Table of contents
GFRFOV ( GF, is ray in FOV? )
SUBROUTINE GFRFOV ( INST, RAYDIR, RFRAME, ABCORR,
. OBSRVR, STEP, CNFINE, RESULT )
Determine time intervals when a specified ray intersects the
space bounded by the field-of-view (FOV) of a specified
PARAMETER ( LBCELL = -5 )
DOUBLE PRECISION RAYDIR ( 3 )
DOUBLE PRECISION STEP
DOUBLE PRECISION CNFINE ( LBCELL : * )
DOUBLE PRECISION RESULT ( LBCELL : * )
VARIABLE I/O DESCRIPTION
-------- --- --------------------------------------------------
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
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
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
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,
'XS' Stellar aberration correction,
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
MARGIN is currently set to 1.D-12.
See INCLUDE file gf.inc 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
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.
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.
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
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: gfrfov_ex1.tm
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
041014R_SCPSE_01066_04199.bsp CASSINI, planetary and
cas_v40.tf Cassini FK
04161_04164ra.bc Cassini bus CK
cas00071.tsc Cassini SCLK kernel
cas_iss_v10.ti Cassini IK
KERNELS_TO_LOAD = ( 'naif0012.tls',
End of meta-kernel
Example code begins here.
C SPICELIB functions
DOUBLE PRECISION J1950
DOUBLE PRECISION J2000
DOUBLE PRECISION JYEAR
DOUBLE PRECISION RPD
C Local parameters
PARAMETER ( META = 'gfrfov_ex1.tm' )
PARAMETER ( TIMFMT =
. 'YYYY-MON-DD HR:MN:SC.######::TDB' )
DOUBLE PRECISION AU
PARAMETER ( AU = 149597870.693D0 )
PARAMETER ( LBCELL = -5 )
PARAMETER ( MAXWIN = 10000 )
PARAMETER ( CORLEN = 10 )
PARAMETER ( BDNMLN = 36 )
PARAMETER ( FRNMLN = 32 )
PARAMETER ( TIMLEN = 35 )
PARAMETER ( LNSIZE = 80 )
C Local variables
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 RESULT ( LBCELL : MAXWIN )
DOUBLE PRECISION RSTAR
DOUBLE PRECISION STEPSZ
DOUBLE PRECISION T
C Saved variables
C The confinement and result windows CNFINE and RESULT are
C saved because this practice helps to prevent stack
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.
CALL GFRFOV ( INST, RAYDIR, RFRAME, ABCORR,
. 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) )
LINE( :3) = ' '
LINE(2: ) = TIMSTR(1)
LINE(34:) = TIMSTR(2)
WRITE (*,*) LINE
WRITE (*,*) ' '
When this program was executed on a Mac/Intel/gfortran/64-bit
platform, the output was:
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
SPICELIB Version 1.0.0, 15-APR-2009 (NJB) (LSE) (EDW)