Table of contents
CSPICE_GFPA determines time intervals for which a specified constraint
on the phase angle between an illumination source, a target, and
observer body centers is met.
Given:
target name of the target body.
[1,c1] = size(target); char = class(target)
or
[1,1] = size(target); cell = class(target)
Optionally, you may supply the integer ID code for the object
as an integer string. 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 name of the illuminating body.
[1,c2] = size(illmn); char = class(illmn)
or
[1,1] = size(illmn); cell = class(illmn)
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 describes the aberration corrections to apply to the state
evaluations to account for one-way light time and stellar
aberration.
[1,c3] = size(abcorr); char = class(abcorr)
or
[1,1] = size(abcorr); cell = class(abcorr)
This routine accepts only reception mode aberration
corrections. See the header of cspice_spkezr for a detailed
description of the aberration correction options.
For convenience, the allowed aberration options are
listed below:
'NONE' Apply no correction.
'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 name of the observing body.
[1,c4] = size(obsrvr); char = class(obsrvr)
or
[1,1] = size(obsrvr); cell = class(obsrvr)
Optionally, you may supply the ID code of the object as an
integer string. 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 describes the constraint relational operator on phase angle.
[1,c5] = size(relate); char = class(relate)
or
[1,1] = size(relate); cell = class(relate)
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.
The caller may indicate that the region of interest
is the set of time intervals where the quantity is
within a specified measure of an absolute extremum.
The argument `adjust' (described below) is used to
specify this measure.
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 reference value used together with `relate' argument to define
an equality or inequality to satisfy by the phase angle.
[1,1] = size(refval); double = class(refval)
See the discussion of `relate' above for further information.
The units of `refval' are radians.
adjust value used to modify searches for absolute extrema.
[1,1] = size(adjust); double = class(adjust)
When `relate' is set to 'ABSMAX' or 'ABSMIN' and adjust is
set to a positive value, cspice_gfdist finds times when the
observer-target vector coordinate is within `adjust' radians
of the specified extreme value.
For `relate' set to 'ABSMAX', the result window contains
time intervals when the observer-target vector coordinate 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 time step size to use in the search.
[1,1] = size(step); double = class(step)
`step' must be short enough for a search using this step size
to locate the time intervals where coordinate function of the
observer-target vector 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.
`step' has units of seconds.
nintvls value specifying the number of intervals in the internal
workspace array used by this routine.
[1,1] = size(nintvls); int32 = class(nintvls)
`nintvls' should be at least as large as the number of
intervals within the search region on which the specified
observer-target vector coordinate function is monotone
increasing or decreasing. It does no harm to pick a value
of `nintvls' larger than the minimum required to execute
the specified search, but if chosen too small, the search
will fail.
cnfine a SPICE window that confines the time period over which the
specified search is conducted.
[2m,1] = size(cnfine); double = class(cnfine)
`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.
See the -Examples section below for a code example
that shows how to create a confinement window.
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.
the call:
[result] = cspice_gfpa( target, illmn, abcorr, obsrvr, relate, ...
refval, adjust, step, nintvls, cnfine)
returns:
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.
All parameters described here are declared in the Mice include file
MiceGF.m. See that file for parameter values.
SPICE_GF_CNVTOL
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.
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.
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 = ( 'naif0009.tls'
'de421.bsp'
'pck00009.tpc' )
\begintext
End of meta-kernel
Example code begins here.
function gfpa_ex1()
MAXWIN = 5000;
TIMFMT = 'YYYY-MON-DD HR:MN:SC.###';
relate = { '=', '<', '>', 'LOCMIN', 'ABSMIN', 'LOCMAX', 'ABSMAX' };
%
% Define the location for the phase angle calculation as the
% geometric center of the target.
%
pos = [ 0, 0, 0 ]';
%
% Load kernels.
%
cspice_furnsh( 'gfpa_ex1.tm' );
%
% Store the time bounds of our search interval in
% the 'cnfine' confinement window.
%
et = cspice_str2et( { '2006 DEC 01', '2007 JAN 31'} );
%
% Search using a step size of 1 day (in units of seconds).
% The reference value is 0.57598845 radians. We're not using the
% adjustment feature, so we set 'adjust' to zero.
%
target = 'MOON';
illmn = 'SUN';
abcorr = 'LT+S';
obsrvr = 'EARTH';
refval = 0.57598845;
adjust = 0.;
step = cspice_spd;
nintvls = MAXWIN;
cnfine = cspice_wninsd( et(1), et(2) );
for j=1:numel( relate )
fprintf( 'Relation condition: %s\n', char( relate(j) ) )
%
% Perform the search. The SPICE window 'result' contains
% the set of times when the condition is met.
%
result = cspice_gfpa( target, illmn, abcorr, obsrvr, ...
relate(j), refval, adjust, ...
step, nintvls, cnfine );
%
% Display the results.
%
count = cspice_wncard(result);
if ( isequal( count, 0 ) )
fprintf( 'Result window is empty.\n\n' );
else
for i=1:count
%
% Fetch the endpoints of the Ith interval
% of the result window.
%
[left, right] = cspice_wnfetd( result, i );
phase = cspice_phaseq( [left, right], target, illmn, ...
obsrvr, abcorr );
output = cspice_timout( [left,right], TIMFMT );
fprintf( 'Start time = %s %16.9f\n', output(1,:), ...
phase(1) )
fprintf( 'Stop time = %s %16.9f\n', output(2,:), ...
phase(2) )
end
disp( ' ')
end
end
%
% It's always good form to unload kernels after use,
% particularly in Matlab due to data persistence.
%
cspice_kclear
When this program was executed on a Mac/Intel/Octave6.x/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
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.
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 SPICE_GF_CNVTOL (defined
in MiceGF.m).
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 );
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 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.
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 cspice_wncond.
3) 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.
4) If an error (typically cell overflow) occurs during
window arithmetic, the error is signaled by a routine
in the call tree of this routine.
5) If the relational operator `relate' is not recognized, an
error is signaled by a routine in the call tree of this
routine.
6) If `adjust' is negative, an error is signaled by a routine in
the call tree of this routine.
7) 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.
8) 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.
9) 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.
10) If required ephemerides or other kernel data are not
available, an error is signaled by a routine in the call tree
of this routine.
11) If the aberration correction specifier contains an
unrecognized value, an error is signaled by a routine in the
call tree of this routine.
12) If a transmit mode aberration correction is requested, an
error is signaled by a routine in the call tree of this
routine.
13) If any of the input arguments, `target', `illmn', `abcorr',
`obsrvr', `relate', `refval', `adjust', `step', `nintvls' or
`cnfine', is undefined, an error is signaled by the Matlab
error handling system.
14) If any of the input arguments, `target', `illmn', `abcorr',
`obsrvr', `relate', `refval', `adjust', `step', `nintvls' or
`cnfine', is not of the expected type, or it does not have the
expected dimensions and size, an error is signaled by the Mice
interface.
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
cspice_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.
1) The kernel files to be used by this routine must be loaded
(normally using the Mice routine cspice_furnsh) before this
routine is called.
MICE.REQ
GF.REQ
NAIF_IDS.REQ
SPK.REQ
CK.REQ
TIME.REQ
WINDOWS.REQ
None.
J. Diaz del Rio (ODC Space)
E.D. Wright (JPL)
-Mice Version 1.1.0, 03-NOV-2021 (EDW) (JDR)
Changed the input argument name "illum" to "illmn" for
consistency with other routines.
Updated header to describe use of expanded confinement window.
Edited the header to comply with NAIF standard.
Added -Parameters, -Exceptions, -Files, -Restrictions,
-Literature_References and -Author_and_Institution sections.
Eliminated use of "lasterror" in rethrow.
Removed reference to the function's corresponding CSPICE header from
-Required_Reading section.
-Mice Version 1.0.1, 13-NOV-2014 (EDW)
Edited -I/O section to conform to NAIF standard for Mice
documentation.
-Mice Version 1.0.0, 15-JUL-2014 (EDW)
GF phase angle search
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