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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

       inrypl_c ( Intersection of ray and plane )

       void inrypl_c ( ConstSpiceDouble     vertex [3],
                       ConstSpiceDouble     dir    [3],
                       ConstSpicePlane    * plane,
                       SpiceInt           * nxpts,
                       SpiceDouble          xpt    [3] )

#### Abstract

       Find the intersection of a ray and a plane.

#### Required_Reading

       PLANES

#### Keywords

       GEOMETRY

#### Brief_I/O

       VARIABLE  I/O  DESCRIPTION
       --------  ---  --------------------------------------------------
       vertex,
       dir        I   Vertex and direction vector of ray.
       plane      I   A SPICE plane.
       nxpts      O   Number of intersection points of ray and plane.
       xpt        O   Intersection point, if nxpts = 1.

#### Detailed_Input

       vertex,
       dir         are a point and direction vector that define a
                   ray in three-dimensional space.

       plane       is a SPICE plane.

#### Detailed_Output

       nxpts       is the number of points of intersection of the
                   input ray and plane. Values and meanings of
                   nxpts are:

                      0     No intersection.

                      1     One point of intersection. Note that
                            this case may occur when the ray's
                            vertex is in the plane.

                     -1     An infinite number of points of
                            intersection; the ray lies in the plane.

       xpt         is the point of intersection of the input ray
                   and plane, when there is exactly one point of
                   intersection.

                   If the ray lies in the plane, xpt is set equal to
                   vertex.

                   If there is no intersection, xpt is the zero vector.

#### Parameters

       None.

#### Exceptions

       1)  If the ray's direction vector is the zero vector, the error
           SPICE(ZEROVECTOR) is signaled. `nxpts' and `xpt' are not modified.

       2)  If the ray's vertex is further than dpmax_c / 3 from the origin,
           the error SPICE(VECTORTOOBIG) is signaled. `nxpts' and `xpt' are not
           modified.

       3)  If the input plane is further than dpmax_c / 3 from the origin, the
           error SPICE(VECTORTOOBIG) is signaled. `nxpts' and `xpt' are not
           modified.

       4)  The input plane should be created by one of the CSPICE
           routines

              nvc2pl_c
              nvp2pl_c
              psv2pl_c

           Invalid input planes will cause unpredictable results.

       5)  In the interest of good numerical behavior, in the case
           where the ray's vertex is not in the plane, this routine
           considers that an intersection of the ray and plane occurs
           only if the distance between the ray's vertex and the
           intersection point is less than dpmax_c / 3.

           If `vertex' is not in the plane and this condition is not
           met, then `nxpts' is set to 0 and `xpt' is set to the zero
           vector.

#### Files

       None.

#### Particulars

       The intersection of a ray and plane in three-dimensional space
       can be a the empty set, a single point, or the ray itself.

#### Examples

       1)  Find the camera projection of the center of an extended
           body. For simplicity, we assume:

              -- The camera has no distortion;  the image of a point
                 is determined by the intersection of the focal plane
                 and the line determined by the point and the camera's
                 focal point.

              -- The camera's pointing matrix (C-matrix) is available
                 in a C-kernel.

                 /.
                 Load Leapseconds and SCLK kernels to support time
                 conversion.
                 ./

                 furnsh_c ( "leap.ker" );
                 furnsh_c ( "sclk.ker" );

                 /.
                 Load an SPK file containing ephemeris data for
                 observer (a spacecraft, whose NAIF integer code
                 is sc) and target at the UTC epoch of observation.
                 ./
                 furnsh_c ( "spk.bsp" );

                 /.
                 Load a C-kernel containing camera pointing for
                 the UTC epoch of observation.
                 ./
                 furnsh_c ( "ck.bc" ) ;

                 /.
                 Find the ephemeris time (barycentric dynamical time)
                 and encoded spacecraft clock times corresponding to
                 the UTC epoch of observation.
                 ./
                 utc2et_c ( utc, &et          );
                 sce2c_c  ( sc,  et,  &sclkdp );

                 /.
                 Encode the pointing lookup tolerance.
                 ./
                 sctiks_c ( sc, tolch, &toldp );

                 /.
                 Find the observer-target vector at the observation
                 epoch. In this example, we'll use a light-time and stellar
                 aberration corrected state vector.
                 ./

                 spkez_c ( target, et, "J2000", "LT+S", sc, state, &lt );

                 /.
                 Look up camera pointing.
                 ./
                 ckgp_c ( camera, sclkdp, toldp, "J2000", cmat, &clkout,
                          &found                                        );

                 if ( !found )
                 {
                    /.
                    No pointing was available.
                    ./

                    [Handle this case...]

                    return;
                 }

                 /.
                 Negate the spacecraft-to-target body vector and
                 convert it to camera coordinates.
                 ./
                 vminus_c ( state, dir       );
                 mxv_c    ( cmat,  dir,  dir );

                 /.
                 If FL is the camera's focal length, the effective
                 focal point is

                    FL * ( 0, 0, 1 )
                 ./

                 vscl_c ( FL, zvec, focus );

                 /.
                 The camera's focal plane contains the origin in
                 camera coordinates, and the z-vector is orthogonal
                 to the plane. Make a SPICE plane representing
                 the focal plane.
                 ./
                 nvc2pl_c ( zvec, 0., &fplane );

                 /.
                 The image of the target body's center in the focal
                 plane is defined by the intersection with the focal
                 plane of the ray whose vertex is the focal point and
                 whose direction is dir.
                 ./

                 inrypl_c ( focus, dir, fplane, &nxpts, image );

                 if ( nxpts == 1 )
                 {
                    /.
                    The body center does project to the focal plane.
                    Check whether the image is actually in the
                    camera's field of view...
                    ./

                    [Handle this case...]
                 }
                 else
                 {
                    /.
                    The body center does not map to the focal plane.
                    ./

                    [Handle this case...]
                 }

       2)  Find the Saturn ring plane intercept of a spacecraft-mounted
           instrument's boresight vector. We want the find the point
           in the ring plane that will be observed by an instrument
           with a give boresight direction at a specified time. We
           must account for light time and stellar aberration in order
           to find this point. The intercept point will be expressed
           in Saturn body-fixed coordinates.

              -- The ring plane is equatorial.

              -- Light travels in a straight line.

              -- The light time correction for the ring plane intercept
                 can be obtained by performing three light-time
                 correction iterations. If this assumption does not
                 lead to a sufficiently accurate result, additional
                 iterations can be performed.

              -- A Newtonian approximation of stellar aberration
                 suffices.

              -- The boresight vector is given in J2000 coordinates.

              -- The observation epoch is et ephemeris seconds past
                 J2000.

              -- The boresight vector, spacecraft and planetary
                 ephemerides, and ring plane orientation are all known
                 with sufficient accuracy for the application.

              -- All necessary kernels are loaded by the caller of
                 this example routine.

           (A similar technique could be used to obtain low-accuracy
           predictions of radio occultations. In that case, the
           instrument boresight ray's direction vector would be replaced
           by the vector from the observer to the light-time corrected
           radio source position.)

           We omit display of the portion of the code that loads SPICE
           kernels.

              #include "SpiceUsr.h"
              #include "SpiceZfc.h"

              void ring_xpt ( ConstSpiceChar    * sc,
                              SpiceDouble         et,
                              ConstSpiceDouble    borvec[3],
                              SpiceDouble       * sbfxpt,
                              SpiceBoolean      * found    )
              {

                 /.
                 Local constants
                 ./
                 #define SATURN          699

                 /.
                 Local variables
                 ./
                 SpiceBoolean            fnd;

                 SpiceDouble             borv2  [3];
                 SpiceDouble             corvec [3];
                 SpiceDouble             lt;
                 SpiceDouble             satssb [6];
                 SpiceDouble             scpos  [3];
                 SpiceDouble             scssb  [6];
                 SpiceDouble             state  [6];
                 SpiceDouble             stcorr [3];
                 SpiceDouble             tau;
                 SpiceDouble             tipm   [3][3];
                 SpiceDouble             xpt    [3];
                 SpiceDouble             zvec   [3];

                 SpiceInt                i;
                 SpiceInt                nxpts;
                 SpiceInt                scid;

                 SpicePlane              plane;

                 /.
                 First step: account for stellar aberration. Since the
                 instrument pointing is given, we need to find the intercept
                 point such that, when the stellar aberration correction is
                 applied to the vector from the spacecraft to that point,
                 the resulting vector is parallel to borvec. An easy solution
                 is to apply the inverse of the normal stellar aberration
                 correction to borvec, and then solve the intercept problem
                 with this corrected boresight vector.

                 Find the position of the observer relative
                 to the solar system barycenter at et.
                 ./
                 bodn2c_c ( sc, &scid, &fnd );

                 if ( !fnd )
                 {
                    setmsg_c ( "ID code for body # was not found." );
                    errch_c  ( "#",  sc                            );
                    sigerr_c ( "SPICE(NOTRANSLATION"               );
                    return;
                 }

                 spkssb_c ( scid, et, "j2000", scssb );

                 /.
                 We now wish to find the vector corvec that, when corrected for
                 stellar aberration, yields borvec. A good first approximation is
                 obtained by applying the stellar aberration correction for
                 transmission to borvec. Note that the routine called is not
                 a wrapper, so there is no letter 'c' at the end of its name.
                 The prototype for this routine is declared in SpiceZfc.h.
                 ./
                 stlabx_ ( (doublereal *) borvec, scssb+3, corvec );

                 /.
                 The inverse of the stellar aberration correction
                 applicable to corvec should be a very good estimate of
                 the correction we need to apply to borvec. Apply
                 this correction to borvec to obtain an improved estimate
                 of corvec.
                 ./
                 stelab_c  ( corvec, scssb+3,  borv2  );
                 vsub_c    ( borv2,  corvec,   stcorr );
                 vsub_c    ( borvec, stcorr,   corvec );

                 /.
                 Because the ring plane intercept may be quite far from
                 Saturn's center, we cannot assume light time from the intercept
                 to the observer is well approximated by light time from
                 Saturn's center to the observer. We compute the light time
                 explicitly using an iterative approach.

                 We can however use the light time from Saturn's center to
                 the observer to obtain a first estimate of the actual light
                 time.
                 ./
                 spkezr_c ( "SATURN", et, "J2000", "LT", sc, state, &lt );

                 tau = lt;

                 /.
                 Find the ring plane intercept and calculate the
                 light time from it to the spacecraft.
                 Perform three iterations.
                 ./
                 i       =  0;
                 *found  =  SPICETRUE;

                 while (  ( i < 3 ) && ( *found )  )
                 {
                    /.
                    Find the position of Saturn relative
                    to the solar system barycenter at et-tau.
                    ./
                    spkssb_c ( SATURN, et-tau, "J2000", satssb );

                    /.
                    Find the Saturn-to-observer vector defined by these
                    two position vectors.
                    ./
                    vsub_c ( scssb, satssb, scpos );

                    /.
                    Look up Saturn's pole at et-tau; this is the third
                    row of the matrix that transforms J2000
                    coordinates to Saturn body-fixed coordinates.
                    ./
                    pxform_c ( "J2000", "IAU_SATURN", et-tau, tipm );

                    vequ_c ( tipm[2], zvec );

                    /.
                    Make a SPICE plane representing the ring plane.
                    We're treating Saturn's center as the origin, so
                    the plane constant is 0.
                    ./
                    nvc2pl_c ( zvec, 0.0, &plane );

                    /.
                    Find the intersection of the ring plane and the
                    ray having vertex scpos and direction vector
                    corvec.
                    ./
                    inrypl_c ( scpos, corvec, &plane, &nxpts, xpt );

                    /.
                    If the number of intersection points is 1,
                    find the next light time estimate.
                    ./
                    if ( nxpts == 1 )
                    {
                       /.
                       Find the light time (zero-order) from the
                       intercept point to the spacecraft.
                       ./
                       tau  =  vdist_c ( scpos, xpt )  /  clight_c();
                       i++;
                    }
                    else
                    {
                       *found = SPICEFALSE;
                    }
                 }
                 /.
                 At this point, if found is SPICETRUE, we iterated
                 three times, and xpt is our estimate of the
                 position of the ring plane intercept point
                 relative to Saturn in the J2000 frame. This is the
                 point observed by an instrument pointed in direction
                 borvec at et at mounted on the spacecraft sc.

                 If found is SPICEFALSE, the boresight ray does not
                 intersect the ring plane.

                 As a final step, transform xpt to Saturn body-fixed
                 coordinates.
                 ./
                 if ( *found )
                 {
                    mxv_c ( tipm, xpt, sbfxpt );
                 }

              }

#### Restrictions

       None.

#### Literature_References

       None.

#### Author_and_Institution

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

#### Version

       -CSPICE Version 1.0.3, 24-AUG-2021 (JDR)

           Edited the header to comply with NAIF standard.

       -CSPICE Version 1.0.2, 01-FEB-2017 (BVS)

           Typo fix: pnv2pl_c -> nvp2pl_c.

       -CSPICE Version 1.0.1, 12-DEC-2002 (NJB)

           Header fix: ring plane intercept algorithm was corrected.
           Now light time is computed accurately, and stellar aberration
           is accounted for. Example was turned into a complete
           subroutine.

       -CSPICE Version 1.0.0, 26-JUN-1999 (NJB)

#### Index_Entries

       intersection of ray and plane

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

    Fri Dec 31 18:41:08 2021