Index Page inelpl_c

A B C D E F G H I J K L M N O P Q R S T U V W X

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

       void inelpl_c ( ConstSpiceEllipse  * ellips,
                       ConstSpicePlane    * plane,
                       SpiceInt           * nxpts,
                       SpiceDouble          xpt1[3],
                       SpiceDouble          xpt2[3] )

#### Abstract

       Find the intersection of an ellipse and a plane.

#### Required_Reading

       ELLIPSES
       PLANES

#### Keywords

       ELLIPSE
       GEOMETRY
       MATH

#### Brief_I/O

       Variable  I/O  Description
       --------  ---  --------------------------------------------------
       ellips     I   A CSPICE ellipse.
       plane      I   A CSPICE plane.
       nxpts      O   Number of intersection points of plane and ellipse.
       xpt1,
       xpt2       O   Intersection points.

#### Detailed_Input

       ellips         is a CSPICE ellipse. The ellipse is allowed to
                      be degenerate: one or both semi-axes may have
                      zero length.

       plane          is a CSPICE plane.  The intersection of plane
                      and ellipse is sought.

#### Detailed_Output

       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.

       xpt1,
       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
                      undefined.

#### Parameters

       None.

#### Exceptions

       1)  The input plane must be a CSPICE plane: the normal vector must
           be non-zero and the constant must be non-negative.
           If the input plane is invalid, the error SPICE(INVALIDPLANE)
           will be signaled.

       2)  If the input ellipse has non-orthogonal axes, the error
           SPICE(INVALIDELLIPSE) will be 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.

#### Files

       None.

#### Particulars

       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

#### Examples

       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
           enough.

           We assume that all vectors are given in body-fixed
           coordinates.

              #include "SpiceUsr.h"
                  .
                  .
                  .
         /.
         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 CSPICE 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
         intersection points.
         ./
         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 );

#### Restrictions

       None.

#### Literature_References

       None.

#### Author_and_Institution

       N.J. Bachman   (JPL)

#### Version

       -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.

          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.

       -CSPICE Version 1.0.0, 28-AUG-2001 (NJB)

#### Index_Entries

       intersection of ellipse and plane

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

    Wed Apr  5 17:54:37 2017