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Required Reading


   CSPICE_SRFNRM maps an array of surface points on a specified target
   body to the corresponding unit length outward surface normal vectors.

   The surface of the target body may be represented by a triaxial
   ellipsoid or by topographic data provided by DSK files.



      method      is a short string providing parameters defining
                  the computation method to be used. In the syntax
                  descriptions below, items delimited by brackets
                  are optional.

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


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

                  `method' may be assigned the following values:


                        The normal vector computation uses a triaxial
                        ellipsoid to model the surface of the target
                        body. The ellipsoid's radii must be available
                        in the kernel pool.

                     'DSK/UNPRIORITIZED[/SURFACES = <surface list>]'

                        The normal vector computation uses topographic
                        data to model the surface of the target body.
                        These data must be provided by loaded DSK

                        The surface list specification is optional. The
                        syntax of the list is

                           <surface 1> [, <surface 2>...]

                        If present, it indicates that data only for the
                        listed surfaces are to be used; however, data
                        need not be available for all surfaces in the
                        list. If absent, loaded DSK data for any surface
                        associated with the target body are used.

                        The surface list may contain surface names or
                        surface ID codes. Names containing blanks must
                        be delimited by double quotes, for example

                           SURFACES = "Mars MEGDR 128 PIXEL/DEG"

                        If multiple surfaces are specified, their names
                        or IDs must be separated by commas.

                        See the Particulars section below for details
                        concerning use of DSK data.

                  Neither case nor white space are significant in
                  `method', except within double-quoted strings. For
                  example, the string ' eLLipsoid ' is valid.

                  Within double-quoted strings, blank characters are
                  significant, but multiple consecutive blanks are
                  considered equivalent to a single blank. Case is
                  not significant. So

                     "Mars MEGDR 128 PIXEL/DEG"

                  is equivalent to

                     " mars megdr  128  pixel/deg "

                  but not to

                     "MARS MEGDR128PIXEL/DEG"

      target      is the name of the target body. `target' is
                  case-insensitive, and leading and trailing blanks in
                  `target' are not significant. Optionally, you may
                  supply a string containing the integer ID code for
                  the object. For example both 'MOON' and '301' are
                  legitimate strings that indicate the Moon is the
                  target body.

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


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

                  When the target body's surface is represented by a
                  tri-axial ellipsoid, this routine assumes that a
                  kernel variable representing the ellipsoid's radii is
                  present in the kernel pool. Normally the kernel
                  variable would be defined by loading a PCK file.

      et          is the epoch for which target surface data will be
                  selected, if the surface is modeled using DSK data.
                  In this case, only segments having time coverage that
                  includes the epoch `et' will be used.

                  [1,1] = size(et); double = class(et)

                  `et' is ignored if the target is modeled as an

                  `et' is expressed as TDB seconds past J2000 TDB.

      fixref      is the name of a body-fixed reference frame centered
                  on the target body. `fixref' may be any such frame
                  supported by the SPICE system, including built-in
                  frames (documented in the Frames Required Reading)
                  and frames defined by a loaded frame kernel (FK). The
                  string `fixref' is case-insensitive, and leading and
                  trailing blanks in `fixref' are not significant.

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


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

                  The input surface points in the array `srfpts' are
                  expressed relative to this reference frame, as are
                  the normal vectors computed by this routine.

      srfpts      is an array of target body surface points.

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



                  are the Cartesian coordinates, expressed in the
                  reference frame designated by `fixref', of the ith
                  surface point in the array. Each surface point
                  represents an offset from the center of that frame.

                  All surface points must actually be "on" the surface,
                  that is, the distance of each point from the surface
                  must be less than a small margin. See the Parameters
                  section below for a description of this margin.

   the call:

      normls = cspice_srfnrm( method, target, et, fixref, srfpts )


      normls      is an array of unit length, outward normal vectors
                  corresponding to the points in `srfpts'.

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



                  are the Cartesian coordinates, expressed in the
                  reference frame designated by `fixref', of the ith
                  normal vector in the array.


   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.

      Compute outward normal vectors at surface points on a target
      body, where the points correspond to a given planetocentric
      longitude/latitude grid. Use both ellipsoid and DSK shape

      Use the meta-kernel shown below to load the required 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
            ---------                        --------
            pck00010.tpc                     Planet orientation and
            phobos512.bds                    DSK based on
                                             Gaskell ICQ Q=512
                                             plate model

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

            KERNELS_TO_LOAD = ( '$GEN/pck/pck00010.tpc',
                                '$GEN/dsk/phobos/phobos512.bds' )


      function srfnrm_t

         % Local constants
         META = '';

         % Set target, reference frame, and epoch.
         target = 'phobos';
         fixref = 'iau_phobos';
         et     = 0.0;

         % Use both a reference ellipsoid and DSK data
         % to represent the surface.
         method = { 'ELLIPSOID', 'DSK/UNPRIORITIZED' };

         % Load the meta-kernel.
         cspice_furnsh( META )

         % Now generate the grid points.  We generate
         % points along latitude bands, working from
         % north to south.  The latitude range is selected
         % to range from +45 to -45 degrees.  Longitude
         % ranges from 0 to 300 degrees.  The increment
         % is 45 degrees for latitude and 60 degrees for
         % longitude.
         lat = 45:-45:-45;
         lon = 0:60:300;
         n   = 0;
         grid = eye(2, numel(lat) * numel(lon) );

         for i=1:numel(lat)
            for j=1:numel(lon)

               n = n+1;

               grid(1,n) = lon(j);
               grid(2,n) = lat(i);


         grid = grid * cspice_rpd();

         % Find the surface points corresponding to the grid points.
         % Compute outward normal vectors at the surface points,
         % using both surface representations.
         for i = 1:2
            srfpts = cspice_latsrf( method(i), target, et, fixref, grid);

            normls = cspice_srfnrm( method(i), target, et, fixref, srfpts);

            for j=1:n

               % Use cspice_recrad rather than cspice_reclat to produce
               % non-negative longitudes.
               [ xr, xlon, xlat] = cspice_recrad( srfpts(1:3, j) );

               fprintf( [ '\n%s\n'                                       ...
                              'Surface point for grid point %d:\n'       ...
                              '  Latitudinal Coordinates:\n'             ...
                              '    Longitude           (deg): %12.6f\n'  ...
                              '    Latitude            (deg): %12.6f\n'  ...
                              '    Radius              (km): %12.6f\n' ],...
                              char( method(i) ), ...
                              j,                 ...
                              xlon*cspice_dpr(), ...
                              xlat*cspice_dpr(), ...
                              xr )

               [ nrmrad, nrmlon, nrmlat] = cspice_recrad( normls(1:3, j) );

               fprintf( [ '\n'                                           ...
                              'Normal vector direction:\n'               ...
                              '    Longitude (deg):           %12.6f\n'  ...
                              '    Latitude  (deg):           %12.6f\n'],...
                              nrmlon * cspice_dpr(), ...
                              nrmlat * cspice_dpr()  )




   Matlab outputs:

      Surface point for grid point 1:
        Latitudinal Coordinates:
          Longitude           (deg):     0.000000
          Latitude            (deg):    45.000000
          Radius              (km):    10.542977

      Normal vector direction:
          Longitude (deg):               0.000000
          Latitude  (deg):              63.895146

      Surface point for grid point 2:
        Latitudinal Coordinates:
          Longitude           (deg):    60.000000
          Latitude            (deg):    45.000000
          Radius              (km):    10.172847

      Normal vector direction:
          Longitude (deg):              66.059787
          Latitude  (deg):              58.877649

      Surface point for grid point 3:
        Latitudinal Coordinates:
          Longitude           (deg):   120.000000
          Latitude            (deg):    45.000000
          Radius              (km):    10.172847

      Normal vector direction:
          Longitude (deg):             113.940213
          Latitude  (deg):              58.877649


      Surface point for grid point 1:
        Latitudinal Coordinates:
          Longitude           (deg):     0.000000
          Latitude            (deg):    45.000000
          Radius              (km):    10.156402

      Normal vector direction:
          Longitude (deg):             341.337568
          Latitude  (deg):              62.610726

      Surface point for grid point 2:
        Latitudinal Coordinates:
          Longitude           (deg):    60.000000
          Latitude            (deg):    45.000000
          Radius              (km):    10.131412

      Normal vector direction:
          Longitude (deg):              48.859884
          Latitude  (deg):              56.924717

      Surface point for grid point 3:
        Latitudinal Coordinates:
          Longitude           (deg):   120.000000
          Latitude            (deg):    45.000000
          Radius              (km):    10.423766

      Normal vector direction:
          Longitude (deg):             118.553200
          Latitude  (deg):              55.906774



   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 UNPRIORITIZED keyword is
      required in the `method' argument.

      Syntax of the `method' input argument

      The keywords and surface list in the `method' argument
      are called "clauses." The clauses may appear in any
      order, for example

         DSK/<surface list>/UNPRIORITIZED
         DSK/UNPRIORITIZED/<surface list>
         UNPRIORITIZED/<surface list>/DSK

      The simplest form of the `method' argument specifying use of
      DSK data is one that lacks a surface list, for example:


      For applications in which all loaded DSK data for the target
      body are for a single surface, and there are no competing
      segments, the above string suffices. This is expected to be
      the usual case.

      When, for the specified target body, there are loaded DSK
      files providing data for multiple surfaces for that body, the
      surfaces to be used by this routine for a given call must be
      specified in a surface list, unless data from all of the
      surfaces are to be used together.

      The surface list consists of the string

         SURFACES =

      followed by a comma-separated list of one or more surface
      identifiers. The identifiers may be names or integer codes in
      string format. For example, suppose we have the surface
      names and corresponding ID codes shown below:

         Surface Name                              ID code
         ------------                              -------
         'Mars MEGDR 128 PIXEL/DEG'                1
         'Mars MEGDR 64 PIXEL/DEG'                 2
         'Mars_MRO_HIRISE'                         3

      If data for all of the above surfaces are loaded, then
      data for surface 1 can be specified by either

         'SURFACES = 1'


         'SURFACES = "Mars MEGDR 128 PIXEL/DEG"'

      Double quotes are used to delimit the surface name because
      it contains blank characters.

      To use data for surfaces 2 and 3 together, any
      of the following surface lists could be used:

         'SURFACES = 2, 3'

         'SURFACES = "Mars MEGDR  64 PIXEL/DEG", 3'

         'SURFACES = 2, Mars_MRO_HIRISE'

         'SURFACES = "Mars MEGDR 64 PIXEL/DEG", Mars_MRO_HIRISE'

      An example of a `method' argument that could be constructed
      using one of the surface lists above is


Required Reading

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



   -Mice Version 1.0.0, 24-MAR-2016, EDW (JPL), NJB (JPL)


   map Cartesian surface points to normal vectors
   compute normal vectors on topographic surface
   compute normal vectors on dsk surface

Wed Apr  5 18:00:35 2017