CSPICE_GFILUM determines the time intervals over which a specified
constraint on the observed phase, solar incidence, or emission angle
at a specified target body surface point is met.
All parameters described here are declared in the header file
SpiceGF.h. See that file for parameter values.
is the convergence tolerance used for finding endpoints of
the intervals comprising the result window.
SPICE_GF_CNVTOL is used to determine when binary searches
for roots should terminate: when a root is bracketed
within an interval of length SPICE_GF_CNVTOL, the root is
considered to have been found.
The accuracy, as opposed to precision, of roots found
by this routine depends on the accuracy of the input
data. In most cases, the accuracy of solutions will be
inferior to their precision.
method name specifying the computation method to use. Parameters
include, but are not limited to, the shape model
used to represent the surface of the target body.
[1,c1] = size(method); char = class(method)
[1,1] = size(method); cell = class(method)
The only choice currently supported is
'Ellipsoid' The illumination angle
computation uses a triaxial
ellipsoid to model the surface
of the target body. The
ellipsoid's radii must be
available in the kernel pool.
Neither case nor white space are significant in
'method'. For example, the string ' eLLipsoid ' is
angtyp name specifying the illumination angle for which a search
is to be performed.
[1,c2] = size(angtyp); char = class(angtyp)
[1,1] = size(angtyp); cell = class(angtyp)
The possible values of 'angtyp' are:
See the Particulars section below for a detailed
description of these angles.
Neither case nor white space are significant in
'angtyp'. For example, the string ' Solar incidence ' is
target name of the target body. The point at which the
illumination angles are defined is located on the
surface of this body.
[1,c3] = size(target); char = class(target)
[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.
illmn name of the illumination source. This source
may be any ephemeris object. Case, blanks, and
numeric values are treated in the same way as for the
[1,c4] = size(illmn); char = class(illmn)
[1,1] = size(illmn); cell = class(illmn)
fixref name of the body-fixed, body-centered
reference frame associated with the target body. The
input surface point 'spoint' is expressed relative to
this reference frame, and this frame is used to
define the orientation of the target body as a
function of time.
[1,c5] = size(fixref); char = class(fixref)
[1,1] = size(fixref); cell = class(fixref)
The string 'fixref' is case-insensitive, and leading
and trailing blanks in 'fixref' are not significant.
abcorr describes the aberration corrections to apply to the state
evaluations to account for one-way light time and stellar
Any 'reception' correction accepted by spkezr_c can be
used here. See the header of spkezr_c for a detailed
description of the aberration correction options.
[1,c6] = size(abcorr); char = class(abcorr)
[1,1] = size(abcorr); cell = class(abcorr)
For convenience, the options are listed below:
'NONE' Apply no correction.
'LT' 'Reception' case: correct for
one-way light time using a Newtonian
'LT+S' 'Reception' case: correct for
one-way light time and stellar
aberration using a Newtonian
'CN' 'Reception' case: converged
Newtonian light time correction.
'CN+S' 'Reception' case: converged
Newtonian light time and stellar
Case and blanks are not significant in the string
obsrvr name of the observing body. Optionally, you
may supply the ID code of the object as an integer
string. For example, both 'EARTH' and '399' are
legitimate strings to supply to indicate that the
observer is Earth.
[1,c7] = size(obsrvr); char = class(obsrvr)
[1,1] = size(obsrvr); cell = class(obsrvr)
spoint a surface point on the target body, expressed in
Cartesian coordinates, relative to the body-fixed
target frame designated by 'fixref'.
[3,1] = size(spoint); double = class(spoint)
'spoint' need not be visible from the observer's
location in order for the constraint specified by
'relate' and 'refval' (see descriptions below) to be
The components of 'spoint' have units of km.
relate describes the constraint relational operator on a specified
illumination angle. The result window found by this routine
indicates the time intervals where the constraint is
[1,c8] = size(relate); char = class(relate)
[1,1] = size(relate); cell = class(relate)
Supported values of 'relate' and corresponding meanings
are shown below:
'>' The angle is greater than the reference
'=' The angle is equal to the reference
'<' The angle is less than the reference
'ABSMAX' The angle is at an absolute maximum.
'ABSMIN' The angle is at an absolute minimum.
'LOCMAX' The angle is at a local maximum.
'LOCMIN' The angle is at a local minimum.
The caller may indicate that the region of interest is
the set of time intervals where the angle is within a
specified separation from an absolute extremum. The
argument 'adjust' (described below) is used to specify
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 is not significant in the string 'relate'.
refval reference value used together with the argument
'relate' to define an equality or inequality to be
satisfied by the specified illumination angle. See the
discussion of 'relate' above for further information.
[1,1] = size(refval); double = class(refval)
The units of 'refval' are radians.
adjust parameter used to modify searches for absolute
extrema: when 'relate' is set to 'ABSMAX' or 'ABSMIN'
and 'adjust' is set to a positive value, gfilum_c will
find times when the observer-target distance is within
'adjust' km of the specified extreme value.
[1,1] = size(adjust); double = class(adjust)
If 'adjust' is non-zero and a search for an absolute
minimum 'min' is performed, the result window contains
time intervals when the observer-target distance has
values between 'min' and min+adjust.
If the search is for an absolute maximum 'max', the
corresponding range is from max-adjust to 'max'.
'adjust' is not used for searches for local extrema,
equality or inequality conditions.
step 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 specified
illumination angle is monotone increasing or
decreasing. However, 'step' must not be *too* short, or
the search will take an unreasonable amount of time.
[1,1] = size(step); double = class(step)
The choice of 'step' affects the completeness but not
the precision of solutions found by this routine; the
precision is controlled by the convergence tolerance.
See the discussion of the parameter SPICE_GF_CNVTOL for
'step' has units of seconds.
nintvls is a parameter specifying the number of intervals that
can be accommodated by each of the dynamically allocated
workspace windows used internally by this routine.
[1,1] = size(nintvls); int32 = class(nintvls)
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
However, since excessively large arrays can prevent
applications from compiling, linking, or running
properly, sometimes 'nintvls' must be set according to
the actual workspace requirement. A rule of thumb for
the number of intervals needed is
nintvls = 2*n + ( m / step )
n is the number of intervals in the confinement
m is the measure of the confinement window, in
units of seconds
step is the search step size in seconds
cnfine 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
[2r,1] = size(cnfine); double = class(cnfine)
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.
result = cspice_gfilum( method, angtyp, target, illmn, ...
fixref, abcorr, obsrvr, spoint, ...
relate, refval, adjust, ...
step, nintvls, cnfine )
result the SPICE window of intervals, contained within the
confinement window 'cnfine', on which the specified
constraint is satisfied.
[2s,1] = size(result); double = class(result)
If the search is for local extrema, or for absolute
extrema with adjust set to zero, then normally each
interval of result will be a singleton: the left and
right endpoints of each interval will be identical.
If no times within the confinement window satisfy the
constraint, 'result' will return with cardinality zero.
Any numerical results shown for this example may differ between
platforms as the results depend on the SPICE kernels used as input
and the machine specific arithmetic implementation.
Use the meta-kernel shown below to load the required SPICE
File name: gfilum.tm
This is the meta-kernel file for the example problem for
the subroutine gfilum_c. These kernel files can be found on
the NAIF website.
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
pck00010.tpc Planet orientation
spk_psp_110101-130101_081216_3pm.bsp MRO predict SPK
KERNELS_TO_LOAD = ( 'de421.bsp',
End of meta-kernel
Determine time intervals over which the planned Mars Science
Laboratory (MSL) Gale Crater landing site satisfies certain
constraints on its illumination and visibility as seen from
the Mars Reconnaissance Orbiter (MRO) spacecraft. The
observation period will range from slightly before the planned
landing time to about 10 days later.
In this case we require the emission angle to be less than
30 degrees and the solar incidence angle to be less than
% Output time format:
TIMFMT = 'YYYY MON DD HR:MN:SC.###### TDB::TDB';
% Meta-kernel name:
META = 'gfilum.tm';
% Maximum number of intervals in the windows
% used in this program:
MAXIVL = 1000;
% Local variables
r2d = cspice_dpr();
% Initial values
% Mars planetodetic coordinates of landing site.
% Angular units are degrees; distance units are km.
gclat = -4.543182;
gclon = 137.420000;
gcalt = -4.876405;
% Load kernels:
cspice_furnsh( META );
% Convert the landing site location from planetodetic
% to Cartesian coordinates for use with GFILUM.
radii = cspice_bodvrd( 'MARS', 'RADII', 3 );
re = radii(1);
rp = radii(3);
f = ( re - rp ) / re;
gcpos = cspice_georec( gclon * cspice_rpd(), ...
gclat * cspice_rpd(), ...
gcalt, re, f);
% Set the search interval:
utcbeg = '2012 AUG 5 00:00:00 UTC';
et0 = cspice_str2et( utcbeg );
utcend = '2012 SEP 15 00:00:00 UTC';
et1 = cspice_str2et( utcend );
cnfine = cspice_wninsd( et0, et1 );
% Set observer, target, aberration correction, and the
% Mars body-fixed, body-centered reference frame. The
% lighting source is the sun.
% Aberration corrections are set for remote observations.
illmn = 'sun';
obsrvr = 'mro';
target = 'mars';
abcorr = 'cn+s';
fixref = 'iau_mars';
% Initialize the adjustment value for absolute
% extremum searches. We're not performing
% such searches in this example, but this input
% to GFILUM must still be set.
adjust = 0.0;
% The computation uses an ellipsoidal model for the
% target body shape.
method = 'Ellipsoid';
% Set the reference value to use for the solar
% incidence angle search.
refval = 45.0 * cspice_rpd();
% Since the period of the solar incidence angle
% is about one Martian day, we can safely use 6 hours
% as the search step.
step = 21600.0;
% Search over the confinement window for times
% when the solar incidence angle is less than
% the reference value.
[wnsolr] = cspice_gfilum( method, 'SOLAR INCIDENCE', target, ...
illmn, fixref, abcorr, ...
obsrvr, gcpos, '<', ...
refval, adjust, step, ...
MAXIVL, cnfine );
% With the search on the incidence angle complete, perform
% a search on the emission angle.
% Set the reference value for the emission angle search.
refval = 80.0 * cspice_rpd();
% We'll use 15 minutes as the search step. This step
% is small enough to be suitable for Mars orbiters.
% Units are seconds.
step = 900.0;
% Search over the previous result window for times when the
% emission angle is less than the reference value.
[result] = cspice_gfilum( method, 'EMISSION', target, illmn, ...
fixref, abcorr, obsrvr, gcpos, ...
'<', refval, adjust, step, ...
MAXIVL, wnsolr );
% Display the result window. Show the solar incidence
% and emission angles at the window's interval
if ( cspice_wncard( result ) == 0 )
disp( ' Window is empty: condition is not met.' )
fprintf( ' ' )
fprintf( ' Solar Incidence Emission\n' )
fprintf( ' ' )
fprintf( ' (deg) (deg)\n\n' )
for i=1:cspice_wncard( result )
[start, finish] = cspice_wnfetd( result, i );
% Compute the angles of interest at the boundary
timstr = cspice_timout( start, TIMFMT );
[trgepc, srfvec, phase, solar, emissn] = ...
cspice_ilumin( method, target, ...
start, fixref, ...
abcorr, obsrvr, ...
fprintf ( ' Start: %s %14.9f %14.9f\n', timstr, ...
timstr = cspice_timout( finish, TIMFMT);
[trgepc, srfvec, phase, solar, emissn] = ...
cspice_ilumin( method, target, ...
finish, fixref, ...
abcorr, obsrvr, ...
fprintf ( ' Start: %s %14.9f %14.9f\n\n', timstr,...
% It's always good form to unload kernels after use,
% particularly in MATLAB due to data persistence.
Solar Incidence Emission
Start: 2012 AUG 12 08:20:03.526171 TDB 43.162554493 80.000000005
Start: 2012 AUG 12 08:24:01.612468 TDB 44.061827678 80.000000003
Start: 2012 AUG 17 11:45:09.843860 TDB 44.655209578 79.999999988
Start: 2012 AUG 17 11:46:39.910178 TDB 45.000000000 75.190270778
Start: 2012 AUG 23 15:32:01.989001 TDB 42.039781850 80.000000002
Start: 2012 AUG 23 15:33:58.603546 TDB 42.488410630 80.000000002
Start: 2012 AUG 28 18:56:36.440913 TDB 43.450078325 80.000000007
Start: 2012 AUG 28 19:01:25.343034 TDB 44.575503232 79.999999990
Start: 2012 SEP 09 02:08:12.664420 TDB 42.294339879 80.000000007
Start: 2012 SEP 09 02:11:45.039261 TDB 43.133576379 80.000000004
Start: 2012 SEP 14 05:33:12.767223 TDB 43.878824441 80.000000018
Start: 2012 SEP 14 05:37:54.330789 TDB 45.000000001 77.289478337
This routine determines a set of one or more time intervals
within the confinement window when the specified illumination
angle satisfies a caller-specified constraint. The resulting set
of intervals is returned as a SPICE window.
The term 'illumination angles' refers to the following set of
phase angle Angle between the vectors from the
surface point to the observer and
from the surface point to the
incidence angle Angle between the surface normal at
the specified surface point and the
vector from the surface point to the
emission angle Angle between the surface normal at
the specified surface point and the
vector from the surface point to the
The diagram below illustrates the geometric relationships
defining these angles. The labels for the incidence, emission,
and phase angles are 'inc.', 'e.', and 'phase'.
surface normal vector
|\ /| illumination
\ phase / source vector
\ . . /
\ ___ /
. \/ \/
. / \ /
. | e. \ /
* <--------------- * surface point on
viewing vector target body
location to viewing
Note that if the target-observer vector, the target normal vector
at the surface point, and the target-illumination source vector
are coplanar, then phase is the sum of the incidence and emission
angles. This rarely occurs; usually
phase angle < incidence angle + emission angle
All of the above angles can be computed using light time
corrections, light time and stellar aberration corrections, or no
aberration corrections. In order to describe apparent geometry as
observed by a remote sensing instrument, both light time and
stellar aberration corrections should be used.
The way aberration corrections are applied by this routine
is described below.
Light time corrections
Observer-target surface point vector
Let ET be the epoch at which an observation or remote
sensing measurement is made, and let ET - LT ('LT' stands
for 'light time') be the epoch at which the photons
received at ET were emitted from the surface point 'spoint'.
Note that the light time between the surface point and
observer will generally differ from the light time between
the target body's center and the observer.
Target body's orientation
Using the definitions of ET and LT above, the target body's
orientation at ET - LT is used. The surface normal is
dependent on the target body's orientation, so the body's
orientation model must be evaluated for the correct epoch.
Target body -- illumination source vector
The surface features on the target body near 'spoint' will
appear in a measurement made at ET as they were at ET-LT.
In particular, lighting on the target body is dependent on
the apparent location of the illumination source as seen
from the target body at ET-LT. So, a second light time
correction is used to compute the position of the
illumination source relative to the surface point.
Stellar aberration corrections
Stellar aberration corrections are applied only if
light time corrections are applied as well.
Observer-target surface point body vector
When stellar aberration correction is performed, the
observer-to-surface point direction vector, which we'll
call SRFVEC, is adjusted so as to point to the apparent
position of 'spoint': considering 'spoint' to be an ephemeris
object, SRFVEC points from the observer's position at ET to
the light time and stellar aberration
corrected position of 'spoint'.
Target body-illumination source vector
The target body-illumination source vector is the apparent
position of the illumination source, corrected for light
time and stellar aberration, as seen from the surface point
'spoint' at time ET-LT.
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 specified
illumination angle is monotone increasing and monotone decreasing.
Each of these time periods is represented by a SPICE window.
Having found these windows, all of the illumination angle'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.
The monotone windows (described above) are found via 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 the illumination 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 range rate is zero can be
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 illumination angle 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 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.
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 illumination angle 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 convergence tolerance used by this
routine is set via the parameter SPICE_GF_CNVTOL.
The value of SPICE_GF_CNVTOL is set to a 'tight' value so that the
tolerance doesn't become the limiting factor in the accuracy of
solutions found by this routine. In general the accuracy of input
data will be the limiting factor.
The user may change the convergence tolerance from the default
SPICE_GF_CNVTOL value by calling the routine cspice_gfstol, e.g.
cspice_gfstol( tolerance value in seconds )
Call cspice_gfstol prior to calling this routine. All subsequent
searches will use the updated tolerance value.
Setting the tolerance tighter than SPICE_GF_CNVTOL is unlikely to be
useful, since the results are unlikely to be more accurate.
Making the tolerance looser will speed up searches somewhat,
since a few convergence steps will be omitted. However, in most
cases, the step size is likely to have a much greater affect on
processing time than would the convergence tolerance.
The Confinement Window
The simplest use of the confinement window is to specify a time
interval within which a solution is sought. However, the
confinement window can, in some cases, be used to make searches
more efficient. Sometimes it's possible to do an efficient search
to reduce the size of the time period over which a relatively
slow search of interest must be performed.
For important details concerning this module's function, please refer to
the CSPICE routine gfilum_c.
-Mice Version 1.0.1, 11-NOV-2014, EDW (JPL)
Edited I/O section to conform to NAIF standard for Mice documentation.
-Mice Version 1.0.0, 07-NOV-2013, EDW (JPL)
solve for illumination_angle constraints
solve for phase_angle constraints
solve for solar_incidence_angle constraints
solve for emission_angle constraints
search using illumination_angle constraints