| gfpa |
|
Table of contents
Procedure
GFPA ( GF, phase angle search )
SUBROUTINE GFPA ( TARGET, ILLMN, ABCORR, OBSRVR,
. RELATE, REFVAL, ADJUST, STEP,
. CNFINE, MW, NW, WORK,
. RESULT )
Abstract
Determine time intervals for which a specified constraint
on the phase angle between an illumination source, a target,
and observer body centers is met.
Required_Reading
GF
NAIF_IDS
SPK
TIME
WINDOWS
Keywords
EPHEMERIS
EVENT
GEOMETRY
SEARCH
WINDOW
Declarations
IMPLICIT NONE
INCLUDE 'gf.inc'
INCLUDE 'zzholdd.inc'
INTEGER LBCELL
PARAMETER ( LBCELL = -5 )
CHARACTER*(*) TARGET
CHARACTER*(*) ILLMN
CHARACTER*(*) ABCORR
CHARACTER*(*) OBSRVR
CHARACTER*(*) RELATE
DOUBLE PRECISION REFVAL
DOUBLE PRECISION ADJUST
DOUBLE PRECISION STEP
DOUBLE PRECISION CNFINE ( LBCELL : * )
INTEGER MW
INTEGER NW
DOUBLE PRECISION WORK ( LBCELL : MW, NW )
DOUBLE PRECISION RESULT ( LBCELL : * )
Brief_I/O
VARIABLE I/O DESCRIPTION
-------- --- --------------------------------------------------
LBCELL P SPICE Cell lower bound.
CNVTOL P Default convergence tolerance.
TARGET I Name of the target body.
ILLMN I Name of the illuminating body.
ABCORR I Aberration correction flag.
OBSRVR I Name of the observing body.
RELATE I Relational operator.
REFVAL I Reference value.
ADJUST I Adjustment value for absolute extrema searches.
STEP I Step size used for locating extrema and roots.
CNFINE I SPICE window to which the search is confined.
MW I Workspace window size.
NW I The number of workspace windows needed for
the search.
WORK O Array of workspace windows.
RESULT I-O SPICE window containing results.
Detailed_Input
TARGET is the name of a target body. Optionally, you may supply
a string containing the integer ID code for the object.
For example both 'MOON' and '301' are legitimate strings
that indicate the Moon is the target body.
Case and leading or trailing blanks are not significant
in the string TARGET.
ILLMN is the name of the illuminating body. This will normally
be 'SUN' but the algorithm can use any ephemeris object.
Case and leading or trailing blanks are not significant
in the string ILLMN.
ABCORR is the description of the aberration corrections to apply
to the state evaluations to account for one-way light
time and stellar aberration.
This routine accepts only reception mode aberration
corrections. See the header of SPKEZR for a detailed
description of the aberration correction options. For
convenience, the allowed aberration options are listed
below:
'NONE' Apply no correction. Returns the "true"
geometric state.
'LT' "Reception" case: correct for
one-way light time using a Newtonian
formulation.
'LT+S' "Reception" case: correct for
one-way light time and stellar
aberration using a Newtonian
formulation.
'CN' "Reception" case: converged
Newtonian light time correction.
'CN+S' "Reception" case: converged
Newtonian light time and stellar
aberration corrections.
Case and leading or trailing blanks are not significant
in the string ABCORR.
OBSRVR is the name of an observing body. Optionally, you may
supply a string containing the integer ID code for the
object. For example both "MOON" and "301" are legitimate
strings that indicate the Moon is the observer.
Case and leading or trailing blanks are not significant
in the string OBSRVR.
RELATE is a relational operator used to define a constraint on a
specified phase angle. The result window found by this
routine indicates the time intervals where the constraint
is satisfied. Supported values of RELATE and
corresponding meanings are shown below:
'>' The phase angle value is greater than the
reference value REFVAL.
'=' The phase angle value is equal to the
reference value REFVAL.
'<' The phase angle value is less than the
reference value REFVAL.
'ABSMAX' The phase angle value is at an absolute
maximum.
'ABSMIN' The phase angle value is at an absolute
minimum.
'LOCMAX' The phase angle value is at a local
maximum.
'LOCMIN' The phase angle value is at a local
minimum.
RELATE may be used to specify an "adjusted" absolute
extremum constraint: this requires the phase angle to be
within a specified offset relative to an absolute
extremum. The argument ADJUST (described below) is used
to specify this offset.
Local extrema are considered to exist only in the
interiors of the intervals comprising the confinement
window: a local extremum cannot exist at a boundary
point of the confinement window.
Case and leading or trailing blanks are not
significant in the string RELATE.
REFVAL is the double precision reference value used together
with the argument RELATE to define an equality or
inequality to be satisfied by the phase angle. See the
discussion of RELATE above for further information.
The units of REFVAL are radians.
ADJUST is a double precision value used to modify searches for
absolute extrema: when RELATE is set to 'ABSMAX' or
'ABSMIN' and ADJUST is set to a positive value, GFPA
finds times when the phase angle is within ADJUST radians
of the specified extreme value.
For RELATE set to 'ABSMAX', the RESULT window contains
time intervals when the phase angle has
values between ABSMAX - ADJUST and ABSMAX.
For RELATE set to 'ABSMIN', the RESULT window contains
time intervals when the phase angle has
values between ABSMIN and ABSMIN + ADJUST.
ADJUST is not used for searches for local extrema,
equality or inequality conditions.
STEP is the double precision time step size to use in the
search.
STEP must be short enough for a search using this step
size to locate the time intervals where the phase angle
function is monotone increasing or decreasing. 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
details.
STEP has units of TDB seconds.
CNFINE is a double precision 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.
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.
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 using the
SPICELIB routine SSIZED.
In some cases the observer's state may be computed at
times outside of CNFINE by as much as 2 seconds. See
$Particulars for details.
MW is a parameter specifying the length of the SPICE
windows in the workspace array WORK (see description
below) used by this routine.
MW should be set to a number at least twice as large
as the maximum number of intervals required by any
workspace window. In many cases, it's not necessary to
compute an accurate estimate of how many intervals are
needed; rather, the user can pick a size considerably
larger than what's really required.
However, since excessively large arrays can prevent
applications from compiling, linking, or running
properly, sometimes MW must be set according to
the actual workspace requirement. A rule of thumb
for the number of intervals NINTVLS needed is
NINTVLS = 2*N + ( M / STEP )
where
N is the number of intervals in the confinement
window
M is the measure of the confinement window, in
units of seconds
STEP is the search step size in seconds
MW should then be set to
2 * NINTVLS
NW is a parameter specifying the number of SPICE windows
in the workspace array WORK (see description below)
used by this routine. NW should be set to the
parameter NWPA; this parameter is declared in the
include file gf.inc. (The reason this dimension is
an input argument is that this allows run-time
error checking to be performed.)
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 GFPA conducts its search.
Detailed_Output
WORK is an array used to store workspace windows.
This array should be declared by the caller as shown:
INCLUDE 'gf.inc'
...
DOUBLE PRECISION WORK ( LBCELL : MW, NWPA )
where MW is a constant declared by the caller and
NWPA is a constant defined in the SPICELIB INCLUDE
file gf.inc. See the discussion of MW above.
WORK need not be initialized by the caller.
WORK is modified by this routine. The caller should
re-initialize this array before attempting to use it for
any other purpose.
RESULT is the SPICE window of intervals, contained within the
confinement window CNFINE, on which the specified phase
angle constraint is satisfied.
The endpoints of the time intervals comprising RESULT are
interpreted as seconds past J2000 TDB.
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
search criteria, RESULT will be returned with a
cardinality of zero.
Parameters
LBCELL is the integer value defining the lower bound for
SPICE Cell arrays (a SPICE window is a kind of cell).
CNVTOL is the default convergence tolerance used for finding
endpoints of the intervals comprising the result
window. CNVTOL is also used for finding intermediate
results; in particular, CNVTOL is used for finding the
windows on which the phase angle is increasing
or decreasing. 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.
See INCLUDE file gf.inc for declarations and descriptions of
parameters used throughout the GF system.
Exceptions
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
roots.
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. One technique to handle such a situation,
slightly contract RESULT using the window routine WNCOND.
3) If workspace window size, MW, is not at least 2 and an even
value, the error SPICE(INVALIDDIMENSION) is signaled is
signaled.
4) If workspace window count, NW, is not at least NWPA, the error
SPICE(INVALIDDIMENSION) is signaled is signaled.
5) If result window, RESULT, is not at least 2 and an even value,
the error SPICE(INVALIDDIMENSION) is signaled is signaled.
6) If RESULT has insufficient capacity to contain the
number of intervals on which the specified angle condition
is met, an error is signaled by a routine in the call
tree of this routine.
7) If an error (typically cell overflow) occurs during
window arithmetic, the error is signaled by a routine
in the call tree of this routine.
8) If the relational operator RELATE is not recognized, an
error is signaled by a routine in the call tree of this
routine.
9) If ADJUST is negative, an error is signaled by a routine in
the call tree of this routine.
10) If ADJUST has a non-zero value when RELATE has any value other
than 'ABSMIN' or 'ABSMAX', an error is signaled by a routine
in the call tree of this routine.
11) If any of the input body names, TARGET, ILLMN, OBSRVR, do
not map to NAIF ID codes, an error is signaled by a routine
in the call tree of this routine.
12) If the input body names, TARGET, ILLMN, OBSRVR, are not
distinct, an error is signaled by a routine in the call
tree of this routine.
13) If required ephemerides or other kernel data are not
available, an error is signaled by a routine in the call tree
of this routine.
14) If the aberration correction specifier contains an
unrecognized value, an error is signaled by a routine in the
call tree of this routine.
15) If a transmit mode aberration correction is requested, an
error is signaled by a routine in the call tree of this
routine.
Files
Appropriate SPK and PCK kernels must be loaded by the calling
program before this routine is called.
The following data are required:
- SPK data: the calling application must load ephemeris data
for the targets, observer, and any intermediate objects in
a chain connecting the targets and observer that cover the
time period specified by the window CNFINE. If aberration
corrections are used, the states of target and 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 using
FURNSH.
- In some cases the observer's state may be computed at times
outside of CNFINE by as much as 2 seconds; data required to
compute this state must be provided by loaded kernels. See
$Particulars for details.
Kernel data are normally loaded once per program run, NOT every
time this routine is called.
Particulars
ILLMN OBS
ILLMN as seen * /
from TARG at | /
ET - LT. | /
>|..../< phase angle
| /
. | /
. | /
. * TARG as seen from OBS
SEP . TARG at ET
. /
/
*
This routine determines if the caller-specified constraint
condition on the geometric event (phase angle) is satisfied for
any time intervals within the confinement window CNFINE. If one
or more such time intervals exist, those intervals are added
to the RESULT window.
This routine provides a simpler, but less flexible interface
than does the routine GFEVNT for conducting searches for
illuminator-target-observer phase angle value events.
Applications that require support for progress reporting,
interrupt handling, non-default step or refinement functions
should call GFEVNT 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
==================
Regardless of the type of constraint selected by the caller, this
routine starts the search for solutions by determining the time
periods, within the confinement window, over which the
phase angle function is monotone increasing and monotone
decreasing. Each of these time periods is represented by a SPICE
window. Having found these windows, all of the phase angle
function's local extrema within the confinement window are known.
Absolute extrema then can be found very easily.
Within any interval of these "monotone" windows, there will be at
most one solution of any equality constraint. Since the boundary
of the solution set for any inequality constraint is contained in
the union of
- the set of points where an equality constraint is met
- the boundary points of the confinement window
the solutions of both equality and inequality constraints can be
found easily once the monotone windows have been found.
Step Size
=========
The monotone windows (described above) are found using a two-step
search process. 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 sign of the rate of
change of phase angle will be sampled. Starting at
the left endpoint of an interval, samples will be taken at each
step. If a change of sign is found, a root has been bracketed; at
that point, the time at which the time derivative of the
phase angle is zero can be found by a refinement process, for
example, using a binary search.
Note that the optimal choice of step size depends on the lengths
of the intervals over which the phase angle function is monotone:
the step size should be shorter than the shortest of these
intervals (within the confinement window).
The optimal step size is *not* necessarily related to the lengths
of the intervals comprising the result window. For example, if
the shortest monotone interval has length 10 days, and if the
shortest result window interval has length 5 minutes, a step size
of 9.9 days is still adequate to find all of the intervals in the
result window. In situations like this, the technique of using
monotone windows yields a dramatic efficiency improvement over a
state-based search that simply tests at each step whether the
specified constraint is satisfied. The latter type of search can
miss solution intervals if the step size is longer than the
shortest solution interval.
Having some knowledge of the relative geometry of the target,
illumination source, 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 time.
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
=====================
As described above, the root-finding process used by this routine
involves first bracketing roots and then using a search process
to locate them. "Roots" are both times when local extrema are
attained and times when the geometric quantity function is equal
to a reference value. All endpoints of the intervals comprising
the result window are either endpoints of intervals of the
confinement window or roots.
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
in gf.inc).
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.
Certain types of searches require the state of the observer,
relative to the solar system barycenter, to be computed at times
slightly outside the confinement window CNFINE. The time window
that is actually used is the result of "expanding" CNFINE by a
specified amount "T": each time interval of CNFINE is expanded by
shifting the interval's left endpoint to the left and the right
endpoint to the right by T seconds. Any overlapping intervals are
merged. (The input argument CNFINE is not modified.)
The window expansions listed below are additive: if both
conditions apply, the window expansion amount is the sum of the
individual amounts.
- If a search uses an equality constraint, the time window
over which the state of the observer is computed is expanded
by 1 second at both ends of all of the time intervals
comprising the window over which the search is conducted.
- If a search uses stellar aberration corrections, the time
window over which the state of the observer is computed is
expanded as described above.
When light time corrections are used, expansion of the search
window also affects the set of times at which the light time-
corrected state of the target is computed.
In addition to the possible 2 second expansion of the search
window that occurs when both an equality constraint and stellar
aberration corrections are used, round-off error should be taken
into account when the need for data availability is analyzed.
Examples
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) Determine the time windows from December 1, 2006 UTC to
January 31, 2007 UTC for which the sun-moon-earth configuration
phase angle satisfies the relation conditions with respect to a
reference value of .57598845 radians (the phase angle at
January 1, 2007 00:00:00.000 UTC, 33.001707 degrees). Also
determine the time windows corresponding to the local maximum
and minimum phase angles, and the absolute maximum and minimum
phase angles during the search interval. The configuration
defines the Sun as the illuminator, the Moon as the target,
and the Earth as the observer.
Use the meta-kernel shown below to load the required SPICE
kernels.
KPL/MK
File name: gfpa_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
--------- --------
de421.bsp Planetary ephemeris
pck00009.tpc Planet orientation and
radii
naif0009.tls Leapseconds
\begindata
KERNELS_TO_LOAD = ( 'de421.bsp',
'pck00009.tpc',
'naif0009.tls' )
\begintext
End of meta-kernel
Example code begins here.
PROGRAM GFPA_EX1
IMPLICIT NONE
C
C Include GF parameter declarations:
C
INCLUDE 'gf.inc'
C
C SPICELIB functions
C
DOUBLE PRECISION SPD
DOUBLE PRECISION PHASEQ
INTEGER WNCARD
C
C Local parameters
C
INTEGER LBCELL
PARAMETER ( LBCELL = -5 )
C
C Use the parameter MAXWIN for both the result window size
C and the workspace size.
C
INTEGER MAXWIN
PARAMETER ( MAXWIN = 1000 )
C
C Length of strings:
C
INTEGER TIMLEN
PARAMETER ( TIMLEN = 26 )
INTEGER NLOOPS
PARAMETER ( NLOOPS = 7 )
C
C Local variables
C
CHARACTER*(TIMLEN) RELATE (NLOOPS)
CHARACTER*(6) ABCORR
CHARACTER*(6) ILLMN
CHARACTER*(6) OBSRVR
CHARACTER*(6) TARGET
CHARACTER*(TIMLEN) TIMSTR
DOUBLE PRECISION CNFINE ( LBCELL : 2 )
DOUBLE PRECISION RESULT ( LBCELL : MAXWIN )
DOUBLE PRECISION WORK ( LBCELL : MAXWIN, NWPA )
DOUBLE PRECISION ADJUST
DOUBLE PRECISION ET0
DOUBLE PRECISION ET1
DOUBLE PRECISION FINISH
DOUBLE PRECISION PHASE
DOUBLE PRECISION REFVAL
DOUBLE PRECISION START
DOUBLE PRECISION STEP
INTEGER I
INTEGER J
C
C Saved variables
C
C The confinement, workspace and result windows CNFINE,
C WORK and RESULT are saved because this practice helps to
C prevent stack overflow.
C
SAVE CNFINE
SAVE RESULT
SAVE WORK
C
C The relation values for the search.
C
DATA RELATE / '=',
. '<',
. '>',
. 'LOCMIN',
. 'ABSMIN',
. 'LOCMAX',
. 'ABSMAX' /
C
C Load kernels.
C
CALL FURNSH ( 'gfpa_ex1.tm' )
C
C Initialize windows.
C
CALL SSIZED ( MAXWIN, RESULT )
CALL SSIZED ( 2, CNFINE )
C
C Store the time bounds of our search interval in
C the confinement window.
C
CALL STR2ET ( '2006 DEC 01', ET0 )
CALL STR2ET ( '2007 JAN 31', ET1 )
CALL WNINSD ( ET0, ET1, CNFINE )
C
C Search using a step size of 1 day (in units of seconds).
C The reference value is 0.57598845 radians. We're not
C using the adjustment feature, so we set ADJUST to zero.
C
STEP = SPD()
REFVAL = 0.57598845D0
ADJUST = 0.D0
C
C Define the values for target, observer, illuminator, and
C aberration correction.
C
TARGET = 'MOON'
ILLMN = 'SUN'
ABCORR = 'LT+S'
OBSRVR = 'EARTH'
DO J=1, NLOOPS
WRITE(*,*) 'Relation condition: ', RELATE(J)
C
C Perform the search. The SPICE window RESULT contains
C the set of times when the condition is met.
C
CALL GFPA ( TARGET, ILLMN, ABCORR, OBSRVR,
. RELATE(J), REFVAL, ADJUST, STEP,
. CNFINE, MAXWIN, NWPA, WORK,
. RESULT )
C
C Display the results.
C
IF ( WNCARD(RESULT) .EQ. 0 ) THEN
WRITE (*, '(A)') 'Result window is empty.'
ELSE
DO I = 1, WNCARD(RESULT)
C
C Fetch the endpoints of the Ith interval
C of the result window.
C
CALL WNFETD ( RESULT, I, START, FINISH )
PHASE = PHASEQ( START, TARGET, ILLMN, OBSRVR,
. ABCORR )
CALL TIMOUT ( START,
. 'YYYY-MON-DD HR:MN:SC.###',
. TIMSTR )
WRITE (*, '(A,F16.9)') 'Start time = '//TIMSTR,
. PHASE
PHASE = PHASEQ( FINISH, TARGET, ILLMN, OBSRVR,
. ABCORR )
CALL TIMOUT ( FINISH,
. 'YYYY-MON-DD HR:MN:SC.###',
. TIMSTR )
WRITE (*, '(A,F16.9)') 'Stop time = '//TIMSTR,
. PHASE
END DO
END IF
WRITE(*,*) ' '
END DO
END
When this program was executed on a Mac/Intel/gfortran/64-bit
platform, the output was:
Relation condition: =
Start time = 2006-DEC-02 13:31:34.414 0.575988450
Stop time = 2006-DEC-02 13:31:34.414 0.575988450
Start time = 2006-DEC-07 14:07:55.470 0.575988450
Stop time = 2006-DEC-07 14:07:55.470 0.575988450
Start time = 2006-DEC-31 23:59:59.997 0.575988450
Stop time = 2006-DEC-31 23:59:59.997 0.575988450
Start time = 2007-JAN-06 08:16:25.512 0.575988450
Stop time = 2007-JAN-06 08:16:25.512 0.575988450
Start time = 2007-JAN-30 11:41:32.557 0.575988450
Stop time = 2007-JAN-30 11:41:32.557 0.575988450
Relation condition: <
Start time = 2006-DEC-02 13:31:34.414 0.575988450
Stop time = 2006-DEC-07 14:07:55.470 0.575988450
Start time = 2006-DEC-31 23:59:59.997 0.575988450
Stop time = 2007-JAN-06 08:16:25.512 0.575988450
Start time = 2007-JAN-30 11:41:32.557 0.575988450
Stop time = 2007-JAN-31 00:00:00.000 0.468279091
Relation condition: >
Start time = 2006-DEC-01 00:00:00.000 0.940714974
Stop time = 2006-DEC-02 13:31:34.414 0.575988450
Start time = 2006-DEC-07 14:07:55.470 0.575988450
Stop time = 2006-DEC-31 23:59:59.997 0.575988450
Start time = 2007-JAN-06 08:16:25.512 0.575988450
Stop time = 2007-JAN-30 11:41:32.557 0.575988450
Relation condition: LOCMIN
Start time = 2006-DEC-05 00:16:50.317 0.086121423
Stop time = 2006-DEC-05 00:16:50.317 0.086121423
Start time = 2007-JAN-03 14:18:31.977 0.079899769
Stop time = 2007-JAN-03 14:18:31.977 0.079899769
Relation condition: ABSMIN
Start time = 2007-JAN-03 14:18:31.977 0.079899769
Stop time = 2007-JAN-03 14:18:31.977 0.079899769
Relation condition: LOCMAX
Start time = 2006-DEC-20 14:09:10.392 3.055062862
Stop time = 2006-DEC-20 14:09:10.392 3.055062862
Start time = 2007-JAN-19 04:27:54.600 3.074603891
Stop time = 2007-JAN-19 04:27:54.600 3.074603891
Relation condition: ABSMAX
Start time = 2007-JAN-19 04:27:54.600 3.074603891
Stop time = 2007-JAN-19 04:27:54.600 3.074603891
Restrictions
1) The kernel files to be used by this routine must be loaded
(normally using the SPICELIB routine FURNSH) before this
routine is called.
Literature_References
None.
Author_and_Institution
N.J. Bachman (JPL)
J. Diaz del Rio (ODC Space)
E.D. Wright (JPL)
Version
SPICELIB Version 1.0.1, 27-OCT-2021 (JDR) (NJB)
Edited the header to comply with NAIF standard.
Updated description of RELATE, REFVAL, WORK and RESULT
arguments in $Brief_I/O, $Detailed_Input and $Detailed_Output.
Added SAVE statements for CNFINE, WORK and RESULT variables in
code example.
Replaced entry #9 by new entries #9 and #10, and added entry
#14 in $Exceptions.
Updated header to describe use of expanded confinement window.
SPICELIB Version 1.0.0, 15-JUL-2014 (EDW) (NJB)
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Fri Dec 31 18:36:24 2021