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   CSPICE_GFRFOV determine time intervals when a specified ray intersects the
   space bounded by the field-of-view (FOV) of a specified instrument.




      All parameters described here are declared in the header file
      SpiceGF.h. See that file for parameter values.


               is the convergence tolerance used for finding endpoints of
               the intervals comprising the result window.
               SPICE_GF_CNVTOL is used to determine when binary searches
               for roots should terminate: when a root is bracketed
               within an interval of length SPICE_GF_CNVTOL, the root is
               considered to have been found.

               The accuracy, as opposed to precision, of roots found
               by this routine depends on the accuracy of the input
               data. In most cases, the accuracy of solutions will be
               inferior to their precision.


               is the maximum number of vertices that may be used
               to define the boundary of the specified instrument's
               field of view.


               is a small positive number used to constrain the
               orientation of the boundary vectors of polygonal
               FOVs. Such FOVs must satisfy the following constraints:

                  1) The boundary vectors must be contained within
                  a right circular cone of angular radius less
                  than (pi/2) - SPICE_GF_MARGIN radians; in other
                  words, there must be a vector A such that all
                  boundary vectors have angular separation from
                  A of less than (pi/2)-SPICE_GF_MARGIN radians.

                  2) There must be a pair of boundary vectors U, V
                  such that all other boundary vectors lie in
                  the same half space bounded by the plane
                  containing U and V. Furthermore, all other
                  boundary vectors must have orthogonal
                  projections onto a plane normal to this plane
                  such that the projections have angular
                  separation of at least 2*SPICE_GF_MARGIN radians
                  from the plane spanned by U and V.


      inst     the string naming the instrument, such as a
               spacecraft-mounted framing camera, the field of view
               (FOV) of which is to be used for an target intersection
               search: the direction from the observer to a target
               is represented by a ray, and times when the specified
               ray intersects the region of space bounded by the FOV
               are sought.

               [1,c1] = size(inst); char = class(inst)

               The position of the instrument designated by 'inst' is
               considered to coincide with that of the ephemeris
               object designated by the input argument 'obsrvr' (see
               description below).

               'inst' must have a corresponding NAIF ID and a frame
               defined, as is normally done in a frame kernel. It
               must also have an associated reference frame and a FOV
               shape, boresight and boundary vertices (or reference
               vector and reference angles) defined, as is usually
               done in an instrument kernel.

               See the header of the Mice routine cspice_getfov for a
               description of the required parameters associated with
               an instrument.

      raydir   the ray pointing toward a target. The ray emanates from
               the location of the ephemeris object designated by the
               input argument 'obsrvr' and is expressed relative to the
               reference frame designated by 'rframe' (see descriptions

                [3,1] = size(raydir); double = class(raydir)

      rframe   the string naming the reference frame associated with
               the input ray's direction vector 'raydir'.

               Since light time corrections are not supported for
               rays, the orientation of the frame is always evaluated
               at the epoch associated with the observer, as opposed
               to the epoch associated with the light-time corrected
               position of the frame center.

               [1,c2] = size(rframe); char = class(rframe)

               Case and leading or trailing blanks bracketing a non-blank
               frame name are not significant in the string 'rframe'.

      abcorr   the string indicating the aberration corrections
               to apply when computing the 'raydir' direction.

               [1,c3] = size(abcorr); char = class(abcorr)

               The supported aberration correction options are

                  'NONE'          No correction.
                  'S'             Stellar aberration correction,
                                  reception case.
                  'XS'            Stellar aberration correction,
                                  transmission case.

               For detailed information, see the geometry finder required
               reading, gf.req.

               Case, leading and trailing blanks are not significant
               in the string 'abcorr'.

      obsrvr   the string naming the body from which the target
               represented by 'raydir' is observed. The instrument designated
               by 'inst' is treated as if it were co-located with the observer.

               [1,c4] = size(obsrvr); char = class(obsrvr)

               Optionally, you may supply the ID code of the object as an
               integer string. For example, both 'EARTH' and '399' are
               legitimate strings to supply to indicate the observer
               is Earth.

      step     the step size to use in the search. 'step' must be shorter
               than any interval, within the confinement window, over which
               the specified occultation condition is met. In other words,
               'step' must be shorter than the shortest occultation event
               the user wishes to detect; 'step' must also be shorter than
               the shortest time interval between two occultation events that
               occur within the confinement window (see below). However,
               'step' must not be *too* short, or the search will take
               an unreasonable amount of time.

               [1,1] = size(step); double = class(step)

               The choice of 'step' affects the completeness but not
               the precision of solutions found by this routine; the
               precision is controlled by the convergence tolerance.
               See the discussion of the parameter SPICE_GF_CNVTOL for

               'step' has units of TDB seconds.

      cnfine   the SPICE window that confines the time
               period over which the specified search is conducted.
               'cnfine' may consist of a single interval or a collection
               of intervals.

               [2m,1] = size(cnfine); double = class(cnfine)

               In some cases the confinement window can be used to
               greatly reduce the time period that must be searched
               for the desired solution. See the Particulars section
               below for further discussion.

      nintvls  the maximum number of intervals to return in 'result'.
               Note: this value should equal at least the number of expected
               intervals. Recall two double precision values define
               an interval.

               [1,1] = size(nintvls); int32 = class(nintvls)

   the call:

      result = cspice_gfrfov( inst, raydir, rframe, abcorr, ...
                              obsrvr, step, cnfine, nintvls)


      result   the SPICE window of intervals, contained within the
               confinement window 'cnfine', on which the specified
               constraint is satisfied.

               [2n,1] = size(result); double = class(result)

               If the search is for local extrema, or for absolute
               extrema with adjust set to zero, then normally each
               interval of result will be a singleton: the left and
               right endpoints of each interval will be identical.

               If no times within the confinement window satisfy the
               constraint, 'result' will return with cardinality zero.


   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.

      This example is an extension of the example in the
      header of


      The problem statement for that example is

         Search for times when Saturn's satellite Phoebe is within the
         FOV of the Cassini narrow angle camera (CASSINI_ISS_NAC). To
         simplify the problem, restrict the search to a short time
         period where continuous Cassini bus attitude data are

         Use a step size of 10 seconds to reduce chances of missing
         short visibility events.

      Here we search the same confinement window for times when a
      selected background star is visible. We use the FOV of the
      Cassini ISS wide angle camera (CASSINI_ISS_WAC) to enhance the
      probability of viewing the star.

      The star we'll use has catalog number 6000 in the Hipparcos
      Catalog. The star's J2000 right ascension and declination,
      proper motion, and parallax are taken from that catalog.

      Use the meta-kernel from the cspice_gftfov example:


           File name:

           This meta-kernel is intended to support operation of SPICE
           example programs. The kernels shown here should not be
           assumed to contain adequate or correct versions of data
           required by SPICE-based user applications.

           In order for an application to use this meta-kernel, the
           kernels referenced here must be present in the user's
           current working directory.

           The names and contents of the kernels referenced
           by this meta-kernel are as follows:

              File name                     Contents
              ---------                     --------
              naif0009.tls                  Leapseconds
              cpck05Mar2004.tpc             Satellite orientation and
              981005_PLTEPH-DE405S.bsp      Planetary ephemeris
              020514_SE_SAT105.bsp          Satellite ephemeris
              030201AP_SK_SM546_T45.bsp     Spacecraft ephemeris
                        Cassini FK
              04135_04171pc_psiv2.bc        Cassini bus CK
              cas00084.tsc                  Cassini SCLK kernel
              cas_iss_v09.ti                Cassini IK


              KERNELS_TO_LOAD = ( 'naif0009.tls',
                                  'cas_iss_v09.ti' )

      MAXWIN  =  1000;
      TIMFMT  = 'YYYY-MON-DD HR:MN:SC.###### (TDB) ::TDB ::RND';
      AU      =  149597870.693;

      % Load kernels.
      cspice_furnsh( '' )

      % Store the time bounds of our search interval in
      % the 'cnfine' confinement window.
      et = cspice_str2et( { '2004 JUN 11 06:30:00 TDB', ...
                            '2004 JUN 11 12:00:00 TDB' } );

      cnfine = cspice_wninsd( et(1), et(2) );

      %Initialize inputs for the search.
      inst = 'CASSINI_ISS_WAC';

      % Create a unit direction vector pointing from observer to star.
      % We'll assume the direction is constant during the confinement
      % window, and we'll use 'et[0]' as the epoch at which to compute the
      % direction from the spacecraft to the star.
      % The data below are for the star with catalog number 6000
      % in the Hipparcos catalog. Angular units are degrees; epochs
      % have units of Julian years and have a reference epoch of J1950.
      % The reference frame is J2000.

      parallax_deg = 0.000001056;

      ra_deg_0     = 19.290789927;
      ra_pm        = -0.000000720;
      ra_epoch     = 41.2000;

      dec_deg_0    =  2.015271007;
      dec_pm       =  0.000001814;
      dec_epoch    = 41.1300;

      rframe       = 'J2000';
      nintvls      = MAXWIN;

      % Correct the star's direction for proper motion.
      % The argument 't' represents 'et[0]' as Julian years past J1950.

      t       = et(1)/cspice_jyear + ( cspice_j2000- cspice_j1950 )/365.25;

      dtra    = t - ra_epoch;
      dtdec   = t - dec_epoch;

      ra_deg  = ra_deg_0  + dtra * ra_pm;
      dec_deg = dec_deg_0 + dtra * dec_pm;

      ra      = ra_deg  * cspice_rpd;
      dec     = dec_deg * cspice_rpd;

      starpos = cspice_radrec( 1, ra, dec );

      % Correct star position for parallax applicable at
      % the Cassini orbiter's position. (The parallax effect
      % is negligible in this case; we're simply demonstrating
      % the computation.)
      parallax = parallax_deg * cspice_rpd;

      stardist = AU/tan(parallax);

      % Scale the star's direction vector by its distance from
      % the solar system barycenter. Subtract off the position
      % of the spacecraft relative to the solar system barycenter;
      % the result is the ray's direction vector.
      starpos = stardist * starpos;

      [pos, ltime] = cspice_spkpos( 'cassini', et(1), 'J2000',  ...
                                   'NONE', 'solar system barycenter' );

      raydir = starpos - pos;

      % Correct the star direction for stellar aberration when
      % we conduct the search.
      abcorr = 'S';
      obsrvr = 'CASSINI';
      stepsz = 100;

      result = cspice_gfrfov( inst,   raydir, rframe, abcorr, ...
                              obsrvr, stepsz, cnfine, nintvls );

      % List the beginning and ending times in each interval
      % if result contains data.
      for i=1:numel(result)/2

         [left, right] = cspice_wnfetd( result, i );

         output = cspice_timout( [left,right], TIMFMT );

         if( isequal( left, right) )

            disp( ['Event time: ' output(1,:)] )


            disp( ['From : ' output(1,:)] )
            disp( ['To   : ' output(2,:)] )
            disp( ' ' )



      % It's always good form to unload kernels after use,
      % particularly in Matlab due to data persistence.

   MATLAB outputs:

      From : 2004-JUN-11 06:30:00.000000 (TDB)
      To   : 2004-JUN-11 12:00:00.000000 (TDB)


   This routine determines a set of one or more time intervals when
   the specified ray in contained within the field of view of a
   specified instrument. We'll use the term "visibility event" to
   designate such an appearance. The set of time intervals resulting
   from the search is returned as a SPICE window.

   The Search Process

   The search for visibility events is treated as a search for state
   transitions: times are sought when the state of the ray
   changes from "not visible" to "visible" or vice versa.

   Step Size

   Each interval of the confinement window is searched as follows:
   first, the input step size is used to determine the time
   separation at which the visibility state will be sampled.
   Starting at the left endpoint of an interval, samples will be
   taken at each step. If a state change is detected, a root has
   been bracketed; at that point, the "root"--the time at which the
   state change occurs---is found by a refinement process, for
   example, by a binary search.

   Note that the optimal choice of step size depends on the lengths
   of the intervals over which the visibility state is constant:
   the step size should be shorter than the shortest visibility event
   duration and the shortest period between visibility events, within
   the confinement window.

   Having some knowledge of the relative geometry of the ray and
   observer can be a valuable aid in picking a reasonable step size.
   In general, the user can compensate for lack of such knowledge by
   picking a very short step size; the cost is increased computation

   Note that the step size is not related to the precision with which
   the endpoints of the intervals of the result window are computed.
   That precision level is controlled by the convergence tolerance.

   Convergence Tolerance

   Once a root has been bracketed, a refinement process is used to
   narrow down the time interval within which the root must lie.
   This refinement process terminates when the location of the root
   has been determined to within an error margin called the
   "convergence tolerance." The convergence tolerance used by this
   routine is set by the parameter SPICE_GF_CNVTOL.

   The value of SPICE_GF_CNVTOL is set to a "tight" value so that the
   tolerance doesn't become the limiting factor in the accuracy of
   solutions found by this routine. In general the accuracy of input
   data will be the limiting factor.

   The user may change the convergence tolerance from the default
   SPICE_GF_CNVTOL value by calling the routine cspice_gfstol, e.g.

      cspice_gfstol( tolerance value in seconds )

   Call cspice_gfstol prior to calling this routine. All subsequent
   searches will use the updated tolerance value.

   Setting the tolerance tighter than SPICE_GF_CNVTOL is unlikely to be
   useful, since the results are unlikely to be more accurate.
   Making the tolerance looser will speed up searches somewhat,
   since a few convergence steps will be omitted. However, in most
   cases, the step size is likely to have a much greater affect on
   processing time than would the convergence tolerance.

   The Confinement Window

   The simplest use of the confinement window is to specify a time
   interval within which a solution is sought. However, the
   confinement window can, in some cases, be used to make searches
   more efficient. Sometimes it's possible to do an efficient search
   to reduce the size of the time period over which a relatively
   slow search of interest must be performed.

Required Reading

   For important details concerning this module's function, please refer to
   the CSPICE routine gfrfov_c.



   -Mice Version 1.0.1, 13-NOV-2014, EDW (JPL)

       Edited I/O section to conform to NAIF standard for Mice documentation.

   -Mice Version 1.0.1, 05-NOV-2013, EDW (JPL)

       Corrected minor typos in header.

       Renamed the argument 'size' to 'nintvls'. "size" is a Matlab function
       name and it's seriously dumb to use a function name word as an
       argument name.

       Edited I/O section to conform to NAIF standard for Mice documentation.

       Header updated to describe use of cspice_gfstol.

   -Mice Version 1.0.0, 15-APR-2009, EDW (JPL)


   GF ray in instrument FOV search

Wed Apr  5 18:00:32 2017