Index Page gfpa_c

A B C D E F G H I J K L M N O P Q R S T U V W X

Procedure Abstract Required_Reading Keywords Brief_I/O Detailed_Input | Detailed_Output Parameters Exceptions Files Particulars Examples | Restrictions Literature_References Author_and_Institution Version Index_Entries

#### Procedure

       void gfpa_c ( ConstSpiceChar     * target,
                     ConstSpiceChar     * illmn,
                     ConstSpiceChar     * abcorr,
                     ConstSpiceChar     * obsrvr,
                     ConstSpiceChar     * relate,
                     SpiceDouble          refval,
                     SpiceDouble          adjust,
                     SpiceDouble          step,
                     SpiceInt             nintvls,
                     SpiceCell          * cnfine,
                     SpiceCell          * 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

       EVENT
       GEOMETRY
       EPHEMERIS
       SEARCH
       WINDOW

#### Brief_I/O

       Variable         I/O  Description
       ---------------  ---  ------------------------------------------------
       SPICE_GF_CNVTOL   P   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.
       nintvls           I   Workspace window interval count.
       cnfine           I-O  SPICE window to which the search is confined.
       result            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       the string 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      indicates the aberration corrections to be applied to
                   the observer-target position vector to account for
                   one-way light time and stellar aberration.

                   Any aberration correction accepted by the SPICE
                   routine spkezr_c is accepted here. See the header
                   of spkezr_c for a detailed description of the
                   aberration correction options. For convenience,
                   the allowed aberation 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.

                   Note that this routine accepts only reception mode
                   aberration corrections.

                   Case and leading or trailing blanks are not significant
                   in the string `abcorr'.

       obsrvr      is the name of the 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
                   the 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 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 parameter used to modify searches for absolute
                   extrema: when `relate' is set to "ABSMAX" or "ABSMIN"
                   and `adjust' is set to a positive value, gfpa_c will
                   find times when the phase angle is within
                   `adjust' radians of the specified extreme value.

                   If `adjust' is non-zero and a search for an absolute
                   minimum `min' is performed, the result window contains
                   time intervals when the phase angle 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        is the step size to be used in the search. `step' must
                   be shorter than any maximal time interval on which the
                   specified phase angle function is monotone increasing or
                   decreasing. That is, if the confinement window is
                   partitioned into alternating intervals on which the
                   phase angle function is either monotone increasing or
                   decreasing, `step' must be shorter than any of these
                   intervals.

                   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 SPICE_GF_CNVTOL for
                   details.

                   STEP has units of TDB 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.

                   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 )

                   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

       cnfine      is a SPICE window that confines the time period over
                   which the specified search is conducted. `cnfine' may
                   consist of a single interval or a collection of
                   intervals.

                   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.

#### Detailed_Output

       cnfine      is the input confinement window, updated if necessary so
                   the control area of its data array indicates the
                   window's size and cardinality. The window data are
                   unchanged.

       result      is the 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 `result' is non-empty on input, its contents will be
                   discarded before gfpa_c conducts its search.

#### Parameters

       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.

                   SPICE_GF_CNVTOL is declared in the header file
                   SpiceGF.h.

#### 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.

           The result window may need to be contracted slightly by the
           caller to achieve desired results. The SPICE window routine
           wncond_c can be used to contract the result window.

       3)  If an error (typically cell overflow) occurs while performing
           window arithmetic, the error will be diagnosed by a routine
           in the call tree of this routine.

       4)  If the relational operator `relate' is not recognized, an
           error is signaled by a routine in the call tree of this
           routine.

       5)  If the aberration correction specifier contains an
           unrecognized value, 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 either of the input body names do not map to NAIF ID
           codes, an error is signaled by a routine in the call tree of
           this routine.

       8)  If required ephemerides or other kernel data are not
           available, an error is signaled by a routine in the call tree
           of this routine.

       9)  If the workspace interval count is less than 1, the error
           SPICE(VALUEOUTOFRANGE) will be signaled.

       10) If the required amount of workspace memory cannot be
           allocated, the error SPICE(MALLOCFAILURE) will be
           signaled.

       11) If the output SPICE window `result' has insufficient capacity to
           contain the number of intervals on which the specified geometric
           condition is met, the error will be diagnosed by a routine in
           the call tree of this routine. If the result window has size
           less than 2, the error SPICE(INVALIDDIMENSION) will be signaled
           by this routine.

       12) If any input string argument pointer is null, the error
           SPICE(NULLPOINTER) will be signaled.

       13) If any input string argument is empty, the error
           SPICE(EMPTYSTRING) will be signaled.

       14) If either input cell has type other than SpiceDouble,
           the error SPICE(TYPEMISMATCH) is signaled.

       15) An error signals from a routine in the call tree of
           this routine for any transmit mode aberration correction.

#### 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_c.

       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_c 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_c 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" include times when extrema are attained and
       times when the geometric quantity function is equal to a reference
       value or adjusted extremum. 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 limit 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 gfstol_c, e.g.

          gfstol_c( tolerance value in seconds )

       Call gfstol_c prior to calling this routine. All subsequent
       searches will use the updated tolerance value.

       Searches over time windows of long duration may require use of
       larger tolerance values than the default: the tolerance must be
       large enough so that it, when added to or subtracted from the
       confinement window's lower and upper bounds, yields distinct time
       values.

       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. See the "CASCADE"
       example program in gf.req for a demonstration.

#### Examples

       The numerical results shown for these examples 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.

          Use the meta-kernel shown below to load the required SPICE
          kernels.

             KPL/MK

             File name: standard.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

       Example:

          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.

          #include <stdio.h>
          #include "SpiceUsr.h"

          #define  TIMFMT  "YYYY MON DD HR:MN:SC.###"
          #define  NINTVL  5000
          #define  TIMLEN  41
          #define  NLOOPS  7

          int main()
             {

             /.
             Local variables
             ./
             SpiceChar               begstr [ TIMLEN ];
             SpiceChar               endstr [ TIMLEN ];

             SPICEDOUBLE_CELL      ( cnfine, 2 );
             SPICEDOUBLE_CELL      ( result, NINTVL*2 );

             SpiceDouble             adjust;
             SpiceDouble             et0;
             SpiceDouble             et1;
             SpiceDouble             phaseq;
             SpiceDouble             refval;
             SpiceDouble             start;
             SpiceDouble             step;
             SpiceDouble             stop;
             SpiceInt                i;
             SpiceInt                j;

             /.
             Define the values for target, observer, illuminator, and
             aberration correction.
             ./

             ConstSpiceChar * target = "moon";
             ConstSpiceChar * illmn  = "sun";
             ConstSpiceChar * abcorr = "lt+s";
             ConstSpiceChar * obsrvr = "earth";

             ConstSpiceChar * relate [NLOOPS] = { "=",
                                                  "<",
                                                  ">",
                                                  "LOCMIN",
                                                  "ABSMIN",
                                                  "LOCMAX",
                                                  "ABSMAX",
                                                };

             /.
             Load kernels.
             ./
             furnsh_c ( "standard.tm" );

             /.
             Store the time bounds of our search interval in
             the confinement window.
             ./
             str2et_c ( "2006 DEC 01", &et0 );
             str2et_c ( "2007 JAN 31", &et1 );

             wninsd_c ( et0, et1, &cnfine );

             /.
             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.
             ./
             step   = spd_c();
             refval = 0.57598845;
             adjust = 0.0;

             for ( j = 0;  j < NLOOPS;  j++ )
                {

                printf ( "Relation condition: %s\n",  relate[j] );

                /.
                Perform the search. The SPICE window `result' contains
                the set of times when the condition is met.
                ./
                gfpa_c ( target,    illmn,   abcorr, obsrvr,
                         relate[j], refval,  adjust, step,
                         NINTVL,    &cnfine, &result        );

                /.
                Display the results.
                ./
                if ( wncard_c(&result) == 0 )
                   {
                   printf ( "Result window is empty.\n\n" );
                   }
                else
                   {

                   for ( i = 0;  i < wncard_c(&result);  i++ )
                      {

                      /.
                      Fetch the endpoints of the Ith interval
                      of the result window.
                      ./
                      wnfetd_c ( &result, i, &start, &stop );

                      phaseq = phaseq_c ( start, target, illmn, obsrvr, abcorr );

                      timout_c ( start, TIMFMT, TIMLEN, begstr );
                      printf ( "Start time = %s %16.9f\n", begstr, phaseq );

                      phaseq = phaseq_c ( stop, target, illmn, obsrvr, abcorr );

                      timout_c ( stop, TIMFMT, TIMLEN, endstr );
                      printf ( "Stop time  = %s %16.9f\n", endstr, phaseq );
                      }

                   printf("\n");

                   }

                }

             return ( 0 );
             }

       The program outputs:

          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 CSPICE routine furnsh_c) before this
          routine is called.

#### Literature_References

       None.

#### Author_and_Institution

       N.J. Bachman   (JPL)
       E.D. Wright    (JPL)

#### Version

       -CSPICE Version 1.0.0, 15-JUL-2014 (EDW) (NJB)

#### Index_Entries

     GF phase angle search

#### Link to routine gfpa_c source file gfpa_c.c

    Wed Apr  5 17:54:36 2017