Index Page gfsubc_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 gfsubc_c ( ConstSpiceChar     * target,
                       ConstSpiceChar     * fixref,
                       ConstSpiceChar     * method,
                       ConstSpiceChar     * abcorr,
                       ConstSpiceChar     * obsrvr,
                       ConstSpiceChar     * crdsys,
                       ConstSpiceChar     * coord,
                       ConstSpiceChar     * relate,
                       SpiceDouble          refval,
                       SpiceDouble          adjust,
                       SpiceDouble          step,
                       SpiceInt             nintvls,
                       SpiceCell          * cnfine,
                       SpiceCell          * result  )

#### Abstract

       Determine time intervals for which a coordinate of an
       subpoint position vector satisfies a numerical constraint.

#### Required_Reading

       GF
       SPK
       CK
       TIME
       WINDOWS

#### Keywords

       COORDINATE
       GEOMETRY
       SEARCH
       EVENT

#### Brief_I/O

       Variable  I/O  Description
       --------  ---  --------------------------------------------------
       SPICE_GF_CNVTOL
                  P   Convergence tolerance.
       target     I   Name of the target body
       fixref     I   Body fixed frame associated with 'target'
       method     I   Name of method type for subpoint calculation
       abcorr     I   Aberration correction flag
       obsrvr     I   Name of the observing body
       crdsys     I   Name of the coordinate system containing 'coord'
       coord      I   Name of the coordinate of interest
       relate     I   Operator that either looks for an extreme value
                      (max, min, local, absolute) or compares the
                      coordinate value and refval
       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 restricted
       result     O   SPICE window containing results

#### Detailed_Input

       target     the string name of a target body.  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.

                  The target and observer define a position vector
                  that points from the observer to the target.

       fixref     the string name of the body-fixed, body-centered
                  reference frame associated with the target body target.

                  The SPICE frame subsystem must recognize the 'fixref' name.

       method     the string name of the method to use for the subpoint
                  calculation. The accepted values for method:

                     "Near point: ellipsoid"   The sub-observer point
                                               computation uses a
                                               triaxial ellipsoid to
                                               model the surface of the
                                               target body. The
                                               sub-observer point is
                                               defined as the nearest
                                               point on the target
                                               relative to the
                                               observer.

                     "Intercept: ellipsoid"    The sub-observer point
                                               computation uses a
                                               triaxial ellipsoid to
                                               model the surface of the
                                               target body. The
                                               sub-observer point is
                                               defined as the target
                                               surface intercept of the
                                               line containing the
                                               observer and the
                                               target's center.

                  The method string lacks sensitivity to case, embedded, leading
                  and trailing blanks.

       abcorr     the string description of the aberration corrections to apply
                  to the state evaluations to account for one-way light time
                  and stellar aberration.

                  This routine accepts the same aberration corrections as does
                  the SPICE routine SPKEZR. See the header of SPKEZR for a
                  detailed description of the aberration correction options.
                  For convenience, the 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.

                      "XLT"      "Transmission" case:  correct for
                                 one-way light time using a Newtonian
                                 formulation.

                      "XLT+S"    "Transmission" case:  correct for
                                 one-way light time and stellar
                                 aberration using a Newtonian
                                 formulation.

                      "XCN"      "Transmission" case:  converged
                                 Newtonian light time correction.

                      "XCN+S"    "Transmission" case:  converged
                                 Newtonian light time and stellar
                                 aberration corrections.

                  The abcorr string lacks sensitivity to case, and to embedded,
                  leading and trailing blanks.

         obsrvr   the string naming 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 the
                  observer is Earth.

         crdsys   the string name of the coordinate system for which the
                  coordinate of interest is a member.

         coord    the string name of the coordinate of interest in crdsys.

                  The supported coordinate systems and coordinate names are:

                  Coordinate System (CRDSYS)    Coordinates (COORD)      Range

                     "RECTANGULAR"                  "X"
                                                    "Y"
                                                    "Z"

                     "LATITUDINAL"                  "RADIUS"
                                                    "LONGITUDE"        (-Pi,Pi]
                                                    "LATITUDE"         [-Pi/2,Pi/2]

                     "RA/DEC"                       "RANGE"
                                                    "RIGHT ASCENSION"  [0,2Pi)
                                                    "DECLINATION"      [-Pi/2,Pi/2]

                     "SPHERICAL"                    "RADIUS"
                                                    "COLATITUDE"       [0,Pi]
                                                    "LONGITUDE"        (-Pi,Pi]

                     "CYLINDRICAL"                  "RADIUS"
                                                    "LONGITUDE"        [0,2Pi)
                                                    "Z"

                     "GEODETIC"                     "LONGITUDE"        (-Pi,Pi]
                                                    "LATITUDE"         [-Pi/2,Pi/2]
                                                    "ALTITUDE"

                     "PLANETOGRAPHIC"               "LONGITUDE"        [0,2Pi)
                                                    "LATITUDE"         [-Pi/2,Pi/2]
                                                    "ALTITUDE"

                      The ALTITUDE coordinates have a constant value
                      of zero +/- roundoff for ellipsoid targets.

                      Limit searches for coordinate events in the GEODETIC and
                      PLANETOGRAPHIC coordinate systems to TARGET bodies with
                      axial symmetry in the equatorial plane, i.e. equality
                      of the body X and Y radii (oblate or prolate spheroids).

         relate    the string or character describing the relational operator
                   used to define a constraint on the selected coordinate of the
                   subpoint vector. 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:

                      ">"      Separation is greater than the reference
                               value refval.

                      "="      Separation is equal to the reference
                               value refval.

                      "<"      Separation is less than the reference
                               value refval.

                     "ABSMAX"  Separation is at an absolute maximum.

                     "ABSMIN"  Separation is at an absolute  minimum.

                     "LOCMAX"  Separation is at a local maximum.

                     "LOCMIN"  Separation 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.

                  The relate string lacks sensitivity to case, leading
                  and trailing blanks.

       refval     the double precision reference value used together with
                  relate argument to define an equality or inequality to
                  satisfy by the selected coordinate of the subpoint
                  vector. See the discussion of relate above for
                  further information.

                  The units of refval correspond to the type as defined
                  by coord, radians for angular measures, kilometers for
                  distance measures.

       adjust     a double precision value used to modify searches for
                  absolute extrema: when 'relate' is set to ABSMAX or ABSMIN and
                  'adjust' is set to a positive value, gfsubc_c finds times
                  when the position vector coordinate is within adjust
                  radians/kilometers of the specified extreme value.

                  For 'relate' set to ABSMAX, the result window contains
                  time intervals when the position vector coordinate has
                  values between ABSMAX - adjust and ABSMAX.

                  For 'relate' set to ABSMIN, the result window contains
                  time intervals when the position vector coordinate has
                  values between ABSMIN and ABSMIN + adjust.

                  'adjust' is not used for searches for local extrema,
                  equality or inequality conditions.

       step       the double precision time step size to use in the search.
                  step must be short enough for a search using this step
                  size to locate the time intervals where coordinate function
                  of the subpoint 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 TDB seconds.

       nintvls    an integer value specifying the number of intervals in the
                  the internal workspace array used by this routine. '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 double precision SPICE window that confines the time
                  period over which the specified search is conducted.
                  cnfine may consist of a single interval or a collection
                  of intervals.

                  In some cases the confinement window can be used to
                  greatly reduce the time period that must be searched
                  for the desired solution. See the Particulars section
                  below for further discussion.

                  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     the SPICE window of intervals, contained within the
                  confinement window cnfine, on which the specified
                  constraint is satisfied.

                  If result is non-empty on input, its contents
                  will be discarded before gfsubc_c conducts its
                  search.

                  result must be declared and initialized with sufficient
                  size to capture the full set of time intervals
                  within the search region on which the specified constraint
                  is satisfied.

                  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 be returned with a
                  cardinality of zero.

#### 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 has the value 1.0e-6. Units are TDB
                  seconds.

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

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

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

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

#### 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.

          - PCK data: bodies modeled as triaxial ellipsoids must have
            semi-axis lengths provided by variables in the kernel pool.
            Typically these data are made available by loading a text
            PCK file using FURNSH.

          - If non-inertial reference frames are used, then PCK
            files, frame kernels, C-kernels, and SCLK kernels may be
            needed.

       Such kernel data are normally loaded once per program
       run, NOT every time this routine is called.

#### Particulars

       This routine provides a simpler, but less flexible interface
       than does the routine gfevnt_c for conducting searches for
       subpoint position vector coordinate value events.
       Applications that require support for progress reporting, interrupt
       handling, non-default step or refinement functions, or non-default
       convergence tolerance should call gfevnt_c rather than this routine.

       This routine determines a set of one or more time intervals
       within the confinement window when the selected coordinate of
       the subpoint position vector satisfies a caller-specified
       constraint. The resulting set of intervals is returned as a SPICE
       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 specified
       coordinate 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 coordinate
       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 coordinate 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 coordinate
       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 coordinate 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 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.

       Practical use of the coordinate search capability would likely
       consist of searches over multiple coordinate constraints to find
       time intervals that satisfies the constraints. An effective
       technique to accomplish such a search is to use the result
       window from one search as the confinement window of the next.

       Longitude and Right Ascension
       =============================

       The cyclic nature of the longitude and right ascension coordinates
       produces branch cuts at +/- 180 degrees longitude and 0-360
       longitude. Round-off error may cause solutions near these branches
       to cross the branch. Use of the SPICE routine wncond_c will contract
       solution windows by some epsilon, reducing the measure of the
       windows and eliminating the branch crossing. A one millisecond
       contraction will in most cases eliminate numerical round-off caused
       branch crossings.

#### 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.

       The example shown below requires a "standard" set of SPICE
       kernels. We list these kernels in a meta kernel named "standard.tm."

          KPL/MK

                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
                   ---------                     --------
                   de414.bsp                     Planetary ephemeris
                   pck00008.tpc                  Planet orientation and
                                                 radii
                   naif0008.tls                  Leapseconds

          \begindata

          KERNELS_TO_LOAD = ( '/kernels/gen/lsk/naif0008.tls'
                              '/kernels/gen/spk/de414.bsp'
                              '/kernels/gen/pck/pck00008.tpc'
                            )

          Example:

          Find the time during 2007 for which the subpoint position vector
          of the sun on earth in the IAU_EARTH frame lies within a geodetic
          latitude-longitude "box" defined as

             16 degrees <= latitude  <= 17 degrees
             85 degrees <= longitude <= 86 degrees

          This problem requires four searches, each search on one of the
          box restrictions. The user needs also realize the temporal
          behavior of latitude greatly differs from that of the longitude. The
          sub-observer point latitude varies between approximately 23.44 degrees
          and -23.44 degrees during the year. The sub-observer point longitude
          varies between -180 degrees and 180 degrees in one day.

          #include <stdio.h>
          #include <stdlib.h>
          #include <string.h>

          #include "SpiceUsr.h"

          #define   MAXWIN   100
          #define   TIMFMT   "YYYY-MON-DD HR:MN:SC.###### (TDB) ::TDB ::RND"
          #define   STRLEN   64

          int main( int argc, char **argv )
             {

             /.
             Create the needed windows. Note, one window
             consists of two values, so the total number
             of cell values to allocate equals twice
             the number of intervals.
             ./
             SPICEDOUBLE_CELL ( result1, 2*MAXWIN );
             SPICEDOUBLE_CELL ( result2, 2*MAXWIN );
             SPICEDOUBLE_CELL ( result3, 2*MAXWIN );
             SPICEDOUBLE_CELL ( result4, 2*MAXWIN );
             SPICEDOUBLE_CELL ( cnfine, 2       );

             SpiceDouble       begtim;
             SpiceDouble       endtim;
             SpiceDouble       step;
             SpiceDouble       adjust;
             SpiceDouble       refval;
             SpiceDouble       beg;
             SpiceDouble       end;

             SpiceChar         begstr [ STRLEN ];
             SpiceChar         endstr [ STRLEN ];
             SpiceChar       * target = "EARTH";
             SpiceChar       * obsrvr = "SUN";
             SpiceChar       * fixref = "IAU_EARTH";
             SpiceChar       * method = "Near point: ellipsoid";
             SpiceChar       * crdsys = "GEODETIC";
             SpiceChar       * abcorr = "NONE";

             SpiceInt          count;
             SpiceInt          i;

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

             /.
             Store the time bounds of our search interval in
             the cnfine confinement window.
             ./
             str2et_c( "2007 JAN 01", &begtim );
             str2et_c( "2008 JAN 01", &endtim );

             wninsd_c ( begtim, endtim, &cnfine );

             /.
             Perform four searches to determine the times when the
             latitude-longitude box restriction conditions apply to
             the subpoint vector.

             Perform the searches such that the result window of a search
             serves as the confinement window of the subsequent search.

             Since the latitude coordinate varies slowly and is well behaved
             over the time of the confinement window, search first for the
             windows satisfying the latitude requirements, then use that result
             as confinement for the longitude search.
             ./

             /.
             The latitude varies relatively slowly, ~46 degrees during the
             year. The extrema occur approximately every six months.
             Search using a step size less than half that value (180 days).
             For this example use ninety days (in units of seconds).
             ./

             step   = (90.)*spd_c();
             adjust = 0.;

             {
             SpiceChar       * coord  = "LATITUDE";
             SpiceChar       * relate = ">";

             refval = 16. *rpd_c();

             gfsubc_c (  target,  fixref,
                         method,  abcorr, obsrvr,
                         crdsys,  coord,
                         relate,  refval,
                         adjust,  step,
                         MAXWIN,
                         &cnfine, &result1 );
             }

             {
             SpiceChar       * coord  = "LATITUDE";
             SpiceChar       * relate = "<";

             refval = 17. *rpd_c();

             gfsubc_c (  target,  fixref,
                         method,  abcorr, obsrvr,
                         crdsys,  coord,
                         relate,  refval,
                         adjust,  step,
                         MAXWIN,
                         &result1, &result2 );
             }

             /.
             Now the longitude search.
             ./

             /.
             Reset the stepsize to something appropriate for the 360
             degrees in 24 hours domain. The longitude shows near
             linear behavior so use a stepsize less than half the period
             of twelve hours. Ten hours will suffice in this case.
             ./
             step   = (10./24.)*spd_c();

             {
             SpiceChar       * coord  = "LONGITUDE";
             SpiceChar       * relate = ">";

             refval = 85. *rpd_c();

             gfsubc_c (  target,  fixref,
                         method,  abcorr, obsrvr,
                         crdsys,  coord,
                         relate,  refval,
                         adjust,  step,
                         MAXWIN,
                         &result2, &result3 );

             /.
             Contract the endpoints of each window to account
             for possible round-off error at the -180/180 degree branch.

             A contraction value of a millisecond should eliminate
             any round-off caused branch crossing.
             ./

             wncond_c( 1e-3, 1e-3, &result3 );
             }

             {
             SpiceChar       * coord  = "LONGITUDE";
             SpiceChar       * relate = "<";

             refval = 86. *rpd_c();

             gfsubc_c (  target,  fixref,
                         method,  abcorr, obsrvr,
                         crdsys,  coord,
                         relate,  refval,
                         adjust,  step,
                         MAXWIN,
                         &result3, &result4 );
             }

             /.
             List the beginning and ending points in each interval
             if result contains data.
             ./
             count = wncard_c( &result4 );

             /.
             Display the results.
             ./
             if (count == 0 )
                {
                printf ( "Result window is empty.\n\n" );
                }
             else
                {
                for ( i = 0;  i < count;  i++ )
                   {

                   /.
                   Fetch the endpoints of the Ith interval
                   of the result window.
                   ./
                   wnfetd_c ( &result4, i, &beg, &end );

                   timout_c ( beg, TIMFMT, STRLEN, begstr );
                   timout_c ( end, TIMFMT, STRLEN, endstr );

                   printf ( "Interval %d\n", i + 1);
                   printf ( "Beginning TDB %s \n",   begstr );
                   printf ( "Ending TDB    %s \n\n", endstr );

                   }
                }

             kclear_c();
             return( 0 );
             }

          The program outputs:

             Interval 1
             Beginning TDB 2007-MAY-05 06:14:04.637735 (TDB)
             Ending TDB    2007-MAY-05 06:18:04.621908 (TDB)

             Interval 2
             Beginning TDB 2007-MAY-06 06:13:59.583483 (TDB)
             Ending TDB    2007-MAY-06 06:17:59.569239 (TDB)

             Interval 3
             Beginning TDB 2007-MAY-07 06:13:55.102939 (TDB)
             Ending TDB    2007-MAY-07 06:17:55.090299 (TDB)

             Interval 4
             Beginning TDB 2007-MAY-08 06:13:51.202604 (TDB)
             Ending TDB    2007-MAY-08 06:17:51.191583 (TDB)

             Interval 5
             Beginning TDB 2007-AUG-06 06:23:17.282927 (TDB)
             Ending TDB    2007-AUG-06 06:27:17.264009 (TDB)

             Interval 6
             Beginning TDB 2007-AUG-07 06:23:10.545441 (TDB)
             Ending TDB    2007-AUG-07 06:27:10.524926 (TDB)

             Interval 7
             Beginning TDB 2007-AUG-08 06:23:03.233996 (TDB)
             Ending TDB    2007-AUG-08 06:27:03.211889 (TDB)

#### Restrictions

       1) The kernel files to be used by this routine must be loaded
          (normally via the CSPICE routine furnsh_c) before this routine
          is called.

       2) This routine has the side effect of re-initializing the
          coordinate quantity utility package.  Callers may
          need to re-initialize the package after calling this routine.

#### Literature_References

       None.

#### Author_and_Institution

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

#### Version

       -CSPICE Version 1.0.2, 29-AUG-2014 (EDW)

          Edit to header, replaced ' character with character " to indicate
          C strings. Removed extraneous line from header.

       -CSPICE Version 1.0.1, 28-FEB-2013 (NJB) (EDW)

          Header was updated to discuss use of gfstol_c.

          Edit to comments to correct search description.

          Edit to Example description, replaced "intercept" with
          "sub-observer point."

          Correction of several typos.

       -CSPICE Version 1.0.0, 10-FEB-2009 (NJB) (EDW)

#### Index_Entries

       GF subpoint coordinate search

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

    Wed Apr  5 17:54:36 2017