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Abstract
I/O
Examples
Particulars
Required Reading
Version
Index_Entries

Abstract


   CSPICE_RECPGR converts rectangular coordinates to
   planetographic coordinates.

I/O


   Given:

      body     the body name with which the planetographic coordinate
               system is associated, optionally, you may supply the
               integer ID code for the object as an integer string,
               i.e. both 'MOON' and '301' are legitimate strings that
               indicate the Moon is the target body

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

                  or

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

      rectan   the array(s) containing the rectangular coordinates of the
               position or set of positions.

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

       re      the value describing equatorial radius of the body
               of interest.

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

       f       the value describing flattening coefficient of the body,
               a dimensionless value defined as:

                    equatorial_radius - polar_radius
                    --------------------------------
                           equatorial_radius

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

   the call:

      [ lon, lat, alt ] = cspice_recpgr( body, rectan, re, f)

   returns:

       lon   the value(s) describing the planetographic longitude of the
             input point.  

             [1,n] = size(lon); double = class(lon)

             This is the angle between the prime meridian and the meridian
             containing 'rectan'.  For bodies having prograde (aka
             direct) rotation, the direction of increasing
             longitude is positive west:  from the +X axis of the
             rectangular coordinate system toward the -Y axis.
             For bodies having retrograde rotation, the direction
             of increasing longitude is positive east:  from the +X
             axis toward the +Y axis.

             The earth, moon, and sun are exceptions: planetographic
             longitude is measured positive east for these bodies.

             The default interpretation of longitude by this
             and the other planetographic coordinate conversion
             routines can be overridden; see the discussion in
             Particulars below for details.

             'lon' is output in radians.  The nominal range of 'lon' is
             given by:

                0  <  lon  <  2*pi
                   -

             However, round-off error could cause 'lon' to equal 2*pi.

       lat   the value(s) describing the planetographic latitude of the
             input point.

             [1,n] = size(lat); double = class(lat)

             For a point P on the reference spheroid, this is the angle
             between the XY plane and the outward normal vector at
             P. For a point P not on the reference spheroid, the
             planetographic latitude is that of the closest point
             to P on the spheroid.

             'lat' is output in radians. The range of 'lat' is given
             by:

                -pi/2  <  lat  <  pi/2
                       -       -

       alt   the value(s) describing the altitude above the
             reference spheroid.

             [1,n] = size(alt); double = class(alt)

             'lon', 'lat', and 'alt' return with the same vectorization
             measure, N, as 'rectan'.

Examples


   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.

      %
      % Load a PCK file containing a triaxial
      % ellipsoidal shape model and orientation
      % data for Mars.
      %
      cspice_furnsh( 'standard.tm' )

      %
      % Example 1: convert a single set of bodyfixed
      %            coordinates to planetographic
      %            coordinates.
      %
      % Look up the radii for Mars.  Although we
      % omit it here, we could check the kernel pool
      % to make sure the variable BODY499_RADII
      % has three elements and numeric data type.
      % If the variable is not present in the kernel
      % pool, cspice_bodvrd will signal an error.
      %
      body = 'MARS';
      radii = cspice_bodvrd( body, 'RADII', 3 );

      %
      %
      % Calculate the flatness coefficient. Set a bodyfixed
      % position vector, 'x'.
      %
      re   = radii(1);
      rp   = radii(3);
      flat = ( re - rp ) / re;
      x    = [ 0.0,
              -2620.678914818178,
               2592.408908856967 ];

      %
      % Do the conversion.
      %
      [lon, lat, alt] = cspice_recpgr( body, x, re, flat );

      %
      % Output.
      %
      disp( 'Scalar:' )
      disp(' ')

      disp( 'Rectangular coordinates in km (x, y, z)' )
      fprintf( '%9.3f   %9.3f   %9.3f\n', x' )

      disp( 'Planetographic coordinates in degs and km (lon, lat, alt)' )
      fprintf( '%9.3f   %9.3f   %9.3f\n', lon *cspice_dpr() ...
                                        , lat *cspice_dpr() ...
                                        , alt               )
      disp(' ')

      %
      % Example 2: convert a vectorized set of bodyfixed coordinates
      %            to planetographic coordinates
      %
      % Define an array of body-fixed 3x1 arrays.
      %
      x = [ [  3396.190;  0.000   ;  0.000    ], ...
            [ -3396.190;  0.000   ;  0.000    ], ...
            [ -3406.190;  0.000   ;  0.000    ], ...
            [ -3406.190;  0.000   ;  0.000    ], ...
            [  0.000   ; -3396.190;  0.000    ], ...
            [  0.000   ;  3396.190;  0.000    ], ...
            [  0.000   ;  0.000   ;  3376.200 ], ...
            [  0.000   ;  0.000   ; -3376.200 ], ...
            [  0.000   ;  0.000   ;   0.000   ] ];

      %
      % Using the same Mars parameters, convert the 3-vectors to
      % planetographic.
      %
      [ lon, lat, alt] = cspice_recpgr( body, x, re, flat );

      disp('Vector:')
      disp(' ')

      disp( ['rectan(1)   rectan(2)   rectan(3)' ...
             '         lon         lat         alt'] )

      disp( ['---------------------------------' ...
             '------------------------------------'] )

      %
      % Create an array of values for output.
      %
      output = [  x(1,:);         x(2,:);         x(3,:); ...
                  lon*cspice_dpr; lat*cspice_dpr; alt ];

      txt = sprintf( '%9.3f   %9.3f   %9.3f   %9.3f   %9.3f   %9.3f\n', ...
                                                                  output);
      disp( txt )

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

   MATLAB outputs:

      Scalar:

      Rectangular coordinates in km (x, y, z)
          0.000   -2620.679    2592.409
      Planetographic coordinates in degs and km (lon, lat, alt)
         90.000      45.000     300.000

      Vector:

      rectan(1)   rectan(2)   rectan(3)         lon         lat         alt
      ---------------------------------------------------------------------
       3396.190      -0.000       0.000       0.000       0.000       0.000
      -3396.190      -0.000       0.000     180.000       0.000       0.000
      -3406.190      -0.000       0.000     180.000       0.000      10.000
      -3406.190      -0.000       0.000     180.000       0.000      10.000
          0.000   -3396.190       0.000      90.000       0.000       0.000
         -0.000    3396.190       0.000     270.000       0.000       0.000
          0.000      -0.000    3376.200       0.000      90.000       0.000
          0.000      -0.000   -3376.200       0.000     -90.000       0.000
          0.000       0.000       0.000       0.000      90.000   -3376.200

Particulars


   Given the planetographic coordinates of a point, this routine
   returns the body-fixed rectangular coordinates of the point.  The
   body-fixed rectangular frame is that having the X-axis pass
   through the 0 degree latitude 0 degree longitude direction, the
   Z-axis pass through the 90 degree latitude direction, and the
   Y-axis equal to the cross product of the unit Z-axis and X-axis
   vectors.

   The planetographic definition of latitude is identical to the
   planetodetic (also called "geodetic" in SPICE documentation)
   definition. In the planetographic coordinate system, latitude is
   defined using a reference spheroid.  The spheroid is
   characterized by an equatorial radius and a polar radius. For a
   point P on the spheroid, latitude is defined as the angle between
   the X-Y plane and the outward surface normal at P.  For a point P
   off the spheroid, latitude is defined as the latitude of the
   nearest point to P on the spheroid.  Note if P is an interior
   point, for example, if P is at the center of the spheroid, there
   may not be a unique nearest point to P.

   In the planetographic coordinate system, longitude is defined
   using the spin sense of the body.  Longitude is positive to the
   west if the spin is prograde and positive to the east if the spin
   is retrograde.  The spin sense is given by the sign of the first
   degree term of the time-dependent polynomial for the body's prime
   meridian Euler angle "W":  the spin is retrograde if this term is
   negative and prograde otherwise.  For the sun, planets, most
   natural satellites, and selected asteroids, the polynomial
   expression for W may be found in a SPICE PCK kernel.

   The earth, moon, and sun are exceptions: planetographic longitude
   is measured positive east for these bodies.

   If you wish to override the default sense of positive longitude
   for a particular body, you can do so by defining the kernel
   variable

      BODY<body ID>_PGR_POSITIVE_LON

   where <body ID> represents the NAIF ID code of the body. This
   variable may be assigned either of the values

      'WEST'
      'EAST'

   For example, you can have this routine treat the longitude
   of the earth as increasing to the west using the kernel
   variable assignment

      BODY399_PGR_POSITIVE_LON = 'WEST'

   Normally such assignments are made by placing them in a text
   kernel and loading that kernel via cspice_furnsh.

   The definition of this kernel variable controls the behavior of
   the CSPICE planetographic routines

      cspice_pgrrec
      cspice_recpgr

Required Reading


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

   MICE.REQ

Version


   -Mice Version 1.0.2, 01-DEC-2014, EDW (JPL)

       Edited I/O section to conform to NAIF standard for Mice documentation.

   -Mice Version 1.0.1, 30-DEC-2008, EDW (JPL)

      Corrected misspellings.

   -Mice Version 1.0.0, 22-JAN-2008, EDW (JPL)

Index_Entries


   convert rectangular to planetographic coordinates


Wed Apr  5 18:00:34 2017