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Required Reading


   CSPICE_DSKXV computes ray-surface intercepts for a set of rays,
   using data provided by multiple loaded DSK segments.



      pri        is a logical flag indicating whether to perform
                 a prioritized or unprioritized DSK segment search.
                 In an unprioritized search, no segment masks another:
                 data from all specified segments are used to
                 define the surface of interest.

                 [1,1] = size(pri); logical = class(pri)

                 The search is unprioritized if and only if `pri'
                 is set to false. In the N0066 SPICE Toolkit, this
                 is the only allowed value.

      target     is the name of the target body on which a surface
                 intercept is sought.

                 [1,c1] = size(target); char = class(target)


                 [1,1] = size(target); cell = class(target)

      srflst     are, respectively, a count of surface ID codes in a
                 list and an containing the list. Only DSK segments for
                 for the body designated by `target' and having surface
                 IDs in this list will considered in the intercept
                 computation. If the list is empty, all DSK segments
                 for `target' will be considered.

      et         is the epoch of the intersection computation,
                 expressed as seconds past J2000 TDB. This epoch is
                 used only for DSK segment selection. Segments used
                 the intercept computation must include `et' in their
                 time coverage intervals.

      fixref     is the name of a body-fixed, body-centered reference
                 frame associated with the target. The input ray vectors
                 are specified in this frame, as is the output intercept

                 [1,c2] = size(fixref); char = class(fixref)


                 [1,1] = size(fixref); cell = class(fixref)

                 The frame designated by `fixref' must have a fixed
                 orientation relative to the frame of any DSK segment
                 used in the computation.

      dirarr     are, respectively, a count of rays, an array containing
                 the vertices of rays, and an array containing the
                 direction vectors of the rays.

                 [3,n] = size(vtxarr); double = class(vtxarr)
                 [3,n] = size(dirarr); double = class(dirarr)

                 The ray's vertices are considered to represent offsets
                 from the center of the target body.

                 The rays' vertices and direction vectors are
                 represented in the reference frame designated by

   the call:

      [ xptarr, fndarr] = cspice_dskxsi( pri,             ...
                                         target, nsurf,   ...
                                         srflst, et,      ...
                                         fixref, vtxarr,  ...
                                         dirarr )


      xptarr     is an array containing the intercepts of the input
                 rays on the surface specified by the inputs


                 [3,n] = size(xptarr); double = class(xptarr)

                 The ith element of `xptarr' is the intercept
                 corresponding to the ith ray, if such an intercept
                 exists. If a ray intersects the surface at multiple
                 points, the intercept closest to the ray's vertex is

                 The ith element of `xptarr' is defined if and only if the
                 ith element of `fndarr' is true.

                 Units are km.

      fndarr     is an array of logical flags indicating whether the
                 input rays intersect the surface. The ith element of
                 `fndarr' is set to true if and only if an intercept
                 was found for the ith ray.

                 [1,n] = size(fndarr); logical = class(fndarr)


   Any numerical results shown for this example may differ between
   platforms as the results depend on the SPICE kernels used as input
   and the machine specific arithmetic implementation.

   Example (1):

      Compute surface intercepts of rays emanating from a set of
      vertices distributed on a longitude-latitude grid. All
      vertices are outside the target body, and all rays point
      toward the target's center.

      Check intercepts against expected values. Indicate the
      number of errors, the number of computations, and the
      number of intercepts found.

      Use the meta-kernel shown below to load example SPICE



          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
             ---------                        --------
             phobos512.bds                    DSK based on
                                              Gaskell ICQ Q=512
                                              plate model

             PATH_SYMBOLS    = 'GEN'
             PATH_VALUES     = '/ftp/pub/naif/generic_kernels'

             KERNELS_TO_LOAD = ( '$GEN/dsk/phobos/phobos512.bds' )


      function dskxv_t( META )

         % This program expects all loaded DSKs
         % to represent the same body and surface.

         % MiceUser globally defines DSK parameters.
         % For more information, please see DSKMiceUser.m and
         % DSKMice02.m.

         DTOL  = 1.0e-14;
         MAXN  = 100000;
         dirarr = zeros( 3, MAXN );
         vtxarr = zeros( 3, MAXN );

         % Get meta-kernel name from the command line.
         switch nargin
            case 1

               % Load the meta-kernel.
               cspice_furnsh( META )


               error( 'Command syntax:  dskxv_t( <meta-kernel> )' )


         % Get a handle for one of the loaded DSKs,
         % then find the first segment and extract
         % the body and surface IDs.
         [file, filtyp, source, handle, found] = cspice_kdata(1, 'DSK');

         if ~found
            error('SPICE(NOINFO)' )

         [dladsc, found] = cspice_dlabfs( handle );

         if ~found
            error('SPICE(NOSEGMENT)' )

         dskdsc = cspice_dskgd( handle, dladsc );

         bodyid = dskdsc(SPICE_DSK_CTRIDX);
         surfid = dskdsc(SPICE_DSK_SRFIDX);
         framid = dskdsc(SPICE_DSK_FRMIDX);

         [target, found ] = cspice_bodc2n( bodyid );

         if ~found

            txt = sprintf( ...
          ['SPICE(BODYNAMENOTFOUND): Cannot map body ID %s to a name.'], ...


         fixref = cspice_frmnam(framid);

         if fixref == ' '

            txt = sprintf( ...
          ['SPICE(BODYNAMENOTFOUND): Cannot map frame ID %s to a name.'], ...


         % Set the magnitude of the ray vertices. Use a large
         % number to ensure the vertices are outside of
         % any realistic target.
         r = 1.0e10;

         % Spear the target with rays pointing toward
         % the origin.  Use a grid of ray vertices
         % located on a sphere enclosing the target.
         % The variable `polmrg' ("pole margin") can
         % be set to a small positive value to reduce
         % the number of intercepts done at the poles.
         % This may speed up the computation for
         % the multi-segment case, since rays parallel
         % to the Z axis will cause all segments converging
         % at the pole of interest to be tested for an
         % intersection.

         polmrg =    0.5;
         latstp =    1.0;
         lonstp =    2.0;

         nhits  =    0;
         nderr  =    0;

         lon    = -180.0;
         lat    =   90.0;
         nlstep =    0;
         nrays  =    1;

         % Generate rays.
         while ( lon < 180.0 )

            while ( nlstep <= 180 )

               if ( lon == 180.0 )

                  lat = 90.0 - nlstep*latstp;


                  if ( nlstep == 0 )
                     lat =  90.0 - polmrg;
                  elseif ( nlstep == 180 )
                     lat = -90.0 + polmrg;
                     lat =  90.0 - nlstep*latstp;

               vtxarr(:,nrays) = cspice_latrec( r, ...
                                 lon*cspice_rpd(), lat*cspice_rpd() );

               nrays  = nrays  + 1;
               nlstep = nlstep + 1;

            lon    = lon + lonstp;
            lat    = 90.0;
            nlstep = 0;

         dirarr = -vtxarr;

         % Assign surface ID list.
         % Note that, if we knew that all files had the desired
         % surface ID, we could set `nsurf' to 0 and omit the
         % initialization of the surface ID list.
         nsurf     = 1;
         srflst(1) = surfid;

         disp( 'Computing intercepts...' )

         nrays = nrays-1;

         % Find the surface intercept of the ith ray.

         [xptarr, fndarr] = cspice_dskxv( false, ...
                                         target, ...
                                         nsurf,  ...
                                         srflst, ...
                                         0,      ...
                                         fixref, ...
                                         vtxarr(:,1:nrays), ...
                                         dirarr(:,1:nrays) );

         for i = 1:nrays

            if ( fndarr(i) )

               % Record that a new intercept was found.
               nhits = nhits + 1;

               % Check results.
               % Compute the latitude and longitude of
               % the intercept. Make sure these agree
               % well with those of the vertex.
               [ radius, lon, lat ] = cspice_reclat( xptarr(:,i) );

               % Recover the vertex longitude and latitude.
               [vrad, vlon, vlat ] = cspice_reclat( vtxarr(:,i) );
               xyzhit = cspice_latrec ( radius, vlon,  vlat );

               d = cspice_vdist( xptarr(:,i), xyzhit );

               if ( d/r > DTOL )

                  fprintf( '===========================\n' );
                  fprintf( 'Lon = %f;  Lat = %f\n', lon, lat );
                  fprintf( 'Bad intercept\n'               );
                  fprintf( 'Distance error = %e\n', d      );
                  fprintf( 'xpt    = (%e %e %e)\n', ...
                            xpt(1), xpt(2), xpt(3) );
                  fprintf( 'xyzhit = (%e %e %e)\n', ...
                            xyzhit(1), xyzhit(2), xyzhit(3) );

                  nderr = nderr + 1;


               % Missing the target entirely is a fatal error.
               % This is true only for this program, not in
               % general. For example, if the target shape is
               % a torus, many rays would miss the target.
               fprintf( '===========================\n' );
               fprintf( 'Lon = %f;  Lat = %f\n', lon, lat );

               error( 'No intercept' );



         fprintf ( 'Done.\n\n' )

         fprintf( 'nrays = %d\n', nrays )
         fprintf( 'nhits = %d\n', nhits )
         fprintf( 'nderr = %d\n', nderr )

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

   Matlab outputs:

      dskxv_t( '' )

      Computing intercepts...

      nrays = 32580
      nhits = 32580
      nderr = 0


   This routine is suitable for efficient ray-surface intercept
   computations in which the relative observer-target geometry is
   constant but the rays vary.

   For cases in which it is necessary to know the source of the
   data defining the surface on which an intercept was found,
   use the CSPICE routine cspice_dskxsi.

   For cases in which a ray's vertex is not explicitly known but is
   defined by relative observer-target geometry, the Mice
   ray-surface intercept routine cspice_sincpt should be used.

   This routine works with multiple DSK files. It places no
   restrictions on the data types or coordinate systems of the DSK
   segments used in the computation. DSK segments using different
   reference frames may be used in a single computation. The only
   restriction is that any pair of reference frames used directly or
   indirectly are related by a constant rotation.

   Using DSK data

      DSK loading and unloading

      DSK files providing data used by this routine are loaded by
      calling cspice_furnsh and can be unloaded by calling cspice_unload or
      cspice_kclear. See the documentation of cspice_furnsh for limits on
      numbers of loaded DSK files.

      For run-time efficiency, it's desirable to avoid frequent
      loading and unloading of DSK files. When there is a reason to
      use multiple versions of data for a given target body---for
      example, if topographic data at varying resolutions are to be
      used---the surface list can be used to select DSK data to be
      used for a given computation. It is not necessary to unload
      the data that are not to be used. This recommendation presumes
      that DSKs containing different versions of surface data for a
      given body have different surface ID codes.

      DSK data priority

      A DSK coverage overlap occurs when two segments in loaded DSK
      files cover part or all of the same domain---for example, a
      given longitude-latitude rectangle---and when the time
      intervals of the segments overlap as well.

      When DSK data selection is prioritized, in case of a coverage
      overlap, if the two competing segments are in different DSK
      files, the segment in the DSK file loaded last takes
      precedence. If the two segments are in the same file, the
      segment located closer to the end of the file takes

      When DSK data selection is unprioritized, data from competing
      segments are combined. For example, if two competing segments
      both represent a surface as sets of triangular plates, the
      union of those sets of plates is considered to represent the

      Currently only unprioritized data selection is supported.
      Because prioritized data selection may be the default behavior
      in a later version of the routine, the presence of the `pri'
      argument is required.

      Round-off errors and mitigating algorithms

      When topographic data are used to represent the surface of a
      target body, round-off errors can produce some results that
      may seem surprising.

      Note that, since the surface in question might have mountains,
      valleys, and cliffs, the points of intersection found for
      nearly identical sets of inputs may be quite far apart from
      each other: for example, a ray that hits a mountain side in a
      nearly tangent fashion may, on a different host computer, be
      found to miss the mountain and hit a valley floor much farther
      from the observer, or even miss the target altogether.

      Round-off errors can affect segment selection: for example, a
      ray that is expected to intersect the target body's surface
      near the boundary between two segments might hit either
      segment, or neither of them; the result may be

      A similar situation exists when a surface is modeled by a set
      of triangular plates, and the ray is expected to intersect the
      surface near a plate boundary.

      To avoid having the routine fail to find an intersection when
      one clearly should exist, this routine uses two "greedy"

         1) If the ray passes sufficiently close to any of the
            boundary surfaces of a segment (for example, surfaces of
            maximum and minimum longitude or latitude), that segment
            is tested for an intersection of the ray with the
            surface represented by the segment's data.

            This choice prevents all of the segments from being
            missed when at least one should be hit, but it could, on
            rare occasions, cause an intersection to be found in a
            segment other than the one that would be found if higher
            precision arithmetic were used.

         2) For type 2 segments, which represent surfaces as
            sets of triangular plates, each plate is expanded very
            slightly before a ray-plate intersection test is
            performed. The default plate expansion factor is

               1 + SPICE_DSK_XFRACT

            where XFRACT is declared in


            For example, given a value for XFRACT of 1.e-10, the
            sides of the plate are lengthened by 1/10 of a micron
            per km. The expansion keeps the centroid of the plate

            Plate expansion prevents all plates from being missed
            in cases where clearly at least one should be hit.

            As with the greedy segment selection algorithm, plate
            expansion can occasionally cause an intercept to be
            found on a different plate than would be found if higher
            precision arithmetic were used. It also can occasionally
            cause an intersection to be found when the ray misses
            the target by a very small distance.

Required Reading

   For important details concerning this module's function, please
   refer to the CSPICE routine dskxv_c.



   -Mice Version 1.0.0, 21-APR-2014, EDW (JPL), NJB (JPL)


   vectorized ray-surface intercept
   vectorized ray-dsk intercept

Wed Apr  5 18:00:31 2017