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     GFRFOV ( GF, is ray in FOV? )

    .                    OBSRVR, STEP,   CNFINE, RESULT )


     Determine time intervals when a specified ray intersects the
     space bounded by the field-of-view (FOV) of a specified







     INCLUDE               ''
     INCLUDE               ''

     INTEGER               LBCELL
     PARAMETER           ( LBCELL = -5 )

     CHARACTER*(*)         INST
     CHARACTER*(*)         RFRAME
     CHARACTER*(*)         ABCORR
     CHARACTER*(*)         OBSRVR


     --------  ---  --------------------------------------------------
     MARGIN     P   Minimum complement of FOV cone angle.
     LBCELL     P   SPICE Cell lower bound.
     CNVTOL     P   Convergence tolerance.
     MAXVRT     P   Maximum number of FOV boundary vertices.
     ZZGET      P   ZZHOLDD retrieves a stored DP value.
     GF_TOL     P   ZZHOLDD acts on the GF subsystem tolerance.
     INST       I   Name of the instrument.
     RAYDIR     I   Ray's direction vector.
     RFRAME     I   Reference frame of ray's direction vector.
     ABCORR     I   Aberration correction flag.
     OBSRVR     I   Name of the observing body.
     STEP       I   Step size in seconds for finding FOV events.
     CNFINE     I   SPICE window to which the search is restricted.
     RESULT    I-O  SPICE window containing results.


     INST     indicates the name of an 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.

              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 SPICELIB routine GETFOV for a
              description of the required parameters associated with
              an instrument.

     RAYDIR   is the direction vector associated with a ray
              representing 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

     RFRAME   is the name of 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.

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

     ABCORR   indicates the aberration corrections to be applied
              when computing the ray's direction.

              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   is the name of 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.

              Optionally, you may supply the integer NAIF ID code
              for the body as a string.

              Case and leading or trailing blanks are not
              significant in the string OBSRVR.

     STEP     is the step size to be used in the search. STEP must
              be shorter than any interval, within the confinement
              window, over which the specified condition is met. In
              other words, STEP must be shorter than the shortest
              visibility event that the user wishes to detect. STEP
              also must be shorter than the minimum duration
              separating any two visibility events. However, STEP
              must not be *too* short, or the search will take an
              unreasonable amount of time.

              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 CNVTOL for

              STEP has units of seconds.

     CNFINE   is a 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

              The endpoints of the time intervals comprising CNFINE
              are interpreted as seconds past J2000 TDB.

              See the $Examples section below for a code example
              that shows how to create a confinement window.

              CNFINE must be initialized by the caller via the
              SPICELIB routine SSIZED.

     RESULT   is a double precision SPICE window which will contain
              the search results. RESULT must be declared and
              initialized with sufficient size to capture the full
              set of time intervals within the search region on which
              the specified condition is satisfied.

              RESULT must be initialized by the caller via the
              SPICELIB routine SSIZED.

              If RESULT is non-empty on input, its contents will be
              discarded before GFRFOV conducts its search.


     RESULT   is a SPICE window representing the set of time intervals,
              within the confinement period, when the input ray is
              "visible"; that is, when the ray is contained in the
              space bounded by the specified instrument's field of

              The endpoints of the time intervals comprising RESULT are
              interpreted as seconds past J2000 TDB.

              If no times within the confinement window satisfy the
              search criteria, RESULT will be returned with a
              cardinality of zero.


     LBCELL   is the lower bound for SPICE cell arrays.

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

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

     MARGIN   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 than (pi/2) - 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)-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 specific plane normal to
                     this plane (the normal plane contains the angle
                     bisector defined by U and V) such that the
                     projections have angular separation of at least
                     2*MARGIN radians from the plane spanned by U
                     and V.

               MARGIN is currently set to 1.D-12.

     See INCLUDE file for declarations and descriptions of
     parameters used throughout the GF system.


     1)  In order for this routine to produce correct results,
         the step size must be appropriate for the problem at hand.
         Step sizes that are too large may cause this routine to miss
         roots; step sizes that are too small may cause this routine
         to run unacceptably slowly and in some cases, find spurious

         This routine does not diagnose invalid step sizes, except that
         if the step size is non-positive, an error is signaled by a
         routine in the call tree of this routine.

     2)  Due to numerical errors, in particular,

            - Truncation error in time values
            - Finite tolerance value
            - Errors in computed geometric quantities

         it is *normal* for the condition of interest to not always be
         satisfied near the endpoints of the intervals comprising the
         result window.

         The result window may need to be contracted slightly by the
         caller to achieve desired results. The SPICE window routine
         WNCOND can be used to contract the result window.

     3)  If the observer's name cannot be mapped to an ID code, an
         error is signaled by a routine in the call tree of this

     4)  If the aberration correction flag calls for light time
         correction, an error is signaled by a routine in the call tree
         of this routine.

     5)  If the ray's direction vector is zero, an error is signaled by
         a routine in the call tree of this routine.

     6)  If the instrument name INST does not have corresponding NAIF
         ID code, an error is signaled by a routine in the call
         tree of this routine.

     7)  If the FOV parameters of the instrument are not present in
         the kernel pool, an error is signaled by a routine
         in the call tree of this routine.

     8)  If the FOV boundary has more than MAXVRT vertices, an error
         is signaled by a routine in the call tree of this

     9)  If the instrument FOV is polygonal, and this routine cannot
         find a ray R emanating from the FOV vertex such that maximum
         angular separation of R and any FOV boundary vector is within
         the limit (pi/2)-MARGIN radians, an error is signaled
         by a routine in the call tree of this routine. If the FOV
         is any other shape, the same error check will be applied with
         the instrument boresight vector serving the role of R.

     10) If the loaded kernels provide insufficient data to compute a
         requested state vector, an error is signaled by a
         routine in the call tree of this routine.

     11) If an error occurs while reading an SPK or other kernel file,
         the error is signaled by a routine in the call tree
         of this routine.

     12) If the output SPICE window RESULT has size less than 2, the
         error SPICE(WINDOWTOOSMALL) is signaled.

     13) If the output SPICE window RESULT has insufficient capacity
         to contain the number of intervals on which the specified
         visibility condition is met, an error is signaled
         by a routine in the call tree of this routine.


     Appropriate SPICE kernels must be loaded by the calling program
     before this routine is called.

     The following data are required:

     -  SPK data: ephemeris data for the observer for the period
        defined by the confinement window CNFINE must be loaded.
        If aberration corrections are used, the state of the
        observer relative to the solar system barycenter must be
        calculable from the available ephemeris data. Typically
        ephemeris data are made available by loading one or more SPK
        files via FURNSH.

     -  Data defining the reference frame associated with the
        instrument designated by INST must be available in the kernel
        pool. Additionally the name INST must be associated with an
        ID code. Normally these data are  made available by loading
        a frame kernel via FURNSH.

     -  IK data: the kernel pool must contain data such that
        the SPICELIB routine GETFOV may be called to obtain
        parameters for INST. Normally such data are provided by
        an IK via FURNSH.

     The following data may be required:

     -  CK data: if the instrument frame is fixed to a spacecraft,
        at least one CK file will be needed to permit transformation
        of vectors between that frame and the J2000 frame.

     -  SCLK data: if a CK file is needed, an associated SCLK
        kernel is required to enable conversion between encoded SCLK
        (used to time-tag CK data) and barycentric dynamical time

     -  Since the input ray direction may be expressed in any
        frame, FKs, CKs, SCLK kernels, PCKs, and SPKs may be
        required to map the direction to the J2000 frame.

     Kernel data are normally loaded once per program run, NOT every
     time this routine is called.


     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.

     This routine provides a simpler, but less flexible, interface
     than does the SPICELIB routine GFFOVE for conducting searches for
     visibility events. Applications that require support for progress
     reporting, interrupt handling, non-default step or refinement
     functions, or non-default convergence tolerance should call
     GFFOVE rather than this routine.

     Below we discuss in greater detail aspects of this routine's
     solution process that are relevant to correct and efficient use
     of this routine in user applications.

     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, via 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 default convergence tolerance
     used by this routine is set by the parameter CNVTOL (defined

     The value of 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
     CNVTOL value by calling the routine GFSTOL, e.g.

        CALL GFSTOL( tolerance value )

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

     Setting the tolerance tighter than 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 effect
     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. For an example, see
     the program CASCADE in the GF Example Programs chapter of the GF
     Required Reading, gf.req.


     The numerical results shown for this example may differ across
     platforms. The results depend on the SPICE kernels used as
     input, the compiler and supporting libraries, and the machine
     specific arithmetic implementation.

     1) This example is an extension of example #1 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 available.

           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 shown below to load the required SPICE


           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
              -----------------------------   ----------------------
              naif0012.tls                    Leapseconds
              041014R_SCPSE_01066_04199.bsp   CASSINI, planetary and
                                              Saturn satellite
                          Cassini FK
              04161_04164ra.bc                Cassini bus CK
              cas00071.tsc                    Cassini SCLK kernel
              cas_iss_v10.ti                  Cassini IK


              KERNELS_TO_LOAD = ( 'naif0012.tls',
                                  'cas_iss_v10.ti'            )

           End of meta-kernel

        Example code begins here.

              PROGRAM GFRFOV_EX1
              IMPLICIT NONE

        C     SPICELIB functions
              DOUBLE PRECISION      J1950
              DOUBLE PRECISION      J2000
              DOUBLE PRECISION      JYEAR
              DOUBLE PRECISION      RPD

              INTEGER               WNCARD

        C     Local parameters
              CHARACTER*(*)         META
              PARAMETER           ( META   = '' )

              CHARACTER*(*)         TIMFMT
              PARAMETER           ( TIMFMT =
             .      'YYYY-MON-DD HR:MN:SC.######::TDB' )

              DOUBLE PRECISION      AU
              PARAMETER           ( AU     = 149597870.693D0 )

              INTEGER               LBCELL
              PARAMETER           ( LBCELL = -5 )

              INTEGER               MAXWIN
              PARAMETER           ( MAXWIN = 10000 )

              INTEGER               CORLEN
              PARAMETER           ( CORLEN = 10 )

              INTEGER               BDNMLN
              PARAMETER           ( BDNMLN = 36 )

              INTEGER               FRNMLN
              PARAMETER           ( FRNMLN = 32 )

              INTEGER               TIMLEN
              PARAMETER           ( TIMLEN = 35 )

              INTEGER               LNSIZE
              PARAMETER           ( LNSIZE = 80 )

        C     Local variables
              CHARACTER*(CORLEN)    ABCORR
              CHARACTER*(BDNMLN)    INST
              CHARACTER*(LNSIZE)    LINE
              CHARACTER*(BDNMLN)    OBSRVR
              CHARACTER*(FRNMLN)    RFRAME
              CHARACTER*(TIMLEN)    TIMSTR ( 2 )

              DOUBLE PRECISION      CNFINE ( LBCELL : 2 )
              DOUBLE PRECISION      DEC
              DOUBLE PRECISION      DECEPC
              DOUBLE PRECISION      DECPM
              DOUBLE PRECISION      DECDEG
              DOUBLE PRECISION      DECDG0
              DOUBLE PRECISION      DTDEC
              DOUBLE PRECISION      DTRA
              DOUBLE PRECISION      ENDPT  ( 2 )
              DOUBLE PRECISION      ET0
              DOUBLE PRECISION      ET1
              DOUBLE PRECISION      LT
              DOUBLE PRECISION      PARLAX
              DOUBLE PRECISION      PLXDEG
              DOUBLE PRECISION      POS    ( 3 )
              DOUBLE PRECISION      PSTAR  ( 3 )
              DOUBLE PRECISION      RA
              DOUBLE PRECISION      RADEG
              DOUBLE PRECISION      RADEG0
              DOUBLE PRECISION      RAEPC
              DOUBLE PRECISION      RAPM
              DOUBLE PRECISION      RAYDIR ( 3 )
              DOUBLE PRECISION      RSTAR
              DOUBLE PRECISION      STEPSZ
              DOUBLE PRECISION      T

              INTEGER               CATNO
              INTEGER               I
              INTEGER               J
              INTEGER               N

        C     Saved variables
        C     The confinement and result windows CNFINE and RESULT are
        C     saved because this practice helps to prevent stack
        C     overflow.
              SAVE                  CNFINE
              SAVE                  RESULT

        C     Load kernels.
              CALL FURNSH ( META )

        C     Initialize windows.
              CALL SSIZED ( 2,      CNFINE )
              CALL SSIZED ( MAXWIN, RESULT )

        C     Insert search time interval bounds into the
        C     confinement window.
              CALL STR2ET ( '2004 JUN 11 06:30:00 TDB', ET0 )
              CALL STR2ET ( '2004 JUN 11 12:00:00 TDB', ET1 )

              CALL WNINSD ( ET0, ET1, CNFINE )

        C     Initialize inputs for the search.
              INST   = 'CASSINI_ISS_WAC'

        C     Create a unit direction vector pointing from
        c     observer to star. We'll assume the direction
        C     is constant during the confinement window, and
        C     we'll use et0 as the epoch at which to compute the
        C     direction from the spacecraft to the star.
        C     The data below are for the star with catalog
        C     number 6000 in the Hipparcos catalog. Angular
        C     units are degrees; epochs have units of Julian
        C     years and have a reference epoch of J1950.
        C     The reference frame is J2000.
              CATNO  = 6000

              PLXDEG = 0.000001056D0

              RADEG0 = 19.290789927D0
              RAPM   = -0.000000720D0
              RAEPC  = 41.2000D0

              DECDG0 =  2.015271007D0
              DECPM  =  0.000001814D0
              DECEPC = 41.1300D0

              RFRAME = 'J2000'

        C     Correct the star's direction for proper motion.
        C     The argument t represents et0 as Julian years
        C     past J1950.
              T      =      ET0/JYEAR()
             .         +  ( J2000()- J1950() ) / 365.25D0

              DTRA   = T - RAEPC
              DTDEC  = T - DECEPC

              RADEG  = RADEG0  +  DTRA  * RAPM
              DECDEG = DECDG0  +  DTDEC * DECPM

              RA     = RADEG  * RPD()
              DEC    = DECDEG * RPD()

              CALL RADREC ( 1.D0, RA, DEC, PSTAR )

        C     Correct star position for parallax applicable at
        C     the Cassini orbiter's position. (The parallax effect
        C     is negligible in this case; we're simply demonstrating
        C     the computation.)
              PARLAX = PLXDEG * RPD()
              RSTAR  = AU / TAN(PARLAX)

        C     Scale the star's direction vector by its distance from
        C     the solar system barycenter. Subtract off the position
        C     of the spacecraft relative to the solar system
        C     barycenter; the result is the ray's direction vector.
              CALL VSCLIP ( RSTAR, PSTAR )

              CALL SPKPOS ( 'CASSINI', ET0, 'J2000',  'NONE',
             .              'SOLAR SYSTEM BARYCENTER', POS,  LT )

              CALL VSUB   ( PSTAR, POS, RAYDIR )

        C     Correct the star direction for stellar aberration when
        C     we conduct the search.
              ABCORR = 'S'
              OBSRVR = 'CASSINI'
              STEPSZ = 10.D0

              WRITE (*,*) ' '
              WRITE (*,*) 'Instrument:              '//INST
              WRITE (*,*) 'Star''s catalog number:  ', CATNO
              WRITE (*,*) ' '

        C     Perform the search.
             .              OBSRVR, STEPSZ, CNFINE, RESULT )

              N = WNCARD( RESULT )

              IF ( N .EQ. 0 ) THEN

                 WRITE (*,*) 'No FOV intersection found.'


                 WRITE (*, '(A)' ) '  Visibility start time (TDB)'
             .    //               '           Stop time (TDB)'
                 WRITE (*, '(A)' ) '  ---------------------------'
             .    //               '     ---------------------------'

                 DO I = 1, N

                    CALL WNFETD ( RESULT, I, ENDPT(1), ENDPT(2) )

                    DO J = 1, 2
                       CALL TIMOUT ( ENDPT(J), TIMFMT, TIMSTR(J) )
                    END DO

                    LINE( :3) = ' '
                    LINE(2: ) = TIMSTR(1)
                    LINE(34:) = TIMSTR(2)

                    WRITE (*,*) LINE

                 END DO

              END IF

              WRITE (*,*) ' '

        When this program was executed on a Mac/Intel/gfortran/64-bit
        platform, the output was:

         Instrument:              CASSINI_ISS_WAC
         Star's catalog number:          6000

          Visibility start time (TDB)           Stop time (TDB)
          ---------------------------     ---------------------------
          2004-JUN-11 06:30:00.000000     2004-JUN-11 12:00:00.000000

        Note that the star is visible throughout the confinement


     1)  The kernel files to be used by GFRFOV must be loaded (normally
         via the SPICELIB routine FURNSH) before GFRFOV is called.




     N.J. Bachman       (JPL)
     J. Diaz del Rio    (ODC Space)
     L.S. Elson         (JPL)
     E.D. Wright        (JPL)


    SPICELIB Version 1.1.1, 06-AUG-2021 (JDR)

        Edited the header to comply with NAIF standard.

        Modified code examples' output to comply with maximum line
        length of header comments. Updated Example's kernels set to use
        PDS archived data. Added SAVE statements for CNFINE and RESULT
        variables in code example.

        Updated description of RESULT argument in $Brief_I/O,
        $Detailed_Input and $Detailed_Output.

    SPICELIB Version 1.1.0, 28-FEB-2012 (EDW)

        Implemented use of ZZHOLDD to allow user to alter convergence

        Removed the STEP > 0 error check. The GFSSTP call includes
        the check.

    SPICELIB Version 1.0.0, 15-APR-2009 (NJB) (LSE) (EDW)
Fri Dec 31 18:36:25 2021