Table of contents
inelpl_c ( Intersection of ellipse and plane )
void inelpl_c ( ConstSpiceEllipse * ellips,
ConstSpicePlane * plane,
SpiceInt * nxpts,
SpiceDouble xpt2 )
Find the intersection of an ellipse and a plane.
VARIABLE I/O DESCRIPTION
-------- --- --------------------------------------------------
ellips I A SPICE ellipse.
plane I A SPICE plane.
nxpts O Number of intersection points of plane and ellipse.
xpt2 O Intersection points.
ellips is a SPICE ellipse. The ellipse is allowed to
be degenerate: one or both semi-axes may have
plane is a SPICE plane. The intersection of plane
and ellipse is sought.
nxpts is the number of points of intersection of the
geometric plane and ellipse represented by `plane' and
`ellips'. `nxpts' may take the values 0, 1, 2 or -1.
The value -1 indicates that the ellipse consists of
more than one point lies in the plane, so the number
of intersection points is infinite.
When the ellipse consists of a single point and
lies in the plane, `nxpts' is set to 1.
xpt2 are the points of intersection of the input plane
and ellipse. If there is only one intersection
point, both xpt1 and xpt2 contain that point. If
the number of intersection points is zero or
infinite, the contents of xpt1 and xpt2 are
1) If the input plane is invalid, the error SPICE(INVALIDPLANE)
is signaled. The input plane must be a SPICE plane: the normal
vector must be non-zero and the constant must be non-negative.
2) If the input ellipse has non-orthogonal axes, the error
SPICE(INVALIDELLIPSE) is signaled.
3) The input ellipse is allowed to be a line segment or a point;
these cases are not considered to be errors. If the ellipse
consists of a single point and lies in the plane, the number
of intersection points is set to 1 (rather than -1) and
the output arguments `xpt1' and `xpt2' are assigned the value
of the ellipse's center.
This routine computes the intersection set of a non-degenerate
plane with a possibly degenerate ellipse. The ellipse is allowed
to consist of a line segment or a point.
A plane may intersect an ellipse in 0, 1, 2, or infinitely many
points. For there to be an infinite set of intersection points,
the ellipse must lie in the plane and consist of more than one
1) If we want to find the angle of some ray above the limb of an
ellipsoid, where the angle is measured in a plane containing
the ray and a "down" vector, we can follow the procedure
given below. We assume the ray does not intersect the
ellipsoid. The result we seek is called angle, imaginatively
We assume that all vectors are given in body-fixed
Find the limb of the ellipsoid as seen from the
point observ. Here a, b, and c are the lengths of
the semi-axes of the ellipsoid. The limb is
returned as a SpiceEllipse.
edlimb_c ( a, b, c, observ, &limb );
The ray direction vector is raydir, so the ray is the
set of points
observ + t * raydir
where t is any non-negative real number.
The `down' vector is just -observ. The vectors
observ and raydir are spanning vectors for the plane
we're interested in. We can use psv2pl_c to represent
this plane by a SPICE plane.
psv2pl_c ( observ, observ, raydir, &plane );
Find the intersection of the plane defined by observ
and raydir with the limb.
inelpl_c ( limb, plane, nxpts, xpt1, xpt2 );
We always expect two intersection points, if the vector
down is valid.
if ( nxpts < 2 )
[ do something about the error ]
Form the vectors from observ to the intersection
points. Find the angular separation between the
boresight ray and each vector from observ to the
vsub_c ( xpt1, observ, vec1 );
vsub_c ( xpt2, observ, vec2 );
sep1 = vsep_c ( vec1, raydir );
sep2 = vsep_c ( vec2, raydir );
The angular separation we're after is the minimum of
the two separations we've computed.
angle = mind_c ( 2, sep1, sep2 );
N.J. Bachman (JPL)
J. Diaz del Rio (ODC Space)
-CSPICE Version 2.1.1, 24-AUG-2021 (JDR)
Edited the header to comply with NAIF standard.
Removed non-standard header section "Revisions", moving its
contents to the relevant entry in -Version section.
-CSPICE Version 2.1.0, 07-OCT-2011 (NJB)
Relaxed ellipse semi-axes orthogonality test limit
SEPLIM from 1.D-12 TO 1.D-9 radians. The angular
separation of the axes of the input ellipse must not
differ from pi/2 radians by more than this limit.
-CSPICE Version 2.0.0, 14-JAN-2008 (NJB)
Bug fix: the routine's specification and behavior have been
updated so the routine now returns a meaningful result for the
case of an ellipse consisting of a single point. In this case,
if an intersection is found, the number of intersection points
is set to 1 and both intersection arguments are set equal to
the ellipse's center.
Bug fix: in the degenerate case where the input ellipse is a
line segment of positive length, and this segment intersects
the plane, the number of intersection points is set to 1
rather than 2.
Invalid input planes and ellipses are now diagnosed.
Error handling code has been added to trap errors that had
been erroneously passed off to lower level routines for
-CSPICE Version 1.0.0, 28-AUG-2001 (NJB)
intersection of ellipse and plane