Main Page Geometric Event Finding Hands-On Lesson (C)
## Table of Contents
       Geometric Event Finding Hands-On Lesson (C)
          Overview
          Note About HTML Links
          References
             Tutorials
             Required Readings
             The Permuted Index
             Source Code Header Comments
          Kernels Used
          CSPICE Routines Used
       Find View Periods
          Task Statement
          Learning Goals
          Approach
             Solution steps
          Solution
             Solution Meta-Kernel
             Solution Code
             Solution Sample Output
       Find Times when Target is Visible
          Task Statement
          Learning Goals
          Approach
             Solution steps
          Solution
             Solution Code
             Solution Sample Output
       Extra Credit
          Task statements
          Solutions
Top # Geometric Event Finding Hands-On Lesson (C) August 31, 2016 Top ## Overview This lesson illustrates how the Geometry Finder (GF) subsystem of the CSPICE Toolkit can be used to find time intervals when specified geometric conditions are satisfied. In this lesson the student is asked to construct a program that finds the time intervals, within a specified time range, when the ExoMars-16 Trace Gas Orbiter (TGO) is visible from ESA's deep space station in New Norcia. Possible occultation of the spacecraft by Mars is to be considered. Top ## Note About HTML Links The HTML version of this lesson contains links pointing to various HTML documents provided with the Toolkit. All of these links are relative and, in order to function, require this document to be in a certain location in the Toolkit HTML documentation directory tree. In order for the links to be resolved, create a subdirectory called ``lessons'' under the ``doc/html'' directory of the ``cspice/'' tree and copy this document to that subdirectory before loading it into a Web browser. Top ## References Top ### Tutorials The following SPICE tutorials serve as references for the discussions in this lesson:
       Name             Lesson steps/functions it describes
       ---------------  -----------------------------------------
       Time             Time Conversion
       SCLK and LSK     Time Conversion
       SPK              Obtaining Ephemeris Data
       Frames           Reference Frames
       Using Frames     Reference Frames
       PCK              Planetary Constants Data
       Lunar-Earth PCK  Lunar and Earth Orientation Data
       GF               The SPICE Geometry Ginder (GF) subsystem
These tutorials are available from the NAIF ftp server at JPL:
       http://naif.jpl.nasa.gov/naif/tutorials.html
Top ### Required Readings The Required Reading documents are provided with the Toolkit and are located under the ``cspice/doc'' directory in the C installation tree.
       Name             Lesson steps/functions that it describes
       ---------------  -----------------------------------------
       cells.req        Cell/window initialization
       frames.req       Using reference frames
       gf.req           The SPICE geometry finder (GF) subsystem
       kernel.req       Loading SPICE kernels
       naif_ids.req     Body and reference frame names
       pck.req          Obtaining planetary constants data
       spk.req          Computing positions and velocities
       time.req         UTC to ET time conversion
       windows.req      The SPICE window data type
Top ### The Permuted Index Another useful document distributed with the Toolkit is the permuted index. This is located under the ``cspice/doc'' directory in the C installation tree. This text document provides a simple mechanism by which users can discover which CSPICE routines perform functions of interest, as well as the names of the source files that contain these routines. Top ### Source Code Header Comments The most detailed specification of a given SPICE C routine is contained in the header section of its source code. The source code is distributed with the Toolkit and is located under the ``cspice/src/cspice'' path. For example path of the source code of the str2et_c routine is
       cspice/src/cspice/str2et_c.c
Top ## Kernels Used The following kernels are used in examples provided in this lesson:
        1.  Solar System Ephemeris SPK, subsetted to cover only the time
            range of interest:

               de430.bsp

        2.  Martian Satellite Ephemeris SPK, subsetted to cover only the
            time range of interest:

               mar085.bsp

        3.  ESA stations SPK:

               estrack_v01.bsp

        4.  ESA stations frame definitions:

               estrack_v01.tf

        5.  EARTH_FIXED/ITRF93 frame connection:

               earthfixeditrf93.tf

        6.  Binary PCK for Earth:

               earth_070425_370426_predict.bpc

        7.  ExoMars-16 TGO Spacecraft Trajectory SPK, subsetted to cover
            only the time range of interest:

               em16_tgo_mlt_20171205_20230115_v01.bsp

        8.  Generic LSK:

               naif0012.tls

        9.  Generic PCK:

               pck00010.tpc

       10.  ExoMars-16 TGO FK, containing the SPICE ID/name mappings for
            the TGO spacecraft:

               em16_tgo_v07.tf
These SPICE kernels are included in the lesson package available from the NAIF server at JPL:
       ftp://naif.jpl.nasa.gov/pub/naif/toolkit_docs/Lessons/
Top ## CSPICE Routines Used This section provides a summary of the functions that are suggested for usage in each of the exercises in this tutorial. (You may wish to not look at this list unless/until you ``get stuck'' while working on your own.)
       Name        Function that it performs
       ----------  ---------------------------------------------------
       furnsh_c    Loads kernels, individually or listed in meta-kernel
       gfoclt_c    Solve for times of occultation or transit
       gfposc_c    Solve for times when a position vector coordinate
                   constraint is met
       str2et_c    Converts a time string to ET seconds past J2000
       timout_c    Format a time string for output
       wncard_c    Return cardinality of a SPICE window
       wndifd_c    Find the difference of two d.p. windows
       wnfetd_c    Fetch a specified interval from a d.p. window
       wninsd_c    Insert an interval into a d.p. window
Refer to the headers of the various functions listed above, as detailed interface specifications are provided with the source code. Top # Find View Periods Top ## Task Statement Write a program that finds the set of time intervals, within the time range
       2018 JUN 10 TDB
       2018 JUN 14 TDB
when the ExoMars-16 Trace Gas Orbiter (TGO) is visible from ESA's New Norcia station. These time intervals are frequently called ``view periods.'' The spacecraft is considered visible if its apparent position (that is, its position corrected for light time and stellar aberration) has elevation of at least 6 degrees in the topocentric reference frame NEW_NORCIA_TOPO. In this exercise, we ignore the possibility of occultation of the spacecraft by Mars. Use a search step size that ensures that no view periods of duration 5 minutes or longer will be missed by the search. Display the start and stop times of these intervals using TDB calendar dates and millisecond precision. Top ## Learning Goals Exposure to SPICE GF event finding routines. Familiarity with SPICE windows and routines that manipulate them. Exposure to SPICE time parsing and output formatting routines. Top ## Approach Top ### Solution steps A possible solution could consist of the following steps: Preparation: `1.` Review the CSPICE cell and window Required Reading. `2.` Decide what SPICE kernels are necessary. Use the SPICE summary tool BRIEF to examine the coverage of the binary kernels and verify the availability of required data. `3.` Create a meta-kernel listing the SPICE kernels to be loaded. (Hint: consult a programming example tutorial, or the Introduction to Kernels tutorial, for a reminder of how to do this.) `` Name the meta-kernel 'viewpr.tm'. Next, write a program that performs the following steps: `1.` Use furnsh_c to load the meta-kernel. `2.` Declare a CSPICE window ```cnfine''' to hold the time period within which the search is to be conducted, and a CSPICE window `riswin' ("rise/set window") to hold the view periods found by the search. `3.` Insert the given time bounds into the confinement window using wninsd_c. `4.` Select a step size for searching for visibility state transitions: in this case, each target rise or set event is a state transition. `` The step size must be large enough so the search proceeds with reasonable speed, but small enough so that no visibility transition events---that is, target rise or set events---are missed. `5.` Use the GF routine gfposc_c to find the window of times, within the confinement window `cnfine', during which the ExoMars-16 TGO spacecraft is above the elevation limit as seen from ESA's New Norcia station, in the the reference frame NEW_NORCIA_TOPO. `` Use light time and stellar aberration corrections for the apparent position of the spacecraft as seen from the station. `6.` Fetch and display the contents of the result window. Use wnfetd_c to extract from the result window the start and stop times of each time interval. Display each of the intervals in the result window as a pair of start and stop times. Express each time as a TDB calendar date using the routine timout_c. You may find it useful to consult the references listed above. In particular, the header of the SPICE GF function gfposc_c contains pertinent documentation. Top ## Solution Top ### Solution Meta-Kernel The meta-kernel we created for the solution to this exercise is named 'viewpr.tm'. Its contents follow:
       KPL/MK

          This is the meta-kernel used in the solution of the tasks in the
          Geometric Event Finding Hands On Lesson.

       \begindata

          KERNELS_TO_LOAD = (

             'kernels/spk/de430.bsp'
             'kernels/spk/mar085.bsp',
             'kernels/spk/estrack_v01.bsp'
             'kernels/fk/estrack_v01.tf'
             'kernels/fk/earthfixeditrf93.tf'
             'kernels/pck/earth_070425_370426_predict.bpc'
             'kernels/lsk/naif0012.tls'
             'kernels/spk/em16_tgo_mlt_20171205_20230115_v01.bsp'
             'kernels/pck/pck00010.tpc'
             'kernels/fk/em16_tgo_v07.tf'

                            )

       \begintext
Top ### Solution Code The example program below shows one possible solution.
       #include <string.h>
       #include <stdio.h>
       #include "SpiceUsr.h"

          /*
          PROGRAM VIEWPR

          Find and display the window of times when the ExoMars-16
          TGO spacecraft is above a specified elevation limit in the
          topocentric reference frame of ESA's New Norcia station.
          */

       int main()
       {
          /*
          Local constants
          */

          /*
          The  meta-kernel:
          */
          #define METAKR          "viewpr.tm"

          /*
          Maximum number of intervals in any window:
          */
          #define MAXIVL          1000

          /*
          Maximum result window size:
          */
          #define MAXWIN          ( 2 * MAXIVL )

          /*
          Format string for time output:
          */
          #define TDBFMT          "YYYY MON DD HR:MN:SC.### (TDB) ::TDB"

          /*
          String lengths and other bounds:
          */
          #define LNSIZE          201
          #define TIMLEN          51

          /*
          Local variables
          */

          /*
          Confinement window used to store interval to be searched:
          */
          SPICEDOUBLE_CELL        ( cnfine, MAXWIN );

          /*
          Window to hold sets of times when
          target is above the elevation limit:
          */
          SPICEDOUBLE_CELL        ( riswin, MAXWIN );

          SpiceChar             * abcorr;
          SpiceChar             * coord;
          SpiceChar             * crdsys;
          SpiceChar             * obsfrm;
          SpiceChar             * relate;
          SpiceChar             * srfpt;
          SpiceChar             * start;
          SpiceChar             * stop;
          SpiceChar             * target;
          SpiceChar               timstr  [ TIMLEN ];

          SpiceDouble             adjust;
          SpiceDouble             elvlim;
          SpiceDouble             etbeg;
          SpiceDouble             etend;
          SpiceDouble             intbeg;
          SpiceDouble             intend;
          SpiceDouble             revlim;

          /*
          stepsz is the step size, measured in seconds, used to search
          for times bracketing a state transition.
          */
          SpiceDouble             stepsz;

          SpiceInt                i;
          SpiceInt                winsiz;

          /*
          Load the meta-kernel.
          */
          furnsh_c ( METAKR );

          /*
          Assign the inputs for our search.

          Since we're interested in the apparent location of the
          target, we use light time and stellar aberration
          corrections. We use the "converged Newtonian" form
          of the light time correction because this choice may
          increase the accuracy of the occultation times we'll
          compute using gfoclt_c.
          */
          srfpt  = "NEW_NORCIA";
          obsfrm = "NEW_NORCIA_TOPO";
          target = "TGO";
          abcorr = "CN+S";
          start  = "2018 JUN 10 TDB";
          stop   = "2018 JUN 14 TDB";
          elvlim =  6.0;

          /*
          The elevation limit above has units of degrees; we convert
          this value to radians for computation using SPICE routines.
          We'll store the equivalent value in radians in REVLIM.
          */
          revlim = rpd_c() * elvlim;

          /*
          Since SPICE doesn't directly support the AZ/EL coordinate
          system, we use the equivalent constraint

             latitude > REVLIM

          in the latitudinal coordinate system, where the reference
          frame is topocentric and is centered at the viewing location.
          */
          crdsys = "LATITUDINAL";
          coord  = "LATITUDE";
          relate = ">";

          /*
          The adjustment value only applies to absolute extrema
          searches; simply give it an initial value of zero
          for this inequality search.
          */
          adjust = 0.0;

          /*
          STEPSZ is the step size, measured in seconds, used to search
          for times bracketing a state transition. Since we don't expect
          any events of interest to be shorter than five minutes, and
          since the separation between events is well over 5 minutes,
          we'll use this value as our step size. Units are seconds.
          */
          stepsz = 300.0;

          /*
          Display a banner for the output report:
          */
          printf ( "\n%s\n\n",
                   "Inputs for target visibility search:" );

          printf ( "   Target                       = %s\n", target );
          printf ( "   Observation surface location = %s\n", srfpt  );
          printf ( "   Observer's reference frame   = %s\n", obsfrm );
          printf ( "   Elevation limit (degrees)    = %f\n", elvlim );
          printf ( "   Aberration correction        = %s\n", abcorr );
          printf ( "   Step size (seconds)          = %f\n", stepsz );

          /*
          Convert the start and stop times to ET.
          */
          str2et_c ( start, &etbeg );
          str2et_c ( stop,  &etend );

          /*
          Display the search interval start and stop times
          using the format shown below.

             2004 MAY 06 20:15:00.000 (TDB)

          */
          timout_c ( etbeg, TDBFMT, TIMLEN, timstr );
          printf ( "   Start time                   = %s\n", timstr  );

          timout_c ( etend, TDBFMT, TIMLEN, timstr );
          printf ( "   Stop time                    = %s\n", timstr  );

          printf ( "\n" );

          /*
          Initialize the "confinement" window with the interval
          over which we'll conduct the search.
          */
          wninsd_c ( etbeg, etend, &cnfine );

          /*
          In the call below, the maximum number of window
          intervals gfposc_c can store internally is set to MAXIVL.

          Now search for the time period, within our confinement
          window, during which the apparent target has elevation
          at least equal to the elevation limit.
          */
          gfposc_c ( target, obsfrm, abcorr, srfpt,
                     crdsys, coord,  relate, revlim,
                     adjust, stepsz, MAXIVL, &cnfine, &riswin );

          /*
          The function wncard_c returns the number of intervals
          in a SPICE window.
          */
          winsiz = wncard_c( &riswin );

          if ( winsiz == 0 )
          {
             printf ( "No events were found.\n" );
          }
          else
          {
             /*
             Display the visibility time periods.
             */
             printf ( "Visibility times of %s as seen from %s:"
                      "\n\n",
                      target, srfpt                               );

             for (  i = 0;   i < winsiz;   i++  )
             {
                /*
                Fetch the start and stop times of the Ith interval
                from the search result window viswin.
                */
                wnfetd_c ( &riswin, i, &intbeg, &intend );

                /*
                Convert the rise time to a TDB calendar string.
                */
                timout_c ( intbeg, TDBFMT, TIMLEN, timstr );

                /*
                Write the string to standard output.
                */
                if ( i == 0 )
                {
                   printf ( "Visibility or window start time:  %s\n",
                             timstr                                  );
                }
                else
                {
                   printf ( "Visibility start time:            %s\n",
                             timstr                                  );
                }

                /*
                Convert the set time to a TDB calendar string.
                */
                timout_c ( intend, TDBFMT, TIMLEN, timstr );

                /*
                Write the string to standard output.
                */
                if ( i == winsiz-1 )
                {
                   printf ( "Visibility or window stop time:   %s\n",
                             timstr                                  );
                }
                else
                {
                   printf ( "Visibility stop time:             %s\n",
                             timstr                                  );
                }

                printf ( "\n" );
             }
          }

          return ( 0 );
       }
Top ### Solution Sample Output Numerical results shown for this example may differ across platforms since the results depend on the SPICE kernels used as input and on the host platform's arithmetic implementation. After compiling the program, execute it. The output is:
       Inputs for target visibility search:

          Target                       = TGO
          Observation surface location = NEW_NORCIA
          Observer's reference frame   = NEW_NORCIA_TOPO
          Elevation limit (degrees)    = 6.000000
          Aberration correction        = CN+S
          Step size (seconds)          = 300.000000
          Start time                   = 2018 JUN 10 00:00:00.000 (TDB)
          Stop time                    = 2018 JUN 14 00:00:00.000 (TDB)

       Visibility times of TGO as seen from NEW_NORCIA:

       Visibility or window start time:  2018 JUN 10 00:00:00.000 (TDB)
       Visibility stop time:             2018 JUN 10 02:11:17.355 (TDB)

       Visibility start time:            2018 JUN 10 13:19:58.777 (TDB)
       Visibility stop time:             2018 JUN 11 02:08:16.008 (TDB)

       Visibility start time:            2018 JUN 11 13:16:50.542 (TDB)
       Visibility stop time:             2018 JUN 12 02:05:12.548 (TDB)

       Visibility start time:            2018 JUN 12 13:13:38.573 (TDB)
       Visibility stop time:             2018 JUN 13 02:02:06.618 (TDB)

       Visibility start time:            2018 JUN 13 13:10:23.432 (TDB)
       Visibility or window stop time:   2018 JUN 14 00:00:00.000 (TDB)
Top # Find Times when Target is Visible Top ## Task Statement Extend the program of the previous chapter to find times when the ExoMars-16 TGO orbiter is: `--` Above the elevation limit in the NEW_NORCIA_TOPO topocentric reference frame. `--` and is not occulted by Mars Store the set of time intervals when the spacecraft is visible in a CSPICE window. We'll call this the ``result window.'' Display each of the intervals in the result window as a pair of start and stop times. Express each time as a TDB calendar date using the same format as in the previous program. Top ## Learning Goals Familiarity with the GF occultation finding routine gfoclt_c. Further experience with the CSPICE window functions. Top ## Approach Top ### Solution steps A possible solution would consist of the following steps: `1.` Use the meta-kernel of the previous lesson. `2.` Include the code from the program of the previous chapter in a new source file; modify this code to create the new program. `3.` Declare a CSPICE window `occwin' to hold the results of the occultation search. Also declare a second CSPICE window `viswin' to hold the final result. `4.` Search for occultations of the ExoMars-16 TGO orbiter as seen from New Norcia station using gfoclt_c. Use as the confinement window for this search the result window from the elevation search performed by gfposc_c. `` Since occultations occur when the apparent ExoMars-16 TGO spacecraft position is behind the apparent figure of Mars, light time correction must be performed for the occultation search. To improve accuracy of the occultation state determination, use ``converged Newtonian'' light time correction. `5.` Use the CSPICE window subtraction routine wndifd_c to subtract the window of times when the spacecraft is occulted from the window of times when the spacecraft is above the elevation limit. The difference window `viswin' is the final result. `6.` Modify the code to display the contents of the window `viswin'. This completes the assignment. Top ## Solution Top ### Solution Code
       #include <string.h>
       #include <stdio.h>
       #include "SpiceUsr.h"

          /*
          PROGRAM VISIBL

          Find and display the window of times when the ExoMars-16
          TGO spacecraft is above a specified elevation limit in the
          topocentric reference frame of ESA's New Norcia station
          and is not occulted by Mars.
          */

       int main()
       {
          /*
          Local constants
          */

          /*
          The  meta-kernel:
          */
          #define METAKR          "viewpr.tm"

          /*
          Maximum number of intervals in any window:
          */
          #define MAXIVL          1000

          /*
          Maximum result window size:
          */
          #define MAXWIN          ( 2 * MAXIVL )

          /*
          Format string for time output:
          */
          #define TDBFMT          "YYYY MON DD HR:MN:SC.### (TDB) ::TDB"

          /*
          String lengths and other bounds:
          */
          #define TIMLEN          51

          /*
          Local variables
          */

          /*
          Confinement window used to store interval to be searched:
          */
          SPICEDOUBLE_CELL        ( cnfine, MAXWIN );

          /*
          Windows to hold sets of times when

             - target is occulted
             - target is above the elevation limit
             - target is visible
          */
          SPICEDOUBLE_CELL        ( occwin, MAXWIN );
          SPICEDOUBLE_CELL        ( riswin, MAXWIN );
          SPICEDOUBLE_CELL        ( viswin, MAXWIN );

          SpiceChar             * abcorr;
          SpiceChar             * back;
          SpiceChar             * bframe;
          SpiceChar             * bshape;
          SpiceChar             * coord;
          SpiceChar             * crdsys;
          SpiceChar             * fframe;
          SpiceChar             * front;
          SpiceChar             * fshape;
          SpiceChar             * obsfrm;
          SpiceChar             * occtyp;
          SpiceChar             * relate;
          SpiceChar             * srfpt;
          SpiceChar             * start;
          SpiceChar             * stop;
          SpiceChar             * target;
          SpiceChar               timstr  [ TIMLEN ];

          SpiceDouble             adjust;
          SpiceDouble             elvlim;
          SpiceDouble             etbeg;
          SpiceDouble             etend;
          SpiceDouble             intbeg;
          SpiceDouble             intend;
          SpiceDouble             revlim;

          /*
          stepsz is the step size, measured in seconds, used to search
          for times bracketing a state transition.
          */
          SpiceDouble             stepsz;

          SpiceInt                i;
          SpiceInt                winsiz;

          /*
          Load the meta-kernel.
          */
          furnsh_c ( METAKR );

          /*
          Assign the inputs for our search.

          Since we're interested in the apparent location of the
          target, we use light time and stellar aberration
          corrections. We use the "converged Newtonian" form
          of the light time correction because this choice may
          increase the accuracy of the occultation times we'll
          compute using gfoclt_c.
          */
          srfpt  = "NEW_NORCIA";
          obsfrm = "NEW_NORCIA_TOPO";
          target = "TGO";
          abcorr = "CN+S";
          start  = "2018 JUN 10 TDB";
          stop   = "2018 JUN 14 TDB";
          elvlim =  6.0;

          /*
          The elevation limit above has units of degrees; we convert
          this value to radians for computation using SPICE routines.
          We'll store the equivalent value in radians in REVLIM.
          */
          revlim = rpd_c() * elvlim;

          /*
          We model the target shape as a point and the blocking body's
          shape as an ellipsoid. No body-fixed reference frame is
          required for the target since its orientation is not used.
          */
          back   = target;
          bshape = "POINT";
          bframe = " ";
          front  = "MARS";
          fshape = "ELLIPSOID";
          fframe = "IAU_MARS";

          /*
          The occultation type should be set to "ANY" for a point
          target.
          */
          occtyp = "any";

          /*
          Since SPICE doesn't directly support the AZ/EL coordinate
          system, we use the equivalent constraint

             latitude > REVLIM

          in the latitudinal coordinate system, where the reference
          frame is topocentric and is centered at the viewing location.
          */
          crdsys = "LATITUDINAL";
          coord  = "LATITUDE";
          relate = ">";

          /*
          The adjustment value only applies to absolute extrema
          searches; simply give it an initial value of zero
          for this inequality search.
          */
          adjust = 0.0;

          /*
          STEPSZ is the step size, measured in seconds, used to search
          for times bracketing a state transition. Since we don't expect
          any events of interest to be shorter than five minutes, and
          since the separation between events is well over 5 minutes,
          we'll use this value as our step size. Units are seconds.
          */
          stepsz = 300.0;

          /*
          Display a banner for the output report:
          */
          printf ( "\n%s\n\n",
                   "Inputs for target visibility search:" );

          printf ( "   Target                       = %s\n", target );
          printf ( "   Observation surface location = %s\n", srfpt  );
          printf ( "   Observer's reference frame   = %s\n", obsfrm );
          printf ( "   Blocking body                = %s\n", front  );
          printf ( "   Blocker's reference frame    = %s\n", fframe );
          printf ( "   Elevation limit (degrees)    = %f\n", elvlim );
          printf ( "   Aberration correction        = %s\n", abcorr );
          printf ( "   Step size (seconds)          = %f\n", stepsz );

          /*
          Convert the start and stop times to ET.
          */
          str2et_c ( start, &etbeg );
          str2et_c ( stop,  &etend );

          /*
          Display the search interval start and stop times
          using the format shown below.

             2004 MAY 06 20:15:00.000 (TDB)
          */
          timout_c ( etbeg, TDBFMT, TIMLEN, timstr );
          printf ( "   Start time                   = %s\n", timstr  );

          timout_c ( etend, TDBFMT, TIMLEN, timstr );
          printf ( "   Stop time                    = %s\n", timstr  );

          printf ( "\n" );

          /*
          Initialize the "confinement" window with the interval
          over which we'll conduct the search.
          */
          wninsd_c ( etbeg, etend, &cnfine );

          /*
          In the call below, the maximum number of window
          intervals gfposc_c can store internally is set to MAXIVL.

          Now search for the time period, within our confinement
          window, during which the apparent target has elevation
          at least equal to the elevation limit.
          */
          gfposc_c ( target, obsfrm, abcorr, srfpt,
                     crdsys, coord,  relate, revlim,
                     adjust, stepsz, MAXIVL, &cnfine, &riswin );

          /*
          Now find the times when the apparent target is above
          the elevation limit and is not occulted by the
          blocking body (Mars). We'll find the window of times when
          the target is above the elevation limit and *is* occulted,
          then subtract that window from the view period window
          riswin found above.

          For this occultation search, we can use riswin as
          the confinement window because we're not interested in
          occultations that occur when the target is below the
          elevation limit.

          Find occultations within the view period window.
          */
          gfoclt_c ( occtyp, front,  fshape,  fframe,
                     back,   bshape, bframe,  abcorr,
                     srfpt,  stepsz, &riswin, &occwin );

          /*
          Subtract the occultation window from the view period
          window: this yields the time periods when the target
          is visible.
          */
          wndifd_c ( &riswin, &occwin, &viswin );

          /*
          The function wncard_c returns the number of intervals
          in a SPICE window.
          */
          winsiz = wncard_c( &viswin );

          if ( winsiz == 0 )
          {
             printf ( "No events were found.\n" );
          }
          else
          {
             /*
             Display the visibility time periods.
             */
             printf ( "Visibility times of %s as seen from %s:"
                      "\n\n",
                      target, srfpt                               );

             for (  i = 0;   i < winsiz;   i++  )
             {
                /*
                Fetch the start and stop times of the Ith interval
                from the search result window viswin.
                */
                wnfetd_c ( &viswin, i, &intbeg, &intend );

                /*
                Convert the rise time to a TDB calendar string.
                */
                timout_c ( intbeg, TDBFMT, TIMLEN, timstr );

                /*
                Write the string to standard output.
                */
                if ( i == 0 )
                {
                   printf ( "Visibility or window start time:  %s\n",
                             timstr                                  );
                }
                else
                {
                   printf ( "Visibility start time:            %s\n",
                             timstr                                  );
                }

                /*
                Convert the set time to a TDB calendar string.
                */
                timout_c ( intend, TDBFMT, TIMLEN, timstr );

                /*
                Write the string to standard output.
                */
                if ( i == winsiz-1 )
                {
                   printf ( "Visibility or window stop time:   %s\n",
                             timstr                                  );
                }
                else
                {
                   printf ( "Visibility stop time:             %s\n",
                             timstr                                  );
                }

                printf ( "\n" );
             }
          }

          return ( 0 );
       }
Top ### Solution Sample Output Numerical results shown for this example may differ across platforms since the results depend on the SPICE kernels used as input and on the host platform's arithmetic implementation. After compiling the program, execute it. The output is:
       Inputs for target visibility search:

          Target                       = TGO
          Observation surface location = NEW_NORCIA
          Observer's reference frame   = NEW_NORCIA_TOPO
          Blocking body                = MARS
          Blocker's reference frame    = IAU_MARS
          Elevation limit (degrees)    = 6.000000
          Aberration correction        = CN+S
          Step size (seconds)          = 300.000000
          Start time                   = 2018 JUN 10 00:00:00.000 (TDB)
          Stop time                    = 2018 JUN 14 00:00:00.000 (TDB)

       Visibility times of TGO as seen from NEW_NORCIA:

       Visibility or window start time:  2018 JUN 10 00:00:00.000 (TDB)
       Visibility stop time:             2018 JUN 10 01:00:30.640 (TDB)

       Visibility start time:            2018 JUN 10 01:41:03.610 (TDB)
       Visibility stop time:             2018 JUN 10 02:11:17.355 (TDB)

       Visibility start time:            2018 JUN 10 13:28:28.785 (TDB)
       Visibility stop time:             2018 JUN 10 14:45:38.197 (TDB)

       Visibility start time:            2018 JUN 10 15:26:21.981 (TDB)
       Visibility stop time:             2018 JUN 10 16:43:32.192 (TDB)

       Visibility start time:            2018 JUN 10 17:24:17.290 (TDB)
       Visibility stop time:             2018 JUN 10 18:41:27.535 (TDB)

       Visibility start time:            2018 JUN 10 19:22:13.628 (TDB)
       Visibility stop time:             2018 JUN 10 20:39:21.785 (TDB)

       Visibility start time:            2018 JUN 10 21:20:08.856 (TDB)
       Visibility stop time:             2018 JUN 10 22:37:12.445 (TDB)

       Visibility start time:            2018 JUN 10 23:18:00.834 (TDB)
       Visibility stop time:             2018 JUN 11 00:35:01.034 (TDB)

       Visibility start time:            2018 JUN 11 01:15:50.883 (TDB)
       Visibility stop time:             2018 JUN 11 02:08:16.008 (TDB)

       Visibility start time:            2018 JUN 11 13:16:50.542 (TDB)
       Visibility stop time:             2018 JUN 11 14:20:09.789 (TDB)

       Visibility start time:            2018 JUN 11 15:01:08.370 (TDB)
       Visibility stop time:             2018 JUN 11 16:18:03.385 (TDB)

       Visibility start time:            2018 JUN 11 16:59:03.014 (TDB)
       Visibility stop time:             2018 JUN 11 18:15:58.739 (TDB)

       Visibility start time:            2018 JUN 11 18:56:59.199 (TDB)
       Visibility stop time:             2018 JUN 11 20:13:54.308 (TDB)

       Visibility start time:            2018 JUN 11 20:54:55.301 (TDB)
       Visibility stop time:             2018 JUN 11 22:11:47.045 (TDB)

       Visibility start time:            2018 JUN 11 22:52:48.925 (TDB)
       Visibility stop time:             2018 JUN 12 00:09:35.868 (TDB)

       Visibility start time:            2018 JUN 12 00:50:39.046 (TDB)
       Visibility stop time:             2018 JUN 12 02:05:12.548 (TDB)

       Visibility start time:            2018 JUN 12 13:13:38.573 (TDB)
       Visibility stop time:             2018 JUN 12 13:54:43.524 (TDB)

       Visibility start time:            2018 JUN 12 14:35:54.054 (TDB)
       Visibility stop time:             2018 JUN 12 15:52:36.256 (TDB)

       Visibility start time:            2018 JUN 12 16:33:47.502 (TDB)
       Visibility stop time:             2018 JUN 12 17:50:30.988 (TDB)

       Visibility start time:            2018 JUN 12 18:31:42.896 (TDB)
       Visibility stop time:             2018 JUN 12 19:48:26.827 (TDB)

       Visibility start time:            2018 JUN 12 20:29:39.039 (TDB)
       Visibility stop time:             2018 JUN 12 21:46:20.933 (TDB)

       Visibility start time:            2018 JUN 12 22:27:33.596 (TDB)
       Visibility stop time:             2018 JUN 12 23:44:11.473 (TDB)

       Visibility start time:            2018 JUN 13 00:25:24.992 (TDB)
       Visibility stop time:             2018 JUN 13 01:42:00.777 (TDB)

       Visibility start time:            2018 JUN 13 13:10:23.432 (TDB)
       Visibility stop time:             2018 JUN 13 13:29:19.789 (TDB)

       Visibility start time:            2018 JUN 13 14:10:38.985 (TDB)
       Visibility stop time:             2018 JUN 13 15:27:11.882 (TDB)

       Visibility start time:            2018 JUN 13 16:08:31.566 (TDB)
       Visibility stop time:             2018 JUN 13 17:25:06.068 (TDB)

       Visibility start time:            2018 JUN 13 18:06:26.219 (TDB)
       Visibility stop time:             2018 JUN 13 19:23:01.820 (TDB)

       Visibility start time:            2018 JUN 13 20:04:22.175 (TDB)
       Visibility stop time:             2018 JUN 13 21:20:57.296 (TDB)

       Visibility start time:            2018 JUN 13 22:02:17.650 (TDB)
       Visibility or window stop time:   2018 JUN 13 23:18:49.624 (TDB)
Top # Extra Credit In this ``extra credit'' section you will be presented with more complex tasks, aimed at improving your understanding of the geometry event finding subsystem and particularly the gfposc_c and gfdist_c functions. These ``extra credit'' tasks are provided as task statements, and unlike the regular tasks, no approach or solution source code is provided. In the next section, you will find the numeric solutions to the questions asked in these tasks. Top ## Task statements `1.` Write a program that finds the times, within the time range
             2018 JUN 10 TDB
             2018 JUN 11 TDB
`` when the ExoMars-16 Trace Gas Orbiter (TGO) crosses Mars' equator. Display the results using TDB calendar dates and millisecond precision. `2.` Write a program that finds the times, within the time range
             2018 JUN 10 TDB
             2018 JUN 11 TDB
`` when the ExoMars-16 Trace Gas Orbiter (TGO) is at periapsis. Display the results using TDB calendar dates and millisecond precision. `3.` Write a program that finds the times, within the time range
             2018 JUN 10 TDB
             2018 JUN 11 TDB
`` when the ExoMars-16 Trace Gas Orbiter (TGO) is at apoapsis. Display the results using TDB calendar dates and millisecond precision. Top ## Solutions
       1. Inputs for the equator crossing search, using gfposc_c for
       the spacecraft latitude in the Mars body-fixed frame equal to 0:

             Target                       = TGO
             Observer                     = MARS
             Observer's reference frame   = IAU_MARS
             Elevation limit (degrees)    = 0.000000
             Aberration correction        = NONE
             Step size (seconds)          = 300.000000
             Start time                   = 2018 JUN 10 00:00:00.000 (TDB)
             Stop time                    = 2018 JUN 11 00:00:00.000 (TDB)

          TGO Mars' equator crossing times:

          Equator crossing time:            2018 JUN 10 00:14:08.836 (TDB)
          Equator crossing time:            2018 JUN 10 01:12:34.582 (TDB)
          Equator crossing time:            2018 JUN 10 02:12:00.375 (TDB)
          Equator crossing time:            2018 JUN 10 03:10:28.808 (TDB)
          Equator crossing time:            2018 JUN 10 04:09:53.955 (TDB)
          Equator crossing time:            2018 JUN 10 05:08:23.919 (TDB)
          Equator crossing time:            2018 JUN 10 06:07:48.630 (TDB)
          Equator crossing time:            2018 JUN 10 07:06:17.539 (TDB)
          Equator crossing time:            2018 JUN 10 08:05:42.659 (TDB)
          Equator crossing time:            2018 JUN 10 09:04:09.120 (TDB)
          Equator crossing time:            2018 JUN 10 10:03:34.270 (TDB)
          Equator crossing time:            2018 JUN 10 11:01:59.269 (TDB)
          Equator crossing time:            2018 JUN 10 12:01:22.866 (TDB)
          Equator crossing time:            2018 JUN 10 12:59:49.352 (TDB)
          Equator crossing time:            2018 JUN 10 13:59:13.289 (TDB)
          Equator crossing time:            2018 JUN 10 14:57:41.242 (TDB)
          Equator crossing time:            2018 JUN 10 15:57:07.576 (TDB)
          Equator crossing time:            2018 JUN 10 16:55:35.266 (TDB)
          Equator crossing time:            2018 JUN 10 17:55:02.773 (TDB)
          Equator crossing time:            2018 JUN 10 18:53:30.271 (TDB)
          Equator crossing time:            2018 JUN 10 19:52:56.383 (TDB)
          Equator crossing time:            2018 JUN 10 20:51:23.966 (TDB)
          Equator crossing time:            2018 JUN 10 21:50:47.729 (TDB)
          Equator crossing time:            2018 JUN 10 22:49:14.385 (TDB)
          Equator crossing time:            2018 JUN 10 23:48:37.583 (TDB)

       2. Inputs for the periapsis search, using gfdist_c for the
       spacecraft distance from Mars at a local minimum:

             Target                       = TGO
             Observer                     = MARS
             Observer's reference frame   = J2000
             Aberration correction        = NONE
             Step size (seconds)          = 300.000000
             Start time                   = 2018 JUN 10 00:00:00.000 (TDB)
             Stop time                    = 2018 JUN 11 00:00:00.000 (TDB)

          TGO periapsis times:

          Periapsis time:                   2018 JUN 10 00:43:06.357 (TDB)
          Periapsis time:                   2018 JUN 10 02:40:47.168 (TDB)
          Periapsis time:                   2018 JUN 10 04:38:45.496 (TDB)
          Periapsis time:                   2018 JUN 10 06:36:32.706 (TDB)
          Periapsis time:                   2018 JUN 10 08:34:10.548 (TDB)
          Periapsis time:                   2018 JUN 10 10:31:49.108 (TDB)
          Periapsis time:                   2018 JUN 10 12:29:20.342 (TDB)
          Periapsis time:                   2018 JUN 10 14:27:07.089 (TDB)
          Periapsis time:                   2018 JUN 10 16:25:36.081 (TDB)
          Periapsis time:                   2018 JUN 10 18:24:02.653 (TDB)
          Periapsis time:                   2018 JUN 10 20:22:23.184 (TDB)
          Periapsis time:                   2018 JUN 10 22:20:12.453 (TDB)

       3. Inputs for the apoapsis search, using gfdist_c for the
       spacecraft distance from Mars at a local maximum:

             Target                       = TGO
             Observer                     = MARS
             Observer's reference frame   = J2000
             Aberration correction        = NONE
             Step size (seconds)          = 300.000000
             Start time                   = 2018 JUN 10 00:00:00.000 (TDB)
             Stop time                    = 2018 JUN 11 00:00:00.000 (TDB)

          TGO apoapsis times:

          Apoapsis time:                    2018 JUN 10 01:41:44.632 (TDB)
          Apoapsis time:                    2018 JUN 10 03:39:31.106 (TDB)
          Apoapsis time:                    2018 JUN 10 05:37:22.115 (TDB)
          Apoapsis time:                    2018 JUN 10 07:34:59.674 (TDB)
          Apoapsis time:                    2018 JUN 10 09:32:25.708 (TDB)
          Apoapsis time:                    2018 JUN 10 11:29:47.945 (TDB)
          Apoapsis time:                    2018 JUN 10 13:27:30.200 (TDB)
          Apoapsis time:                    2018 JUN 10 15:26:02.524 (TDB)
          Apoapsis time:                    2018 JUN 10 17:24:37.842 (TDB)
          Apoapsis time:                    2018 JUN 10 19:23:11.265 (TDB)
          Apoapsis time:                    2018 JUN 10 21:21:13.530 (TDB)
          Apoapsis time:                    2018 JUN 10 23:18:56.796 (TDB)