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Required Reading


   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:

                   'SOLAR INCIDENCE'

                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
                input 'target'.

                [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
                              aberration corrections.

                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
                           value 'refval'.

                    '='      The angle is equal to the reference
                             value 'refval'.

                    '<'      The angle is less than the reference
                             value 'refval'.

                   '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
                this separation.

                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
                really required.

                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.

   the call:

      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:

         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
                                                  and radii
            naif0010.tls                          Leapseconds
            spk_psp_110101-130101_081216_3pm.bsp  MRO predict SPK


         KERNELS_TO_LOAD = ( 'de421.bsp',
                             '_081216_3pm.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
      40 degrees.

      % Output time format:
      TIMFMT = 'YYYY MON DD HR:MN:SC.###### TDB::TDB';

      % Meta-kernel name:
      META = '';

      % 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
      % boundaries.
      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
            % epochs.
            timstr = cspice_timout( start, TIMFMT );
            [trgepc, srfvec, phase, solar, emissn] =                ...
                                     cspice_ilumin( method, target, ...
                                                    start,  fixref, ...
                                                    abcorr, obsrvr, ...
                                                    gcpos );

               fprintf ( '    Start: %s %14.9f %14.9f\n', timstr, ...
                                                       solar*r2d, ...
                                                       emissn*r2d )

            timstr = cspice_timout( finish, TIMFMT);
            [trgepc, srfvec, phase, solar, emissn] =                ...
                                     cspice_ilumin( method, target, ...
                                                    finish, fixref, ...
                                                    abcorr, obsrvr, ...
                                                    gcpos );

               fprintf ( '    Start: %s %14.9f %14.9f\n\n', timstr,...
                                                       solar*r2d,  ...
                                                       emissn*r2d )



      % It's always good form to unload kernels after use,
      % particularly in MATLAB due to data persistence.

   MATLAB outputs:

                                              Solar Incidence   Emission
                                                    (deg)         (deg)

      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
                               illumination source.

      incidence angle          Angle between the surface normal at
                               the specified surface point and the
                               vector from the surface point to the
                               illumination source.

      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'.

                                            illumination source

                  surface normal vector
                            ._                 _.
                            |\                 /|  illumination
                              \    phase      /    source vector
                               \   .    .    /
                               .            .
                                 \   ___   /
                            .     \/     \/
                                  _\ inc./
                           .    /   \   /
                           .   |  e. \ /
       *             <--------------- *  surface point on
    viewing            vector            target body
    location           to viewing
    (observer)         location

   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.

   Step Size

   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.

   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.

Required Reading

   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

Wed Apr  5 18:00:32 2017