Main Page Geometric Event Finding Hands-On Lesson, using TGO (MATLAB)
## Table of Contents
       Geometric Event Finding Hands-On Lesson, using TGO (MATLAB)
          Overview
          Note About HTML Links
          References
             Tutorials
             Required Readings
             The Permuted Index
             Mice API Documentation
          Kernels Used
          Mice Modules 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 Meta-Kernel
             Solution Code
             Solution Sample Output
       Extra Credit
          Task statements
          Solutions
Top # Geometric Event Finding Hands-On Lesson, using TGO (MATLAB) May 21, 2018 Top ## Overview This lesson illustrates how the Geometry Finder (GF) subsystem of the Mice 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, if not done already by installing the lessons package under the Toolkit's ``doc/html'' directory, create a subdirectory called ``lessons'' under the ``doc/html'' directory of the ``mice/'' tree and copy this document to that subdirectory before loading it into a Web browser. Top ## References This section lists SPICE documents referred to in this lesson. Of these documents, the ``Tutorials'' contains the highest level descriptions with the least number of details while the ``Required Reading'' documents contain much more detailed specifications. The most complete specifications are provided in the ``API Documentation''. In some cases the lesson explanations also refer to the information provided in the meta-data area of the kernels used in the lesson examples. It is especially true in case of the FK and IK files, which often contain comprehensive descriptions of the frames, instrument FOVs, etc. Since both FK and IK are text kernels, the information provided in them can be viewed using any text editor, while the meta information provided in binary kernels -- SPKs and CKs -- can be viewed using ``commnt'' or ``spacit'' utility programs located in ``mice/exe'' of Toolkit installation tree. 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 Finder (GF) subsystem
       DSK               Detailed Target Shape (Topography) Data
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 ``mice/doc'' directory in the Mice installation tree.
       Name             Lesson steps/functions that it describes
       ---------------  -----------------------------------------
       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
       mice.req         The Mice API
Top ### The Permuted Index Another useful document distributed with the Toolkit is the permuted index. This is located under the ``mice/doc'' directory in the MATLAB installation tree. This text document provides a simple mechanism by which users can discover which Mice functions perform functions of interest, as well as the names of the source files that contain these functions.
Top ### Mice API Documentation A Mice routine's specification is found in the HTML API documentation page located under ``mice/doc/html/mice''. For example, the document
       mice/doc/html/mice/cspice_str2et.html
describes the cspice_str2et routine. 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. Low-resolution Mars DSK:

              mars_lowres.bds
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 ## Mice Modules Used This section provides a complete list of the functions and kernels that are suggested for usage in each of the exercises in this lesson. (You may wish to not look at this list unless/until you ``get stuck'' while working on your own.)
       CHAPTER EXERCISE   FUNCTIONS      NON-VOID       KERNELS
       ------- ---------  -------------  -------------  ----------
          1    viewpr     cspice_furnsh  cspice_rpd     1-9
                          cspice_kclear  cspice_str2et
                                         cspice_timout
                                         cspice_wninsd
                                         cspice_gfposc
                                         cspice_wnfetd

          2    visibl     cspice_furnsh  cspice_rpd     1-10
                          cspice_unload  cspice_str2et
                                         cspice_timout
                                         cspice_wninsd
                                         cspice_gfposc
                                         cspice_gfoclt
                                         cspice_wndifd
                                         cspice_wncard
                                         cspice_wnfetd

               extra (*)                 cspice_gfdist  1-2,7-9

          (*) Additional APIs and kernels used in Extra Credit tasks.
Refer to the Mice HTML API documentation pages located under ``mice/doc/html/mice'' for detailed interface specifications of these functions. 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.` 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. `2.` 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 cspice_furnsh to load the meta-kernel. `2.` Insert the given time bounds into the confinement window using cspice_wninsd. `3.` 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. `4.` Use the GF routine cspice_gfposc to find the window of times, within the confinement window, during which the ExoMars-16 TGO spacecraft is above the elevation limit as seen from ESA's New Norcia station, in 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. `5.` Fetch and display the contents of the result window. Use cspice_wnfetd 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 cspice_timout. You may find it useful to consult the references listed above. In particular, the header of the SPICE GF function cspice_gfposc 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.

          The names and contents of the kernels referenced by this
          meta-kernel are as follows:

             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

       \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'

                            )

       \begintext
Top ### Solution Code The example program below shows one possible solution.
       %
       % 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.
       %
       function viewpr()

       %
       % The meta-kernel:
       %
       META   = 'viewpr.tm';

       %
       % Maximum number of intervals in any window:
       %
       MAXIVL = 1000;

       %
       % Time string length:
       %
       TIMLEN = 50;

       %
       % Format string for time output:
       %
       TDBFMT = 'YYYY MON DD HR:MN:SC.### (TDB) ::TDB';

       %
       % Load the meta-kernel.
       %
       cspice_furnsh( META );

       %
       % 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 cspice_gfoclt.
       %
       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 = cspice_rpd() * 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:
       %

       disp( ' ' );
       disp( 'Inputs for target visibility search:' );
       disp( ' ' );

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

       %
       % Convert the start and stop times to ET.
       %
       etbeg = cspice_str2et( start );
       etend = cspice_str2et( stop  );

       %
       % Display the search interval start time and stop
       % times using the format shown below.
       %
       %     2004 MAY 06 20:15:00.000 (TDB)
       %
       timstr0 = cspice_timout( etbeg, TDBFMT );
       timstr1 = cspice_timout( etend, TDBFMT );

       fprintf( '   Start time                   = %s\n', timstr0 );
       fprintf( '   Stop time                    = %s\n', timstr1 );
       disp( ' ' );

       %
       % Create the "confinement" window; store in this window
       % the interval over which we'll conduct the search.
       %
       cnfine = cspice_wninsd( etbeg, etend );

       %
       % In the call below, the maximum number of window
       % intervals cspice_gfposc can store internally is
       % set to MAXIVL. We'll also use MAXIVL as the maximum
       % number of intervals in the result window.
       %
       % Now search for the time period, within our confinement
       % window, during which the apparent target has elevation
       % at least equal to the elevation limit.
       %
       riswin = cspice_gfposc ( target, obsfrm, abcorr, srfpt,  ...
                                crdsys, coord,  relate, revlim, ...
                                adjust, stepsz, MAXIVL, cnfine     );

       %
       % Let winsiz contain the number of intervals
       % in the SPICE window riswin.
       %
       winsiz = length( riswin )/2;

       %
       % Display the rise and set times.
       %

       if  winsiz == 0

          disp( 'No events were found.' );

       else

          %
          %  Display the visibility time periods.
          %
          fprintf( [ 'Visibility times of %s '  ...
                     'as seen from %s:\n\n' ], target, srfpt );

          for i = 1:winsiz

             %
             % Fetch the Ith interval from the window.
             %
             [intbeg, intend] = cspice_wnfetd( riswin, i );

             %
             % Convert the rise time to a TDB calendar string.
             %
             timstr = cspice_timout( intbeg, TDBFMT );

             %
             % Write the string to standard output.
             %
             if  i == 1

                line = 'Visibility or window start time:  ';

             else

                line = 'Visibility start time:            ';

             end

             fprintf( '%s%s\n', line, timstr );

             %
             % Convert the set time to a TDB calendar string.
             %
             timstr = cspice_timout( intend, TDBFMT );

             %
             % Write the string to standard output.
             %
             if  i == winsiz

                line = 'Visibility or window stop time:   ';

             else

                line = 'Visibility stop time:             ';

             end

             fprintf( '%s%s\n\n', line, timstr );

          end

       end

       %
       % Unload kernels so they are not accidentally used by another
       % SPICE-based program during the current MATLAB session.
       %
       cspice_kclear;

       %
       % End of function viewpr
       %
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. Execute the program. 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 Finding time intervals that satisfy the second condition requires a search for occultations of the spacecraft by Mars. Perform this search twice: once using an ellipsoidal shape model for Mars, and once using a DSK shape model. Compute the final results twice as well, using the results of both occultation searches. For each of the two shape model cases, store the set of time intervals when the spacecraft is visible in a Mice 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 cspice_gfoclt. Experience with Digital Shape Kernel (DSK) shape models. Further experience with the Mice window functions. Top ## Approach Top ### Solution steps A possible solution would consist of the following steps: `1.` Use the meta-kernel from the previous chapter as the starting point. Add more kernels to it as needed. `` Name the meta-kernel 'visibl.tm'. `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.` The remaining steps can be performed twice: once using an ellipsoidal shape model for Mars, and once using a DSK Mars shape model. Alternatively, two copies of the entire solution program can be created: one for each shape model. `4.` Search for occultations of the ExoMars-16 TGO orbiter as seen from New Norcia station using cspice_gfoclt. Use as the confinement window for this search the result window from the elevation search performed by cspice_gfposc. `` 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 Mice window subtraction routine cspice_wndifd 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 is the final result. `6.` Modify the code to display the contents of the difference window. This completes the assignment. Top ## Solution Top ### Solution Meta-Kernel The meta-kernel we created for the solution to this exercise is named 'visibl.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.

          The names and contents of the kernels referenced by this
          meta-kernel are as follows:

             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. Low-resolution Mars DSK:

                   mars_lowres.bds

       \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/dsk/mars_lowres.bds'

                            )

       \begintext
Top ### Solution Code
       %
       % 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.
       %
       function visibl_m()

       %
       % The meta-kernel:
       %
       METAKR = 'visibl.tm';

       %
       % MAXIVL is the maximum number of result window intervals.
       %
       MAXIVL = 1000;

       %
       % Format string for time output:
       %
       TDBFMT = 'YYYY MON DD HR:MN:SC.### TDB ::TDB';

       %
       % Load the meta-kernel.
       %
       cspice_furnsh( 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 cspice_gfoclt.
       %
       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 = cspice_rpd() * elvlim;

       %
       % We model the target shape as a point. We either model the
       % blocking body's shape as an ellipsoid, or we represent
       % its shape using actual topographic data. No body-fixed
       % reference frame is required for the target since its
       % orientation is not used.
       %
       back   = target;
       bshape = 'POINT';
       bframe = ' ';
       front  = 'MARS';
       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:
       %

       disp( ' ' );
       disp( 'Inputs for target visibility search:' )
       disp( ' ' );

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

       %
       % Convert the start and stop times to ET.
       %
       etbeg = cspice_str2et( start );
       etend = cspice_str2et( stop  );

       %
       % Display the search interval start time and stop
       % times using the format shown below.
       %
       %     2004 MAY 06 20:15:00.000 (TDB)
       %
       timstr0 = cspice_timout( etbeg, TDBFMT );
       timstr1 = cspice_timout( etend, TDBFMT );

       fprintf( '   Start time                   = %s\n', timstr0 )
       fprintf( '   Stop time                    = %s\n', timstr1 )
       disp( ' ' );

       %
       % Create the "confinement" window; store in this window
       % the interval over which we'll conduct the search.
       %
       cnfine = cspice_wninsd( etbeg, etend );

       %
       % In the call below, the maximum number of window
       % intervals cspice_gfposc can store internally is
       % set to MAXIVL. We'll also use MAXIVL as the maximum
       % number of intervals in the result window.
       %
       % Now search for the time period, within our confinement
       % window, during which the apparent target has elevation
       % at least equal to the elevation limit.
       %
       riswin = cspice_gfposc( target, obsfrm, abcorr, srfpt,  ...
                               crdsys, coord,  relate, revlim, ...
                               adjust, stepsz, MAXIVL, cnfine    );

       %
       % 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.
       %
       fprintf( ' Searching using ellipsoid target shape model...\n' )

       fshape = 'ELLIPSOID';

       eocwin = cspice_gfoclt( occtyp, front,  fshape, fframe, ...
                               back,   bshape, bframe, abcorr, ...
                               srfpt,  stepsz, riswin, MAXIVL    );
       fprintf( ' Done.\n' )

       %
       % Subtract the occultation window from the view period
       % window: this yields the time periods when the target
       % is visible.
       %
       evswin = cspice_wndifd( riswin, eocwin );

       %
       % Repeat the search using low-resolution DSK data
       % for the front body.
       %
       fprintf( ' Searching using DSK target shape model...\n' )

       fshape = 'DSK/UNPRIORITIZED';

       docwin = cspice_gfoclt( occtyp, front,  fshape, fframe, ...
                               back,   bshape, bframe, abcorr, ...
                               srfpt,  stepsz, riswin, MAXIVL   );
       fprintf( ' Done.\n\n' )

       dvswin = cspice_wndifd( riswin, docwin );

       %
       % The function cspice_wncard returns the number of intervals
       % in a SPICE window.
       %
       winsiz = cspice_wncard( evswin );

       %
       % Display the rise and set times.
       %
       if  winsiz == 0

          disp( 'No events were found.' );

       else
          %
          %  Display the visibility time periods.
          %
          fprintf( [ 'Visibility start and stop times of %s ' ...
                     'as seen from %s\n'                      ...
                     'using both ellipsoidal and DSK target ' ...
                     'shape models:\n\n' ],  target, srfpt )

          for i = 1:winsiz
             %
             % Fetch the start and stop times of the ith interval
             % from the ellipsoid search result window evswin.
             %
             [intbeg, intend] = cspice_wnfetd( evswin, i );

             %
             % Convert the rise and set times to TDB calendar strings.
             % Write the results.
             %
             btmstr = cspice_timout( intbeg, TDBFMT );
             etmstr = cspice_timout( intend, TDBFMT );

             fprintf( ' Ell: %s : %s\n', btmstr, etmstr )

             %
             % Fetch the start and stop times of the ith interval
             % from the DSK search result window dvswin.
             %
             [dintbg, dinten] = cspice_wnfetd( dvswin, i );

             %
             % Convert the rise and set times to TDB calendar strings.
             % Write the results.
             %
             btmstr = cspice_timout( dintbg, TDBFMT );
             etmstr = cspice_timout( dinten, TDBFMT );

             fprintf( ' DSK: %s : %s\n\n', btmstr, etmstr )

          end

       end

       %
       % Unload kernels so they're not accidentally used by another
       % SPICE-based program during the current MATLAB session.
       %
       cspice_unload( METAKR );

       %
       % End of function visibl
       %
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. Execute the program. 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

        Searching using ellipsoid target shape model...
        Done.
        Searching using DSK target shape model...
        Done.

       Visibility start and stop times of TGO as seen from NEW_NORCIA
       using both ellipsoidal and DSK target shape models:

        Ell: 2018 JUN 10 00:00:00.000 TDB : 2018 JUN 10 01:00:30.640 TDB
        DSK: 2018 JUN 10 00:00:00.000 TDB : 2018 JUN 10 01:00:28.220 TDB

        Ell: 2018 JUN 10 01:41:03.610 TDB : 2018 JUN 10 02:11:17.355 TDB
        DSK: 2018 JUN 10 01:41:01.630 TDB : 2018 JUN 10 02:11:17.355 TDB

        Ell: 2018 JUN 10 13:28:28.785 TDB : 2018 JUN 10 14:45:38.197 TDB
        DSK: 2018 JUN 10 13:28:26.205 TDB : 2018 JUN 10 14:45:35.493 TDB

        Ell: 2018 JUN 10 15:26:21.981 TDB : 2018 JUN 10 16:43:32.192 TDB
        DSK: 2018 JUN 10 15:26:19.598 TDB : 2018 JUN 10 16:43:28.927 TDB

        Ell: 2018 JUN 10 17:24:17.290 TDB : 2018 JUN 10 18:41:27.535 TDB
        DSK: 2018 JUN 10 17:24:15.690 TDB : 2018 JUN 10 18:41:24.797 TDB

        Ell: 2018 JUN 10 19:22:13.628 TDB : 2018 JUN 10 20:39:21.785 TDB
        DSK: 2018 JUN 10 19:22:12.222 TDB : 2018 JUN 10 20:39:19.310 TDB

        Ell: 2018 JUN 10 21:20:08.856 TDB : 2018 JUN 10 22:37:12.445 TDB
        DSK: 2018 JUN 10 21:20:07.160 TDB : 2018 JUN 10 22:37:09.488 TDB

        Ell: 2018 JUN 10 23:18:00.834 TDB : 2018 JUN 11 00:35:01.034 TDB
        DSK: 2018 JUN 10 23:17:58.772 TDB : 2018 JUN 11 00:34:58.698 TDB

        Ell: 2018 JUN 11 01:15:50.883 TDB : 2018 JUN 11 02:08:16.008 TDB
        DSK: 2018 JUN 11 01:15:48.915 TDB : 2018 JUN 11 02:08:16.008 TDB

        Ell: 2018 JUN 11 13:16:50.542 TDB : 2018 JUN 11 14:20:09.789 TDB
        DSK: 2018 JUN 11 13:16:50.542 TDB : 2018 JUN 11 14:20:07.002 TDB

        Ell: 2018 JUN 11 15:01:08.370 TDB : 2018 JUN 11 16:18:03.385 TDB
        DSK: 2018 JUN 11 15:01:05.872 TDB : 2018 JUN 11 16:18:00.245 TDB

        Ell: 2018 JUN 11 16:59:03.014 TDB : 2018 JUN 11 18:15:58.739 TDB
        DSK: 2018 JUN 11 16:59:00.798 TDB : 2018 JUN 11 18:15:55.713 TDB

        Ell: 2018 JUN 11 18:56:59.199 TDB : 2018 JUN 11 20:13:54.308 TDB
        DSK: 2018 JUN 11 18:56:57.725 TDB : 2018 JUN 11 20:13:51.980 TDB

        Ell: 2018 JUN 11 20:54:55.301 TDB : 2018 JUN 11 22:11:47.045 TDB
        DSK: 2018 JUN 11 20:54:53.724 TDB : 2018 JUN 11 22:11:44.029 TDB

        Ell: 2018 JUN 11 22:52:48.925 TDB : 2018 JUN 12 00:09:35.868 TDB
        DSK: 2018 JUN 11 22:52:47.004 TDB : 2018 JUN 12 00:09:33.513 TDB

        Ell: 2018 JUN 12 00:50:39.046 TDB : 2018 JUN 12 02:05:12.548 TDB
        DSK: 2018 JUN 12 00:50:37.040 TDB : 2018 JUN 12 02:05:12.548 TDB

        Ell: 2018 JUN 12 13:13:38.573 TDB : 2018 JUN 12 13:54:43.524 TDB
        DSK: 2018 JUN 12 13:13:38.573 TDB : 2018 JUN 12 13:54:41.265 TDB

        Ell: 2018 JUN 12 14:35:54.054 TDB : 2018 JUN 12 15:52:36.256 TDB
        DSK: 2018 JUN 12 14:35:51.624 TDB : 2018 JUN 12 15:52:34.091 TDB

        Ell: 2018 JUN 12 16:33:47.502 TDB : 2018 JUN 12 17:50:30.988 TDB
        DSK: 2018 JUN 12 16:33:45.089 TDB : 2018 JUN 12 17:50:29.020 TDB

        Ell: 2018 JUN 12 18:31:42.896 TDB : 2018 JUN 12 19:48:26.827 TDB
        DSK: 2018 JUN 12 18:31:41.085 TDB : 2018 JUN 12 19:48:23.878 TDB

        Ell: 2018 JUN 12 20:29:39.039 TDB : 2018 JUN 12 21:46:20.933 TDB
        DSK: 2018 JUN 12 20:29:37.575 TDB : 2018 JUN 12 21:46:18.430 TDB

        Ell: 2018 JUN 12 22:27:33.596 TDB : 2018 JUN 12 23:44:11.473 TDB
        DSK: 2018 JUN 12 22:27:31.895 TDB : 2018 JUN 12 23:44:08.681 TDB

        Ell: 2018 JUN 13 00:25:24.992 TDB : 2018 JUN 13 01:42:00.777 TDB
        DSK: 2018 JUN 13 00:25:22.950 TDB : 2018 JUN 13 01:41:58.417 TDB

        Ell: 2018 JUN 13 13:10:23.432 TDB : 2018 JUN 13 13:29:19.789 TDB
        DSK: 2018 JUN 13 13:10:23.432 TDB : 2018 JUN 13 13:29:18.021 TDB

        Ell: 2018 JUN 13 14:10:38.985 TDB : 2018 JUN 13 15:27:11.882 TDB
        DSK: 2018 JUN 13 14:10:36.850 TDB : 2018 JUN 13 15:27:09.686 TDB

        Ell: 2018 JUN 13 16:08:31.566 TDB : 2018 JUN 13 17:25:06.068 TDB
        DSK: 2018 JUN 13 16:08:29.172 TDB : 2018 JUN 13 17:25:04.013 TDB

        Ell: 2018 JUN 13 18:06:26.219 TDB : 2018 JUN 13 19:23:01.820 TDB
        DSK: 2018 JUN 13 18:06:23.924 TDB : 2018 JUN 13 19:22:59.754 TDB

        Ell: 2018 JUN 13 20:04:22.175 TDB : 2018 JUN 13 21:20:57.296 TDB
        DSK: 2018 JUN 13 20:04:20.652 TDB : 2018 JUN 13 21:20:54.998 TDB

        Ell: 2018 JUN 13 22:02:17.650 TDB : 2018 JUN 13 23:18:49.624 TDB
        DSK: 2018 JUN 13 22:02:16.147 TDB : 2018 JUN 13 23:18:47.458 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 cspice_gfposc and cspice_gfdist 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.` Solution for the equator crossing search, using cspice_gfposc for the ExoMars-16 Trace Gas Orbiter (TGO) spacecraft latitude in the Mars body-fixed frame equal to 0 degrees:
       Inputs for equator crossing search:

          Target                       = TGO
          Observer                     = MARS
          Observer's reference frame   = IAU_MARS
          Latitude 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 or start 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 or stop time:   2018 JUN 10 23:48:37.583 (TDB)
`2.` Solution for the periapsis search, using cspice_gfdist for the ExoMars-16 Trace Gas Orbiter (TGO) spacecraft distance from Mars at a local minimum:
       Inputs for periapsis search:

          Target                       = TGO
          Observer                     = MARS
          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 or start 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 or end time:           2018 JUN 10 22:20:12.453 (TDB)
`3.` Solution for the apoapsis search, using cspice_gfdist for the ExoMars-16 Trace Gas Orbiter (TGO) spacecraft distance from Mars at a local maximum:
       Inputs for apoapsis search:

          Target                       = TGO
          Observer                     = MARS
          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 or start 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 or stop time:           2018 JUN 10 23:18:56.796 (TDB)