Edited the header to comply with NAIF standard. Added example's
problem statement and reformatted example's output.
Added -Parameters, -Exceptions, -Files, -Restrictions,
-Literature_References and -Author_and_Institution sections.
Removed reference to the routine's corresponding CSPICE header from
-Abstract section.
Added arguments' type and size information in the -I/O section.
-Icy Version 1.0.1, 13-JUN-2011 (EDW)
Edits to comply with NAIF standard for Icy headers. -Particulars
section now parallels Mice version.
-Icy Version 1.0.0, 16-JUN-2003 (EDW)
nearest point on ellipse to point
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